commit 37c264e26ef7dce1e5f955dfadf59b7279a29106 Author: Yi-Ting Shih Date: Mon Apr 6 05:24:23 2026 +0800 Feat: hw2 done diff --git a/.gitignore b/.gitignore new file mode 100644 index 0000000..61f2dc9 --- /dev/null +++ b/.gitignore @@ -0,0 +1 @@ +**/__pycache__/ diff --git a/111550013_hw2.zip b/111550013_hw2.zip new file mode 100644 index 0000000..efbda82 Binary files /dev/null and b/111550013_hw2.zip differ diff --git a/111550013_hw2/multiAgents.py b/111550013_hw2/multiAgents.py new file mode 100644 index 0000000..d3e78db --- /dev/null +++ b/111550013_hw2/multiAgents.py @@ -0,0 +1,271 @@ +from util import manhattanDistance +from game import Directions +import random, util +from game import Agent + +class ReflexAgent(Agent): + """ + A reflex agent chooses an action at each choice point by examining + its alternatives via a state evaluation function. + + The code below is provided as a guide. You are welcome to change + it in any way you see fit, so long as you don't touch our method + headers. + """ + + def getAction(self, gameState): + """ + You do not need to change this method, but you're welcome to. + + getAction chooses among the best options according to the evaluation function. + + Just like in the previous project, getAction takes a GameState and returns + some Directions.X for some X in the set {NORTH, SOUTH, WEST, EAST, STOP} + """ + # Collect legal moves and child states + legalMoves = gameState.getLegalActions() + + # Choose one of the best actions + scores = [self.evaluationFunction(gameState, action) for action in legalMoves] + bestScore = max(scores) + bestIndices = [index for index in range(len(scores)) if scores[index] == bestScore] + chosenIndex = random.choice(bestIndices) # Pick randomly among the best + + return legalMoves[chosenIndex] + + def evaluationFunction(self, currentGameState, action): + """ + The evaluation function takes in the current and proposed child + GameStates (pacman.py) and returns a number, where higher numbers are better. + + The code below extracts some useful information from the state, like the + remaining food (newFood) and Pacman position after moving (newPos). + newScaredTimes holds the number of moves that each ghost will remain + scared because of Pacman having eaten a power pellet. + """ + # Useful information you can extract from a GameState (pacman.py) + childGameState = currentGameState.getPacmanNextState(action) + newPos = childGameState.getPacmanPosition() + newFood = childGameState.getFood() + newGhostStates = childGameState.getGhostStates() + newScaredTimes = [ghostState.scaredTimer for ghostState in newGhostStates] + + minGhostDistance = min([manhattanDistance(newPos, state.getPosition()) for state in newGhostStates]) + + scoreDiff = childGameState.getScore() - currentGameState.getScore() + + pos = currentGameState.getPacmanPosition() + nearestFoodDistance = min([manhattanDistance(pos, food) for food in currentGameState.getFood().asList()]) + newFoodsDistances = [manhattanDistance(newPos, food) for food in newFood.asList()] + newNearestFoodDistance = 0 if not newFoodsDistances else min(newFoodsDistances) + isFoodNearer = nearestFoodDistance - newNearestFoodDistance + + direction = currentGameState.getPacmanState().getDirection() + if minGhostDistance <= 1 or action == Directions.STOP: + return 0 + if scoreDiff > 0: + return 8 + elif isFoodNearer > 0: + return 4 + elif action == direction: + return 2 + else: + return 1 + + +def scoreEvaluationFunction(currentGameState): + """ + This default evaluation function just returns the score of the state. + The score is the same one displayed in the Pacman GUI. + + This evaluation function is meant for use with adversarial search agents + (not reflex agents). + """ + return currentGameState.getScore() + + +class MultiAgentSearchAgent(Agent): + """ + This class provides some common elements to all of your + multi-agent searchers. Any methods defined here will be available + to the MinimaxPacmanAgent, AlphaBetaPacmanAgent & ExpectimaxPacmanAgent. + + You *do not* need to make any changes here, but you can if you want to + add functionality to all your adversarial search agents. Please do not + remove anything, however. + + Note: this is an abstract class: one that should not be instantiated. It's + only partially specified, and designed to be extended. Agent (game.py) + is another abstract class. + """ + + def __init__(self, evalFn = 'scoreEvaluationFunction', depth = '2'): + self.index = 0 # Pacman is always agent index 0 + self.evaluationFunction = util.lookup(evalFn, globals()) + self.depth = int(depth) + + +class MinimaxAgent(MultiAgentSearchAgent): + """ + Your minimax agent (Part 1) + """ + + def getAction(self, gameState): + """ + Returns the minimax action from the current gameState using self.depth + and self.evaluationFunction. + + Here are some method calls that might be useful when implementing minimax. + + gameState.getLegalActions(agentIndex): + Returns a list of legal actions for an agent + agentIndex=0 means Pacman, ghosts are >= 1 + + gameState.getNextState(agentIndex, action): + Returns the child game state after an agent takes an action + + gameState.getNumAgents(): + Returns the total number of agents in the game + + gameState.isWin(): + Returns whether or not the game state is a winning state + + gameState.isLose(): + Returns whether or not the game state is a losing state + """ + # Begin your code (Part 1) + def minimax(s, d, agent): + if s.isWin() or s.isLose() or d == 0: + return self.evaluationFunction(s), None + + nxt = (agent + 1) % s.getNumAgents() + d2 = d - 1 if nxt == 0 else d + actions = s.getLegalActions(agent) + + if agent == 0: + best = (float('-inf'), None) + for a in actions: + v = minimax(s.getNextState(agent, a), d2, nxt)[0] + if v > best[0]: + best = (v, a) + return best + else: + best = (float('inf'), None) + for a in actions: + v = minimax(s.getNextState(agent, a), d2, nxt)[0] + if v < best[0]: + best = (v, a) + return best + + return minimax(gameState, self.depth, 0)[1] + # End your code (Part 1) + + +class AlphaBetaAgent(MultiAgentSearchAgent): + """ + Your minimax agent with alpha-beta pruning (Part 2) + """ + + def getAction(self, gameState): + """ + Returns the minimax action using self.depth and self.evaluationFunction + """ + # Begin your code (Part 2) + def ab(s, d, agent, a, b): + if s.isWin() or s.isLose() or d == 0: + return self.evaluationFunction(s), None + + nxt = (agent + 1) % s.getNumAgents() + d2 = d - 1 if nxt == 0 else d + actions = s.getLegalActions(agent) + + if agent == 0: + best = (float('-inf'), None) + for act in actions: + v = ab(s.getNextState(agent, act), d2, nxt, a, b)[0] + if v > best[0]: + best = (v, act) + if best[0] > b: + return best + a = max(a, best[0]) + return best + else: + best = (float('inf'), None) + for act in actions: + v = ab(s.getNextState(agent, act), d2, nxt, a, b)[0] + if v < best[0]: + best = (v, act) + if best[0] < a: + return best + b = min(b, best[0]) + return best + + return ab(gameState, self.depth, 0, float('-inf'), float('inf'))[1] + # End your code (Part 2) + + +class ExpectimaxAgent(MultiAgentSearchAgent): + """ + Your expectimax agent (Part 3) + """ + + def getAction(self, gameState): + """ + Returns the expectimax action using self.depth and self.evaluationFunction + + All ghosts should be modeled as choosing uniformly at random from their + legal moves. + """ + # Begin your code (Part 3) + def expmax(s, d, agent): + if s.isWin() or s.isLose() or d == 0: + return self.evaluationFunction(s), None + + nxt = (agent + 1) % s.getNumAgents() + d2 = d - 1 if nxt == 0 else d + actions = s.getLegalActions(agent) + + if agent == 0: + best = (float('-inf'), None) + for a in actions: + v = expmax(s.getNextState(agent, a), d2, nxt)[0] + if v > best[0]: + best = (v, a) + return best + else: + vals = [expmax(s.getNextState(agent, a), d2, nxt)[0] for a in actions] + return sum(vals) / len(vals), None + + return expmax(gameState, self.depth, 0)[1] + # End your code (Part 3) + + +def betterEvaluationFunction(currentGameState): + """ + Your extreme ghost-hunting, pellet-nabbing, food-gobbling, unstoppable + evaluation function (Part 4). + """ + # Begin your code (Part 4) + pos = currentGameState.getPacmanPosition() + foodList = currentGameState.getFood().asList() + ghosts = currentGameState.getGhostStates() + + score = currentGameState.getScore() + score -= 10 * len(foodList) + score -= 20 * len(currentGameState.getCapsules()) + + if foodList: + score += 1.0 / min(manhattanDistance(pos, f) for f in foodList) + + for g in ghosts: + d = manhattanDistance(pos, g.getPosition()) + if g.scaredTimer > 0: + score += 200 / (d + 1) + else: + score -= 10000 / (10 ** d) + + return score + # End your code (Part 4) + +# Abbreviation +better = betterEvaluationFunction diff --git a/111550013_hw2_report.pdf b/111550013_hw2_report.pdf new file mode 100644 index 0000000..7d7339b Binary files /dev/null and b/111550013_hw2_report.pdf differ diff --git a/HW2_pacman.zip b/HW2_pacman.zip new file mode 100644 index 0000000..040e2d2 Binary files /dev/null and b/HW2_pacman.zip differ diff --git a/HW2_pacman/.python-version b/HW2_pacman/.python-version new file mode 100644 index 0000000..eae0123 --- /dev/null +++ b/HW2_pacman/.python-version @@ -0,0 +1 @@ +3.10.19 diff --git a/HW2_pacman/VERSION b/HW2_pacman/VERSION new file mode 100644 index 0000000..259e855 --- /dev/null +++ b/HW2_pacman/VERSION @@ -0,0 +1 @@ +v1.004 diff --git a/HW2_pacman/autograder.py b/HW2_pacman/autograder.py new file mode 100644 index 0000000..e65d1a4 --- /dev/null +++ b/HW2_pacman/autograder.py @@ -0,0 +1,306 @@ +import grading +import imp +import optparse +import os +import pprint +import re +import sys +import projectParams +import random +random.seed(0) +try: + from pacman import GameState +except: + pass + +# register arguments and set default values +def readCommand(argv): + parser = optparse.OptionParser( + description='Run public tests on student code') + parser.set_defaults(generateSolutions=False, edxOutput=False, gsOutput=False, + muteOutput=False, printTestCase=False, noGraphics=False) + parser.add_option('--test-directory', + dest='testRoot', + default='test_cases', + help='Root test directory which contains subdirectories corresponding to each question') + parser.add_option('--student-code', + dest='studentCode', + default=projectParams.STUDENT_CODE_DEFAULT, + help='comma separated list of student code files') + parser.add_option('--code-directory', + dest='codeRoot', + default="", + help='Root directory containing the student and testClass code') + parser.add_option('--test-case-code', + dest='testCaseCode', + default=projectParams.PROJECT_TEST_CLASSES, + help='class containing testClass classes for this project') + parser.add_option('--generate-solutions', + dest='generateSolutions', + action='store_true', + help='Write solutions generated to .solution file') + parser.add_option('--edx-output', + dest='edxOutput', + action='store_true', + help='Generate edX output files') + parser.add_option('--gradescope-output', + dest='gsOutput', + action='store_true', + help='Generate GradeScope output files') + parser.add_option('--mute', + dest='muteOutput', + action='store_true', + help='Mute output from executing tests') + parser.add_option('--print-tests', '-p', + dest='printTestCase', + action='store_true', + help='Print each test case before running them.') + parser.add_option('--test', '-t', + dest='runTest', + default=None, + help='Run one particular test. Relative to test root.') + parser.add_option('--question', '-q', + dest='gradeQuestion', + default=None, + help='Grade one particular question.') + parser.add_option('--no-graphics', + dest='noGraphics', + action='store_true', + help='No graphics display for pacman games.') + (options, args) = parser.parse_args(argv) + return options + + +# confirm we should author solution files +def confirmGenerate(): + print('WARNING: this action will overwrite any solution files.') + print('Are you sure you want to proceed? (yes/no)') + while True: + ans = sys.stdin.readline().strip() + if ans == 'yes': + break + elif ans == 'no': + sys.exit(0) + else: + print('please answer either "yes" or "no"') + + +# TODO: Fix this so that it tracebacks work correctly +# Looking at source of the traceback module, presuming it works +# the same as the intepreters, it uses co_filename. This is, +# however, a readonly attribute. +def setModuleName(module, filename): + functionType = type(confirmGenerate) + classType = type(optparse.Option) + + for i in dir(module): + o = getattr(module, i) + if hasattr(o, '__file__'): + continue + + if type(o) == functionType: + setattr(o, '__file__', filename) + elif type(o) == classType: + setattr(o, '__file__', filename) + # TODO: assign member __file__'s? + # print i, type(o) + + +def loadModuleString(moduleSource): + tmp = imp.new_module(k) + exec(moduleCodeDict[k], tmp.__dict__) + setModuleName(tmp, k) + return tmp + + +def loadModuleFile(moduleName, filePath): + with open(filePath, 'r') as f: + return imp.load_module(moduleName, f, "%s.py" % moduleName, (".py", "r", imp.PY_SOURCE)) + + +def readFile(path, root=""): + "Read file from disk at specified path and return as string" + with open(os.path.join(root, path), 'r') as handle: + return handle.read() + +def splitStrings(d): + d2 = dict(d) + for k in d: + if k[0:2] == "__": + del d2[k] + continue + if d2[k].find("\n") >= 0: + d2[k] = d2[k].split("\n") + return d2 + + +def printTest(testDict, solutionDict): + pp = pprint.PrettyPrinter(indent=4) + print("Test case:") + for line in testDict["__raw_lines__"]: + print(" |", line) + print("Solution:") + for line in solutionDict["__raw_lines__"]: + print(" |", line) + + +def runTest(testName, moduleDict, printTestCase=False, display=None): + import testParser + import testClasses + for module in moduleDict: + setattr(sys.modules[__name__], module, moduleDict[module]) + + testDict = testParser.TestParser(testName + ".test").parse() + solutionDict = testParser.TestParser(testName + ".solution").parse() + test_out_file = os.path.join('%s.test_output' % testName) + testDict['test_out_file'] = test_out_file + testClass = getattr(projectTestClasses, testDict['class']) + + questionClass = getattr(testClasses, 'Question') + question = questionClass({'max_points': 0}, display) + testCase = testClass(question, testDict) + + if printTestCase: + printTest(testDict, solutionDict) + + # This is a fragile hack to create a stub grades object + grades = grading.Grades(projectParams.PROJECT_NAME, [(None, 0)]) + testCase.execute(grades, moduleDict, solutionDict) + + +# returns all the tests you need to run in order to run question +def getDepends(testParser, testRoot, question): + allDeps = [question] + questionDict = testParser.TestParser( + os.path.join(testRoot, question, 'CONFIG')).parse() + if 'depends' in questionDict: + depends = questionDict['depends'].split() + for d in depends: + # run dependencies first + allDeps = getDepends(testParser, testRoot, d) + allDeps + return allDeps + +# get list of questions to grade +def getTestSubdirs(testParser, testRoot, questionToGrade): + problemDict = testParser.TestParser( + os.path.join(testRoot, 'CONFIG')).parse() + if questionToGrade != None: + questions = getDepends(testParser, testRoot, questionToGrade) + if len(questions) > 1: + print('Note: due to dependencies, the following tests will be run: %s' % + ' '.join(questions)) + return questions + if 'order' in problemDict: + return problemDict['order'].split() + return sorted(os.listdir(testRoot)) + + +# evaluate student code +def evaluate(generateSolutions, testRoot, moduleDict, + edxOutput=False, muteOutput=False, gsOutput=False, + printTestCase=False, questionToGrade=None, display=None): + # imports of testbench code. note that the testClasses import must follow + # the import of student code due to dependencies + import testParser + import testClasses + for module in moduleDict: + setattr(sys.modules[__name__], module, moduleDict[module]) + + questions = [] + questionDicts = {} + test_subdirs = getTestSubdirs(testParser, testRoot, questionToGrade) + for q in test_subdirs: + subdir_path = os.path.join(testRoot, q) + if not os.path.isdir(subdir_path) or q[0] == '.': + continue + + # create a question object + questionDict = testParser.TestParser( + os.path.join(subdir_path, 'CONFIG')).parse() + questionClass = getattr(testClasses, questionDict['class']) + question = questionClass(questionDict, display) + questionDicts[q] = questionDict + + # load test cases into question + tests = [t for t in os.listdir( + subdir_path) if re.match('[^#~.].*\.test\Z', t)] + tests = [re.match('(.*)\.test\Z', t).group(1) for t in tests] + for t in sorted(tests): + test_file = os.path.join(subdir_path, '%s.test' % t) + solution_file = os.path.join(subdir_path, '%s.solution' % t) + test_out_file = os.path.join(subdir_path, '%s.test_output' % t) + testDict = testParser.TestParser(test_file).parse() + if testDict.get("disabled", "false").lower() == "true": + continue + testDict['test_out_file'] = test_out_file + testClass = getattr(projectTestClasses, testDict['class']) + testCase = testClass(question, testDict) + + def makefun(testCase, solution_file): + if generateSolutions: + # write solution file to disk + return lambda grades: testCase.writeSolution(moduleDict, solution_file) + else: + # read in solution dictionary and pass as an argument + testDict = testParser.TestParser(test_file).parse() + solutionDict = testParser.TestParser(solution_file).parse() + if printTestCase: + return lambda grades: printTest(testDict, solutionDict) or testCase.execute(grades, moduleDict, solutionDict) + else: + return lambda grades: testCase.execute(grades, moduleDict, solutionDict) + question.addTestCase(testCase, makefun(testCase, solution_file)) + + # Note extra function is necessary for scoping reasons + def makefun(question): + return lambda grades: question.execute(grades) + setattr(sys.modules[__name__], q, makefun(question)) + questions.append((q, question.getMaxPoints())) + + grades = grading.Grades(projectParams.PROJECT_NAME, questions, + gsOutput=gsOutput, edxOutput=edxOutput, muteOutput=muteOutput) + if questionToGrade == None: + for q in questionDicts: + for prereq in questionDicts[q].get('depends', '').split(): + grades.addPrereq(q, prereq) + + grades.grade(sys.modules[__name__], bonusPic=projectParams.BONUS_PIC) + return grades.points + + +def getDisplay(graphicsByDefault, options=None): + graphics = graphicsByDefault + if options is not None and options.noGraphics: + graphics = False + if graphics: + try: + import graphicsDisplay + return graphicsDisplay.PacmanGraphics(1, frameTime=.05) + except ImportError: + pass + import textDisplay + return textDisplay.NullGraphics() + + +if __name__ == '__main__': + options = readCommand(sys.argv) + if options.generateSolutions: + confirmGenerate() + codePaths = options.studentCode.split(',') + + moduleDict = {} + for cp in codePaths: + moduleName = re.match('.*?([^/]*)\.py', cp).group(1) + moduleDict[moduleName] = loadModuleFile( + moduleName, os.path.join(options.codeRoot, cp)) + moduleName = re.match('.*?([^/]*)\.py', options.testCaseCode).group(1) + moduleDict['projectTestClasses'] = loadModuleFile( + moduleName, os.path.join(options.codeRoot, options.testCaseCode)) + + if options.runTest != None: + runTest(options.runTest, moduleDict, printTestCase=options.printTestCase, + display=getDisplay(True, options)) + else: + evaluate(options.generateSolutions, options.testRoot, moduleDict, + gsOutput=options.gsOutput, + edxOutput=options.edxOutput, muteOutput=options.muteOutput, printTestCase=options.printTestCase, + questionToGrade=options.gradeQuestion, display=getDisplay(options.gradeQuestion != None, options)) diff --git a/HW2_pacman/game.py b/HW2_pacman/game.py new file mode 100644 index 0000000..4ec3649 --- /dev/null +++ b/HW2_pacman/game.py @@ -0,0 +1,751 @@ +from util import * +import time +import os +import traceback +import sys + +class Agent: + """ + An agent must define a getAction method, but may also define the + following methods which will be called if they exist: + + def registerInitialState(self, state): # inspects the starting state + """ + + def __init__(self, index=0): + self.index = index + + def getAction(self, state): + """ + The Agent will receive a GameState (from either {pacman, capture, sonar}.py) and + must return an action from Directions.{North, South, East, West, Stop} + """ + raiseNotDefined() + + +class Directions: + NORTH = 'North' + SOUTH = 'South' + EAST = 'East' + WEST = 'West' + STOP = 'Stop' + + LEFT = {NORTH: WEST, + SOUTH: EAST, + EAST: NORTH, + WEST: SOUTH, + STOP: STOP} + + RIGHT = dict([(y, x) for x, y in list(LEFT.items())]) + + REVERSE = {NORTH: SOUTH, + SOUTH: NORTH, + EAST: WEST, + WEST: EAST, + STOP: STOP} + + +class Configuration: + """ + A Configuration holds the (x,y) coordinate of a character, along with its + traveling direction. + + The convention for positions, like a graph, is that (0,0) is the lower left corner, x increases + horizontally and y increases vertically. Therefore, north is the direction of increasing y, or (0,1). + """ + + def __init__(self, pos, direction): + self.pos = pos + self.direction = direction + + def getPosition(self): + return (self.pos) + + def getDirection(self): + return self.direction + + def isInteger(self): + x, y = self.pos + return x == int(x) and y == int(y) + + def __eq__(self, other): + if other == None: + return False + return (self.pos == other.pos and self.direction == other.direction) + + def __hash__(self): + x = hash(self.pos) + y = hash(self.direction) + return hash(x + 13 * y) + + def __str__(self): + return "(x,y)="+str(self.pos)+", "+str(self.direction) + + def getNextState(self, vector): + """ + Generates a new configuration reached by translating the current + configuration by the action vector. This is a low-level call and does + not attempt to respect the legality of the movement. + + Actions are movement vectors. + """ + x, y = self.pos + dx, dy = vector + direction = Actions.vectorToDirection(vector) + if direction == Directions.STOP: + direction = self.direction # There is no stop direction + return Configuration((x + dx, y+dy), direction) + + +class AgentState: + """ + AgentStates hold the state of an agent (configuration, speed, scared, etc). + """ + + def __init__(self, startConfiguration, isPacman): + self.start = startConfiguration + self.configuration = startConfiguration + self.isPacman = isPacman + self.scaredTimer = 0 + # state below potentially used for contest only + self.numCarrying = 0 + self.numReturned = 0 + + def __str__(self): + if self.isPacman: + return "Pacman: " + str(self.configuration) + else: + return "Ghost: " + str(self.configuration) + + def __eq__(self, other): + if other == None: + return False + return self.configuration == other.configuration and self.scaredTimer == other.scaredTimer + + def __hash__(self): + return hash(hash(self.configuration) + 13 * hash(self.scaredTimer)) + + def copy(self): + state = AgentState(self.start, self.isPacman) + state.configuration = self.configuration + state.scaredTimer = self.scaredTimer + state.numCarrying = self.numCarrying + state.numReturned = self.numReturned + return state + + def getPosition(self): + if self.configuration == None: + return None + return self.configuration.getPosition() + + def getDirection(self): + return self.configuration.getDirection() + + +class Grid: + """ + A 2-dimensional array of objects backed by a list of lists. Data is accessed + via grid[x][y] where (x,y) are positions on a Pacman map with x horizontal, + y vertical and the origin (0,0) in the bottom left corner. + + The __str__ method constructs an output that is oriented like a pacman board. + """ + + def __init__(self, width, height, initialValue=False, bitRepresentation=None): + if initialValue not in [False, True]: + raise Exception('Grids can only contain booleans') + self.CELLS_PER_INT = 30 + + self.width = width + self.height = height + self.data = [[initialValue for y in range( + height)] for x in range(width)] + if bitRepresentation: + self._unpackBits(bitRepresentation) + + def __getitem__(self, i): + return self.data[i] + + def __setitem__(self, key, item): + self.data[key] = item + + def __str__(self): + out = [[str(self.data[x][y])[0] for x in range(self.width)] + for y in range(self.height)] + out.reverse() + return '\n'.join([''.join(x) for x in out]) + + def __eq__(self, other): + if other == None: + return False + return self.data == other.data + + def __hash__(self): + # return hash(str(self)) + base = 1 + h = 0 + for l in self.data: + for i in l: + if i: + h += base + base *= 2 + return hash(h) + + def copy(self): + g = Grid(self.width, self.height) + g.data = [x[:] for x in self.data] + return g + + def deepCopy(self): + return self.copy() + + def shallowCopy(self): + g = Grid(self.width, self.height) + g.data = self.data + return g + + def count(self, item=True): + return sum([x.count(item) for x in self.data]) + + def asList(self, key=True): + list = [] + for x in range(self.width): + for y in range(self.height): + if self[x][y] == key: + list.append((x, y)) + return list + + def packBits(self): + """ + Returns an efficient int list representation + + (width, height, bitPackedInts...) + """ + bits = [self.width, self.height] + currentInt = 0 + for i in range(self.height * self.width): + bit = self.CELLS_PER_INT - (i % self.CELLS_PER_INT) - 1 + x, y = self._cellIndexToPosition(i) + if self[x][y]: + currentInt += 2 ** bit + if (i + 1) % self.CELLS_PER_INT == 0: + bits.append(currentInt) + currentInt = 0 + bits.append(currentInt) + return tuple(bits) + + def _cellIndexToPosition(self, index): + x = index / self.height + y = index % self.height + return x, y + + def _unpackBits(self, bits): + """ + Fills in data from a bit-level representation + """ + cell = 0 + for packed in bits: + for bit in self._unpackInt(packed, self.CELLS_PER_INT): + if cell == self.width * self.height: + break + x, y = self._cellIndexToPosition(cell) + self[x][y] = bit + cell += 1 + + def _unpackInt(self, packed, size): + bools = [] + if packed < 0: + raise ValueError("must be a positive integer") + for i in range(size): + n = 2 ** (self.CELLS_PER_INT - i - 1) + if packed >= n: + bools.append(True) + packed -= n + else: + bools.append(False) + return bools + + +def reconstituteGrid(bitRep): + if type(bitRep) is not type((1, 2)): + return bitRep + width, height = bitRep[:2] + return Grid(width, height, bitRepresentation=bitRep[2:]) + +#################################### +# Parts you shouldn't have to read # +#################################### + + +class Actions: + """ + A collection of static methods for manipulating move actions. + """ + # Directions + _directions = {Directions.WEST: (-1, 0), + Directions.STOP: (0, 0), + Directions.EAST: (1, 0), + Directions.NORTH: (0, 1), + Directions.SOUTH: (0, -1)} + + _directionsAsList = [('West', (-1, 0)), ('Stop', (0, 0)), ('East', (1, 0)), ('North', (0, 1)), ('South', (0, -1))] + + TOLERANCE = .001 + + def reverseDirection(action): + if action == Directions.NORTH: + return Directions.SOUTH + if action == Directions.SOUTH: + return Directions.NORTH + if action == Directions.EAST: + return Directions.WEST + if action == Directions.WEST: + return Directions.EAST + return action + reverseDirection = staticmethod(reverseDirection) + + def vectorToDirection(vector): + dx, dy = vector + if dy > 0: + return Directions.NORTH + if dy < 0: + return Directions.SOUTH + if dx < 0: + return Directions.WEST + if dx > 0: + return Directions.EAST + return Directions.STOP + vectorToDirection = staticmethod(vectorToDirection) + + def directionToVector(direction, speed=1.0): + dx, dy = Actions._directions[direction] + return (dx * speed, dy * speed) + directionToVector = staticmethod(directionToVector) + + def getPossibleActions(config, walls): + possible = [] + x, y = config.pos + x_int, y_int = int(x + 0.5), int(y + 0.5) + + # In between grid points, all agents must continue straight + if (abs(x - x_int) + abs(y - y_int) > Actions.TOLERANCE): + return [config.getDirection()] + + for dir, vec in Actions._directionsAsList: + dx, dy = vec + next_y = y_int + dy + next_x = x_int + dx + if not walls[next_x][next_y]: + possible.append(dir) + + return possible + + getPossibleActions = staticmethod(getPossibleActions) + + def getLegalNeighbors(position, walls): + x, y = position + x_int, y_int = int(x + 0.5), int(y + 0.5) + neighbors = [] + for dir, vec in Actions._directionsAsList: + dx, dy = vec + next_x = x_int + dx + if next_x < 0 or next_x == walls.width: + continue + next_y = y_int + dy + if next_y < 0 or next_y == walls.height: + continue + if not walls[next_x][next_y]: + neighbors.append((next_x, next_y)) + return neighbors + getLegalNeighbors = staticmethod(getLegalNeighbors) + + def getNextState(position, action): + dx, dy = Actions.directionToVector(action) + x, y = position + return (x + dx, y + dy) + getNextState = staticmethod(getNextState) + + +class GameStateData: + + def __init__(self, prevState=None): + """ + Generates a new data packet by copying information from its predecessor. + """ + if prevState != None: + self.food = prevState.food.shallowCopy() + self.capsules = prevState.capsules[:] + self.agentStates = self.copyAgentStates(prevState.agentStates) + self.layout = prevState.layout + self._eaten = prevState._eaten + self.score = prevState.score + + self._foodEaten = None + self._foodAdded = None + self._capsuleEaten = None + self._agentMoved = None + self._lose = False + self._win = False + self.scoreChange = 0 + + def deepCopy(self): + state = GameStateData(self) + state.food = self.food.deepCopy() + state.layout = self.layout.deepCopy() + state._agentMoved = self._agentMoved + state._foodEaten = self._foodEaten + state._foodAdded = self._foodAdded + state._capsuleEaten = self._capsuleEaten + return state + + def copyAgentStates(self, agentStates): + copiedStates = [] + for agentState in agentStates: + copiedStates.append(agentState.copy()) + return copiedStates + + def __eq__(self, other): + """ + Allows two states to be compared. + """ + if other == None: + return False + # TODO Check for type of other + if not self.agentStates == other.agentStates: + return False + if not self.food == other.food: + return False + if not self.capsules == other.capsules: + return False + if not self.score == other.score: + return False + return True + + def __hash__(self): + """ + Allows states to be keys of dictionaries. + """ + for i, state in enumerate(self.agentStates): + try: + int(hash(state)) + except TypeError as e: + print(e) + # hash(state) + return int((hash(tuple(self.agentStates)) + 13*hash(self.food) + 113 * hash(tuple(self.capsules)) + 7 * hash(self.score)) % 1048575) + + def __str__(self): + width, height = self.layout.width, self.layout.height + map = Grid(width, height) + if type(self.food) == type((1, 2)): + self.food = reconstituteGrid(self.food) + for x in range(width): + for y in range(height): + food, walls = self.food, self.layout.walls + map[x][y] = self._foodWallStr(food[x][y], walls[x][y]) + + for agentState in self.agentStates: + if agentState == None: + continue + if agentState.configuration == None: + continue + x, y = [int(i) for i in nearestPoint(agentState.configuration.pos)] + agent_dir = agentState.configuration.direction + if agentState.isPacman: + map[x][y] = self._pacStr(agent_dir) + else: + map[x][y] = self._ghostStr(agent_dir) + + for x, y in self.capsules: + map[x][y] = 'o' + + return str(map) + ("\nScore: %d\n" % self.score) + + def _foodWallStr(self, hasFood, hasWall): + if hasFood: + return '.' + elif hasWall: + return '%' + else: + return ' ' + + def _pacStr(self, dir): + if dir == Directions.NORTH: + return 'v' + if dir == Directions.SOUTH: + return '^' + if dir == Directions.WEST: + return '>' + return '<' + + def _ghostStr(self, dir): + return 'G' + if dir == Directions.NORTH: + return 'M' + if dir == Directions.SOUTH: + return 'W' + if dir == Directions.WEST: + return '3' + return 'E' + + def initialize(self, layout, numGhostAgents): + """ + Creates an initial game state from a layout array (see layout.py). + """ + self.food = layout.food.copy() + #self.capsules = [] + self.capsules = layout.capsules[:] + self.layout = layout + self.score = 0 + self.scoreChange = 0 + + self.agentStates = [] + numGhosts = 0 + for isPacman, pos in layout.agentPositions: + if not isPacman: + if numGhosts == numGhostAgents: + continue # Max ghosts reached already + else: + numGhosts += 1 + self.agentStates.append(AgentState( + Configuration(pos, Directions.STOP), isPacman)) + self._eaten = [False for a in self.agentStates] + + +try: + import boinc + _BOINC_ENABLED = True +except: + _BOINC_ENABLED = False + + +class Game: + """ + The Game manages the control flow, soliciting actions from agents. + """ + + def __init__(self, agents, display, rules, startingIndex=0, muteAgents=False, catchExceptions=False): + self.agentCrashed = False + self.agents = agents + self.display = display + self.rules = rules + self.startingIndex = startingIndex + self.gameOver = False + self.muteAgents = muteAgents + self.catchExceptions = catchExceptions + self.moveHistory = [] + self.totalAgentTimes = [0 for agent in agents] + self.totalAgentTimeWarnings = [0 for agent in agents] + self.agentTimeout = False + import io + self.agentOutput = [io.StringIO() for agent in agents] + + def getProgress(self): + if self.gameOver: + return 1.0 + else: + return self.rules.getProgress(self) + + def _agentCrash(self, agentIndex, quiet=False): + "Helper method for handling agent crashes" + if not quiet: + traceback.print_exc() + self.gameOver = True + self.agentCrashed = True + self.rules.agentCrash(self, agentIndex) + + OLD_STDOUT = None + OLD_STDERR = None + + def mute(self, agentIndex): + if not self.muteAgents: + return + global OLD_STDOUT, OLD_STDERR + import io + OLD_STDOUT = sys.stdout + OLD_STDERR = sys.stderr + sys.stdout = self.agentOutput[agentIndex] + sys.stderr = self.agentOutput[agentIndex] + + def unmute(self): + if not self.muteAgents: + return + global OLD_STDOUT, OLD_STDERR + # Revert stdout/stderr to originals + sys.stdout = OLD_STDOUT + sys.stderr = OLD_STDERR + + def run(self): + """ + Main control loop for game play. + """ + self.display.initialize(self.state.data) + self.numMoves = 0 + + # self.display.initialize(self.state.makeObservation(1).data) + # inform learning agents of the game start + for i in range(len(self.agents)): + agent = self.agents[i] + if not agent: + self.mute(i) + # this is a null agent, meaning it failed to load + # the other team wins + print("Agent %d failed to load" % i, file=sys.stderr) + self.unmute() + self._agentCrash(i, quiet=True) + return + if ("registerInitialState" in dir(agent)): + self.mute(i) + if self.catchExceptions: + try: + timed_func = TimeoutFunction( + agent.registerInitialState, int(self.rules.getMaxStartupTime(i))) + try: + start_time = time.time() + timed_func(self.state.deepCopy()) + time_taken = time.time() - start_time + self.totalAgentTimes[i] += time_taken + except TimeoutFunctionException: + print("Agent %d ran out of time on startup!" % + i, file=sys.stderr) + self.unmute() + self.agentTimeout = True + self._agentCrash(i, quiet=True) + return + except Exception as data: + self._agentCrash(i, quiet=False) + self.unmute() + return + else: + agent.registerInitialState(self.state.deepCopy()) + # TODO: could this exceed the total time + self.unmute() + + agentIndex = self.startingIndex + numAgents = len(self.agents) + + while not self.gameOver: + # Fetch the next agent + agent = self.agents[agentIndex] + move_time = 0 + skip_action = False + # Generate an observation of the state + if 'observationFunction' in dir(agent): + self.mute(agentIndex) + if self.catchExceptions: + try: + timed_func = TimeoutFunction(agent.observationFunction, int( + self.rules.getMoveTimeout(agentIndex))) + try: + start_time = time.time() + observation = timed_func(self.state.deepCopy()) + except TimeoutFunctionException: + skip_action = True + move_time += time.time() - start_time + self.unmute() + except Exception as data: + self._agentCrash(agentIndex, quiet=False) + self.unmute() + return + else: + observation = agent.observationFunction( + self.state.deepCopy()) + self.unmute() + else: + observation = self.state.deepCopy() + + # Solicit an action + action = None + self.mute(agentIndex) + if self.catchExceptions: + try: + timed_func = TimeoutFunction(agent.getAction, int( + self.rules.getMoveTimeout(agentIndex)) - int(move_time)) + try: + start_time = time.time() + if skip_action: + raise TimeoutFunctionException() + action = timed_func(observation) + except TimeoutFunctionException: + print("Agent %d timed out on a single move!" % + agentIndex, file=sys.stderr) + self.agentTimeout = True + self._agentCrash(agentIndex, quiet=True) + self.unmute() + return + + move_time += time.time() - start_time + + if move_time > self.rules.getMoveWarningTime(agentIndex): + self.totalAgentTimeWarnings[agentIndex] += 1 + print("Agent %d took too long to make a move! This is warning %d" % ( + agentIndex, self.totalAgentTimeWarnings[agentIndex]), file=sys.stderr) + if self.totalAgentTimeWarnings[agentIndex] > self.rules.getMaxTimeWarnings(agentIndex): + print("Agent %d exceeded the maximum number of warnings: %d" % ( + agentIndex, self.totalAgentTimeWarnings[agentIndex]), file=sys.stderr) + self.agentTimeout = True + self._agentCrash(agentIndex, quiet=True) + self.unmute() + return + + self.totalAgentTimes[agentIndex] += move_time + # print "Agent: %d, time: %f, total: %f" % (agentIndex, move_time, self.totalAgentTimes[agentIndex]) + if self.totalAgentTimes[agentIndex] > self.rules.getMaxTotalTime(agentIndex): + print("Agent %d ran out of time! (time: %1.2f)" % ( + agentIndex, self.totalAgentTimes[agentIndex]), file=sys.stderr) + self.agentTimeout = True + self._agentCrash(agentIndex, quiet=True) + self.unmute() + return + self.unmute() + except Exception as data: + self._agentCrash(agentIndex) + self.unmute() + return + else: + action = agent.getAction(observation) + self.unmute() + + # Execute the action + self.moveHistory.append((agentIndex, action)) + if self.catchExceptions: + try: + self.state = self.state.getNextState( + agentIndex, action) + except Exception as data: + self.mute(agentIndex) + self._agentCrash(agentIndex) + self.unmute() + return + else: + self.state = self.state.getNextState(agentIndex, action) + + # Change the display + self.display.update(self.state.data) + ###idx = agentIndex - agentIndex % 2 + 1 + ###self.display.update( self.state.makeObservation(idx).data ) + + # Allow for game specific conditions (winning, losing, etc.) + self.rules.process(self.state, self) + # Track progress + if agentIndex == numAgents + 1: + self.numMoves += 1 + # Next agent + agentIndex = (agentIndex + 1) % numAgents + + if _BOINC_ENABLED: + boinc.set_fraction_done(self.getProgress()) + + # inform a learning agent of the game result + for agentIndex, agent in enumerate(self.agents): + if "final" in dir(agent): + try: + self.mute(agentIndex) + agent.final(self.state) + self.unmute() + except Exception as data: + if not self.catchExceptions: + raise + self._agentCrash(agentIndex) + self.unmute() + return + self.display.finish() diff --git a/HW2_pacman/ghostAgents.py b/HW2_pacman/ghostAgents.py new file mode 100644 index 0000000..9c3b860 --- /dev/null +++ b/HW2_pacman/ghostAgents.py @@ -0,0 +1,79 @@ +from game import Agent +from game import Actions +from game import Directions +import random +from util import manhattanDistance +import util + + +class GhostAgent(Agent): + def __init__(self, index): + self.index = index + + def getAction(self, state): + dist = self.getDistribution(state) + if len(dist) == 0: + return Directions.STOP + else: + return util.chooseFromDistribution(dist) + + def getDistribution(self, state): + "Returns a Counter encoding a distribution over actions from the provided state." + util.raiseNotDefined() + + +class RandomGhost(GhostAgent): + "A ghost that chooses a legal action uniformly at random." + + def getDistribution(self, state): + dist = util.Counter() + for a in state.getLegalActions(self.index): + dist[a] = 1.0 + dist.normalize() + return dist + + +class DirectionalGhost(GhostAgent): + "A ghost that prefers to rush Pacman, or flee when scared." + + def __init__(self, index, prob_attack=0.8, prob_scaredFlee=0.8): + self.index = index + self.prob_attack = prob_attack + self.prob_scaredFlee = prob_scaredFlee + + def getDistribution(self, state): + # Read variables from state + ghostState = state.getGhostState(self.index) + legalActions = state.getLegalActions(self.index) + pos = state.getGhostPosition(self.index) + isScared = ghostState.scaredTimer > 0 + + speed = 1 + if isScared: + speed = 0.5 + + actionVectors = [Actions.directionToVector( + a, speed) for a in legalActions] + newPositions = [(pos[0]+a[0], pos[1]+a[1]) for a in actionVectors] + pacmanPosition = state.getPacmanPosition() + + # Select best actions given the state + distancesToPacman = [manhattanDistance( + pos, pacmanPosition) for pos in newPositions] + if isScared: + bestScore = max(distancesToPacman) + bestProb = self.prob_scaredFlee + else: + bestScore = min(distancesToPacman) + bestProb = self.prob_attack + bestActions = [action for action, distance in zip( + legalActions, distancesToPacman) if distance == bestScore] + + # Construct distribution + dist = util.Counter() + for a in bestActions: + dist[a] = bestProb / len(bestActions) + for a in legalActions: + dist[a] += (1-bestProb) / len(legalActions) + dist.normalize() + return dist diff --git a/HW2_pacman/grading.py b/HW2_pacman/grading.py new file mode 100644 index 0000000..59334bb --- /dev/null +++ b/HW2_pacman/grading.py @@ -0,0 +1,307 @@ +import html +import time +import sys +import json +import traceback +import pdb +from collections import defaultdict +import util + + +class Grades: + "A data structure for project grades, along with formatting code to display them" + + def __init__(self, projectName, questionsAndMaxesList, + gsOutput=False, edxOutput=False, muteOutput=False): + """ + Defines the grading scheme for a project + projectName: project name + questionsAndMaxesDict: a list of (question name, max points per question) + """ + self.questions = [el[0] for el in questionsAndMaxesList] + self.maxes = dict(questionsAndMaxesList) + self.points = Counter() + self.messages = dict([(q, []) for q in self.questions]) + self.project = projectName + self.start = time.localtime()[1:6] + self.sane = True # Sanity checks + self.currentQuestion = None # Which question we're grading + self.edxOutput = edxOutput + self.gsOutput = gsOutput # GradeScope output + self.mute = muteOutput + self.prereqs = defaultdict(set) + + # print 'Autograder transcript for %s' % self.project + print('Starting on %d-%d at %d:%02d:%02d' % self.start) + + def addPrereq(self, question, prereq): + self.prereqs[question].add(prereq) + + def grade(self, gradingModule, exceptionMap={}, bonusPic=False): + """ + Grades each question + gradingModule: the module with all the grading functions (pass in with sys.modules[__name__]) + """ + + completedQuestions = set([]) + for q in self.questions: + print('\nQuestion %s' % q) + print('=' * (9 + len(q))) + print() + self.currentQuestion = q + + incompleted = self.prereqs[q].difference(completedQuestions) + if len(incompleted) > 0: + prereq = incompleted.pop() + print("""*** NOTE: Make sure to complete Question %s before working on Question %s, +*** because Question %s builds upon your answer for Question %s. +""" % (prereq, q, q, prereq)) + continue + + if self.mute: + util.mutePrint() + try: + util.TimeoutFunction(getattr(gradingModule, q), 1800)( + self) # Call the question's function + # TimeoutFunction(getattr(gradingModule, q),1200)(self) # Call the question's function + except Exception as inst: + self.addExceptionMessage(q, inst, traceback) + self.addErrorHints(exceptionMap, inst, q[1]) + except: + self.fail('FAIL: Terminated with a string exception.') + finally: + if self.mute: + util.unmutePrint() + + if self.points[q] >= self.maxes[q]: + completedQuestions.add(q) + + print('\n### Question %s: %d/%d ###\n' % + (q, self.points[q], self.maxes[q])) + + print('\nFinished at %d:%02d:%02d' % time.localtime()[3:6]) + print("\nProvisional grades\n==================") + + for q in self.questions: + print('Question %s: %d/%d' % (q, self.points[q], self.maxes[q])) + print('------------------') + print('Total: %d/%d' % + (self.points.totalCount(), sum(self.maxes.values()))) + if self.points.totalCount() == 80: + print(""" + + ALL HAIL GRANDPAC. + LONG LIVE THE GHOSTBUSTING KING. + + --- ---- --- + | \ / + \ / | + | + \--/ \--/ + | + | + + | + | + + + | + @@@@@@@@@@@@@@@@@@@@@@@@@@ + @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ + @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ + @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ + \ @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ + \ / @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ + V \ @@@@@@@@@@@@@@@@@@@@@@@@@@@@ + \ / @@@@@@@@@@@@@@@@@@@@@@@@@@ + V @@@@@@@@@@@@@@@@@@@@@@@@ + @@@@@@@@@@@@@@@@@@@@@@ + /\ @@@@@@@@@@@@@@@@@@@@@@ + / \ @@@@@@@@@@@@@@@@@@@@@@@@@ + /\ / @@@@@@@@@@@@@@@@@@@@@@@@@@@ + / \ @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ + / @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ + @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ + @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ + @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ + @@@@@@@@@@@@@@@@@@@@@@@@@@ + @@@@@@@@@@@@@@@@@@ + +""") + if self.edxOutput: + self.produceOutput() + if self.gsOutput: + self.produceGradeScopeOutput() + + def addExceptionMessage(self, q, inst, traceback): + """ + Method to format the exception message, this is more complicated because + we need to cgi.escape the traceback but wrap the exception in a 
 tag
+        """
+        self.fail('FAIL: Exception raised: %s' % inst)
+        self.addMessage('')
+        for line in traceback.format_exc().split('\n'):
+            self.addMessage(line)
+
+    def addErrorHints(self, exceptionMap, errorInstance, questionNum):
+        typeOf = str(type(errorInstance))
+        questionName = 'q' + questionNum
+        errorHint = ''
+
+        # question specific error hints
+        if exceptionMap.get(questionName):
+            questionMap = exceptionMap.get(questionName)
+            if (questionMap.get(typeOf)):
+                errorHint = questionMap.get(typeOf)
+        # fall back to general error messages if a question specific
+        # one does not exist
+        if (exceptionMap.get(typeOf)):
+            errorHint = exceptionMap.get(typeOf)
+
+        # dont include the HTML if we have no error hint
+        if not errorHint:
+            return ''
+
+        for line in errorHint.split('\n'):
+            self.addMessage(line)
+
+    def produceGradeScopeOutput(self):
+        out_dct = {}
+
+        # total of entire submission
+        total_possible = sum(self.maxes.values())
+        total_score = sum(self.points.values())
+        out_dct['score'] = total_score
+        out_dct['max_score'] = total_possible
+        out_dct['output'] = "Total score (%d / %d)" % (
+            total_score, total_possible)
+
+        # individual tests
+        tests_out = []
+        for name in self.questions:
+            test_out = {}
+            # test name
+            test_out['name'] = name
+            # test score
+            test_out['score'] = self.points[name]
+            test_out['max_score'] = self.maxes[name]
+            # others
+            is_correct = self.points[name] >= self.maxes[name]
+            test_out['output'] = "  Question {num} ({points}/{max}) {correct}".format(
+                num=(name[1] if len(name) == 2 else name),
+                points=test_out['score'],
+                max=test_out['max_score'],
+                correct=('X' if not is_correct else ''),
+            )
+            test_out['tags'] = []
+            tests_out.append(test_out)
+        out_dct['tests'] = tests_out
+
+        # file output
+        with open('gradescope_response.json', 'w') as outfile:
+            json.dump(out_dct, outfile)
+        return
+
+    def produceOutput(self):
+        edxOutput = open('edx_response.html', 'w')
+        edxOutput.write("
")
+
+        # first sum
+        total_possible = sum(self.maxes.values())
+        total_score = sum(self.points.values())
+        checkOrX = ''
+        if (total_score >= total_possible):
+            checkOrX = ''
+        header = """
+        

+            Total score ({total_score} / {total_possible})
+        

+    """.format(total_score=total_score,
+               total_possible=total_possible,
+               checkOrX=checkOrX
+               )
+        edxOutput.write(header)
+
+        for q in self.questions:
+            if len(q) == 2:
+                name = q[1]
+            else:
+                name = q
+            checkOrX = ''
+            if (self.points[q] >= self.maxes[q]):
+                checkOrX = ''
+            #messages = '\n
\n'.join(self.messages[q])
+            messages = "
%s
" % '\n'.join(self.messages[q])
+            output = """
+        

+          

+          

+            Question {q} ({points}/{max}) {checkOrX}
+          

+        

+          {messages}
+        

+        

+      

+      """.format(q=name,
+                 max=self.maxes[q],
+                 messages=messages,
+                 checkOrX=checkOrX,
+                 points=self.points[q]
+                 )
+            # print "*** output for Question %s " % q[1]
+            # print output
+            edxOutput.write(output)
+        edxOutput.write("
")
+        edxOutput.close()
+        edxOutput = open('edx_grade', 'w')
+        edxOutput.write(str(self.points.totalCount()))
+        edxOutput.close()
+
+    def fail(self, message, raw=False):
+        "Sets sanity check bit to false and outputs a message"
+        self.sane = False
+        self.assignZeroCredit()
+        self.addMessage(message, raw)
+
+    def assignZeroCredit(self):
+        self.points[self.currentQuestion] = 0
+
+    def addPoints(self, amt):
+        self.points[self.currentQuestion] += amt
+
+    def deductPoints(self, amt):
+        self.points[self.currentQuestion] -= amt
+
+    def assignFullCredit(self, message="", raw=False):
+        self.points[self.currentQuestion] = self.maxes[self.currentQuestion]
+        if message != "":
+            self.addMessage(message, raw)
+
+    def addMessage(self, message, raw=False):
+        if not raw:
+                # We assume raw messages, formatted for HTML, are printed separately
+            if self.mute:
+                util.unmutePrint()
+            print('*** ' + message)
+            if self.mute:
+                util.mutePrint()
+            message = html.escape(message)
+        self.messages[self.currentQuestion].append(message)
+
+    def addMessageToEmail(self, message):
+        print("WARNING**** addMessageToEmail is deprecated %s" % message)
+        for line in message.split('\n'):
+            pass
+            # print '%%% ' + line + ' %%%'
+            # self.messages[self.currentQuestion].append(line)
+
+
+class Counter(dict):
+    """
+    Dict with default 0
+    """
+
+    def __getitem__(self, idx):
+        try:
+            return dict.__getitem__(self, idx)
+        except KeyError:
+            return 0
+
+    def totalCount(self):
+        """
+        Returns the sum of counts for all keys.
+        """
+        return sum(self.values())
diff --git a/HW2_pacman/graphicsDisplay.py b/HW2_pacman/graphicsDisplay.py
new file mode 100644
index 0000000..356c5d7
--- /dev/null
+++ b/HW2_pacman/graphicsDisplay.py
@@ -0,0 +1,718 @@
+from graphicsUtils import *
+import math
+import time
+from game import Directions
+
+
+DEFAULT_GRID_SIZE = 30.0
+INFO_PANE_HEIGHT = 35
+BACKGROUND_COLOR = formatColor(0, 0, 0)
+WALL_COLOR = formatColor(0.0/255.0, 51.0/255.0, 255.0/255.0)
+INFO_PANE_COLOR = formatColor(.4, .4, 0)
+SCORE_COLOR = formatColor(.9, .9, .9)
+PACMAN_OUTLINE_WIDTH = 2
+PACMAN_CAPTURE_OUTLINE_WIDTH = 4
+
+GHOST_COLORS = []
+GHOST_COLORS.append(formatColor(.9, 0, 0))  # Red
+GHOST_COLORS.append(formatColor(0, .3, .9))  # Blue
+GHOST_COLORS.append(formatColor(.98, .41, .07))  # Orange
+GHOST_COLORS.append(formatColor(.1, .75, .7))  # Green
+GHOST_COLORS.append(formatColor(1.0, 0.6, 0.0))  # Yellow
+GHOST_COLORS.append(formatColor(.4, 0.13, 0.91))  # Purple
+
+TEAM_COLORS = GHOST_COLORS[:2]
+
+GHOST_SHAPE = [
+    (0,     0.3),
+    (0.25,  0.75),
+    (0.5,   0.3),
+    (0.75,  0.75),
+    (0.75,  -0.5),
+    (0.5,   -0.75),
+    (-0.5,  -0.75),
+    (-0.75, -0.5),
+    (-0.75, 0.75),
+    (-0.5,  0.3),
+    (-0.25, 0.75)
+]
+GHOST_SIZE = 0.65
+SCARED_COLOR = formatColor(1, 1, 1)
+
+GHOST_VEC_COLORS = list(map(colorToVector, GHOST_COLORS))
+
+PACMAN_COLOR = formatColor(255.0/255.0, 255.0/255.0, 61.0/255)
+PACMAN_SCALE = 0.5
+#pacman_speed = 0.25
+
+# Food
+FOOD_COLOR = formatColor(1, 1, 1)
+FOOD_SIZE = 0.1
+
+# Laser
+LASER_COLOR = formatColor(1, 0, 0)
+LASER_SIZE = 0.02
+
+# Capsule graphics
+CAPSULE_COLOR = formatColor(1, 1, 1)
+CAPSULE_SIZE = 0.25
+
+# Drawing walls
+WALL_RADIUS = 0.15
+
+
+class InfoPane:
+    def __init__(self, layout, gridSize):
+        self.gridSize = gridSize
+        self.width = (layout.width) * gridSize
+        self.base = (layout.height + 1) * gridSize
+        self.height = INFO_PANE_HEIGHT
+        self.fontSize = 24
+        self.textColor = PACMAN_COLOR
+        self.drawPane()
+
+    def toScreen(self, pos, y=None):
+        """
+          Translates a point relative from the bottom left of the info pane.
+        """
+        if y == None:
+            x, y = pos
+        else:
+            x = pos
+
+        x = self.gridSize + x  # Margin
+        y = self.base + y
+        return x, y
+
+    def drawPane(self):
+        self.scoreText = text(self.toScreen(
+            0, 0), self.textColor, "SCORE:    0", "Times", self.fontSize, "bold")
+
+    def initializeGhostDistances(self, distances):
+        self.ghostDistanceText = []
+
+        size = 20
+        if self.width < 240:
+            size = 12
+        if self.width < 160:
+            size = 10
+
+        for i, d in enumerate(distances):
+            t = text(self.toScreen(self.width/2 + self.width/8 * i, 0),
+                     GHOST_COLORS[i+1], d, "Times", size, "bold")
+            self.ghostDistanceText.append(t)
+
+    def updateScore(self, score):
+        changeText(self.scoreText, "SCORE: % 4d" % score)
+
+    def setTeam(self, isBlue):
+        text = "RED TEAM"
+        if isBlue:
+            text = "BLUE TEAM"
+        self.teamText = text(self.toScreen(
+            300, 0), self.textColor, text, "Times", self.fontSize, "bold")
+
+    def updateGhostDistances(self, distances):
+        if len(distances) == 0:
+            return
+        if 'ghostDistanceText' not in dir(self):
+            self.initializeGhostDistances(distances)
+        else:
+            for i, d in enumerate(distances):
+                changeText(self.ghostDistanceText[i], d)
+
+    def drawGhost(self):
+        pass
+
+    def drawPacman(self):
+        pass
+
+    def drawWarning(self):
+        pass
+
+    def clearIcon(self):
+        pass
+
+    def updateMessage(self, message):
+        pass
+
+    def clearMessage(self):
+        pass
+
+
+class PacmanGraphics:
+    def __init__(self, zoom=1.0, frameTime=0.0, capture=False):
+        self.have_window = 0
+        self.currentGhostImages = {}
+        self.pacmanImage = None
+        self.zoom = zoom
+        self.gridSize = DEFAULT_GRID_SIZE * zoom
+        self.capture = capture
+        self.frameTime = frameTime
+
+    def checkNullDisplay(self):
+        return False
+
+    def initialize(self, state, isBlue=False):
+        self.isBlue = isBlue
+        self.startGraphics(state)
+
+        # self.drawDistributions(state)
+        self.distributionImages = None  # Initialized lazily
+        self.drawStaticObjects(state)
+        self.drawAgentObjects(state)
+
+        # Information
+        self.previousState = state
+
+    def startGraphics(self, state):
+        self.layout = state.layout
+        layout = self.layout
+        self.width = layout.width
+        self.height = layout.height
+        self.make_window(self.width, self.height)
+        self.infoPane = InfoPane(layout, self.gridSize)
+        self.currentState = layout
+
+    def drawDistributions(self, state):
+        walls = state.layout.walls
+        dist = []
+        for x in range(walls.width):
+            distx = []
+            dist.append(distx)
+            for y in range(walls.height):
+                (screen_x, screen_y) = self.to_screen((x, y))
+                block = square((screen_x, screen_y),
+                               0.5 * self.gridSize,
+                               color=BACKGROUND_COLOR,
+                               filled=1, behind=2)
+                distx.append(block)
+        self.distributionImages = dist
+
+    def drawStaticObjects(self, state):
+        layout = self.layout
+        self.drawWalls(layout.walls)
+        self.food = self.drawFood(layout.food)
+        self.capsules = self.drawCapsules(layout.capsules)
+        refresh()
+
+    def drawAgentObjects(self, state):
+        self.agentImages = []  # (agentState, image)
+        for index, agent in enumerate(state.agentStates):
+            if agent.isPacman:
+                image = self.drawPacman(agent, index)
+                self.agentImages.append((agent, image))
+            else:
+                image = self.drawGhost(agent, index)
+                self.agentImages.append((agent, image))
+        refresh()
+
+    def swapImages(self, agentIndex, newState):
+        """
+          Changes an image from a ghost to a pacman or vis versa (for capture)
+        """
+        prevState, prevImage = self.agentImages[agentIndex]
+        for item in prevImage:
+            remove_from_screen(item)
+        if newState.isPacman:
+            image = self.drawPacman(newState, agentIndex)
+            self.agentImages[agentIndex] = (newState, image)
+        else:
+            image = self.drawGhost(newState, agentIndex)
+            self.agentImages[agentIndex] = (newState, image)
+        refresh()
+
+    def update(self, newState):
+        agentIndex = newState._agentMoved
+        agentState = newState.agentStates[agentIndex]
+
+        if self.agentImages[agentIndex][0].isPacman != agentState.isPacman:
+            self.swapImages(agentIndex, agentState)
+        prevState, prevImage = self.agentImages[agentIndex]
+        if agentState.isPacman:
+            self.animatePacman(agentState, prevState, prevImage)
+        else:
+            self.moveGhost(agentState, agentIndex, prevState, prevImage)
+        self.agentImages[agentIndex] = (agentState, prevImage)
+
+        if newState._foodEaten != None:
+            self.removeFood(newState._foodEaten, self.food)
+        if newState._capsuleEaten != None:
+            self.removeCapsule(newState._capsuleEaten, self.capsules)
+        self.infoPane.updateScore(newState.score)
+        if 'ghostDistances' in dir(newState):
+            self.infoPane.updateGhostDistances(newState.ghostDistances)
+
+    def make_window(self, width, height):
+        grid_width = (width-1) * self.gridSize
+        grid_height = (height-1) * self.gridSize
+        screen_width = 2*self.gridSize + grid_width
+        screen_height = 2*self.gridSize + grid_height + INFO_PANE_HEIGHT
+
+        begin_graphics(screen_width,
+                       screen_height,
+                       BACKGROUND_COLOR,
+                       "CS188 Pacman")
+
+    def drawPacman(self, pacman, index):
+        position = self.getPosition(pacman)
+        screen_point = self.to_screen(position)
+        endpoints = self.getEndpoints(self.getDirection(pacman))
+
+        width = PACMAN_OUTLINE_WIDTH
+        outlineColor = PACMAN_COLOR
+        fillColor = PACMAN_COLOR
+
+        if self.capture:
+            outlineColor = TEAM_COLORS[index % 2]
+            fillColor = GHOST_COLORS[index]
+            width = PACMAN_CAPTURE_OUTLINE_WIDTH
+
+        return [circle(screen_point, PACMAN_SCALE * self.gridSize,
+                       fillColor=fillColor, outlineColor=outlineColor,
+                       endpoints=endpoints,
+                       width=width)]
+
+    def getEndpoints(self, direction, position=(0, 0)):
+        x, y = position
+        pos = x - int(x) + y - int(y)
+        width = 30 + 80 * math.sin(math.pi * pos)
+
+        delta = width / 2
+        if (direction == 'West'):
+            endpoints = (180+delta, 180-delta)
+        elif (direction == 'North'):
+            endpoints = (90+delta, 90-delta)
+        elif (direction == 'South'):
+            endpoints = (270+delta, 270-delta)
+        else:
+            endpoints = (0+delta, 0-delta)
+        return endpoints
+
+    def movePacman(self, position, direction, image):
+        screenPosition = self.to_screen(position)
+        endpoints = self.getEndpoints(direction, position)
+        r = PACMAN_SCALE * self.gridSize
+        moveCircle(image[0], screenPosition, r, endpoints)
+        refresh()
+
+    def animatePacman(self, pacman, prevPacman, image):
+        if self.frameTime < 0:
+            print('Press any key to step forward, "q" to play')
+            keys = wait_for_keys()
+            if 'q' in keys:
+                self.frameTime = 0.1
+        if self.frameTime > 0.01 or self.frameTime < 0:
+            start = time.time()
+            fx, fy = self.getPosition(prevPacman)
+            px, py = self.getPosition(pacman)
+            frames = 4.0
+            for i in range(1, int(frames) + 1):
+                pos = px*i/frames + fx * \
+                    (frames-i)/frames, py*i/frames + fy*(frames-i)/frames
+                self.movePacman(pos, self.getDirection(pacman), image)
+                refresh()
+                sleep(abs(self.frameTime) / frames)
+        else:
+            self.movePacman(self.getPosition(pacman),
+                            self.getDirection(pacman), image)
+        refresh()
+
+    def getGhostColor(self, ghost, ghostIndex):
+        if ghost.scaredTimer > 0:
+            return SCARED_COLOR
+        else:
+            return GHOST_COLORS[ghostIndex]
+
+    def drawGhost(self, ghost, agentIndex):
+        pos = self.getPosition(ghost)
+        dir = self.getDirection(ghost)
+        (screen_x, screen_y) = (self.to_screen(pos))
+        coords = []
+        for (x, y) in GHOST_SHAPE:
+            coords.append((x*self.gridSize*GHOST_SIZE + screen_x,
+                           y*self.gridSize*GHOST_SIZE + screen_y))
+
+        colour = self.getGhostColor(ghost, agentIndex)
+        body = polygon(coords, colour, filled=1)
+        WHITE = formatColor(1.0, 1.0, 1.0)
+        BLACK = formatColor(0.0, 0.0, 0.0)
+
+        dx = 0
+        dy = 0
+        if dir == 'North':
+            dy = -0.2
+        if dir == 'South':
+            dy = 0.2
+        if dir == 'East':
+            dx = 0.2
+        if dir == 'West':
+            dx = -0.2
+        leftEye = circle((screen_x+self.gridSize*GHOST_SIZE*(-0.3+dx/1.5), screen_y -
+                          self.gridSize*GHOST_SIZE*(0.3-dy/1.5)), self.gridSize*GHOST_SIZE*0.2, WHITE, WHITE)
+        rightEye = circle((screen_x+self.gridSize*GHOST_SIZE*(0.3+dx/1.5), screen_y -
+                           self.gridSize*GHOST_SIZE*(0.3-dy/1.5)), self.gridSize*GHOST_SIZE*0.2, WHITE, WHITE)
+        leftPupil = circle((screen_x+self.gridSize*GHOST_SIZE*(-0.3+dx), screen_y -
+                            self.gridSize*GHOST_SIZE*(0.3-dy)), self.gridSize*GHOST_SIZE*0.08, BLACK, BLACK)
+        rightPupil = circle((screen_x+self.gridSize*GHOST_SIZE*(0.3+dx), screen_y -
+                             self.gridSize*GHOST_SIZE*(0.3-dy)), self.gridSize*GHOST_SIZE*0.08, BLACK, BLACK)
+        ghostImageParts = []
+        ghostImageParts.append(body)
+        ghostImageParts.append(leftEye)
+        ghostImageParts.append(rightEye)
+        ghostImageParts.append(leftPupil)
+        ghostImageParts.append(rightPupil)
+
+        return ghostImageParts
+
+    def moveEyes(self, pos, dir, eyes):
+        (screen_x, screen_y) = (self.to_screen(pos))
+        dx = 0
+        dy = 0
+        if dir == 'North':
+            dy = -0.2
+        if dir == 'South':
+            dy = 0.2
+        if dir == 'East':
+            dx = 0.2
+        if dir == 'West':
+            dx = -0.2
+        moveCircle(eyes[0], (screen_x+self.gridSize*GHOST_SIZE*(-0.3+dx/1.5), screen_y -
+                             self.gridSize*GHOST_SIZE*(0.3-dy/1.5)), self.gridSize*GHOST_SIZE*0.2)
+        moveCircle(eyes[1], (screen_x+self.gridSize*GHOST_SIZE*(0.3+dx/1.5), screen_y -
+                             self.gridSize*GHOST_SIZE*(0.3-dy/1.5)), self.gridSize*GHOST_SIZE*0.2)
+        moveCircle(eyes[2], (screen_x+self.gridSize*GHOST_SIZE*(-0.3+dx), screen_y -
+                             self.gridSize*GHOST_SIZE*(0.3-dy)), self.gridSize*GHOST_SIZE*0.08)
+        moveCircle(eyes[3], (screen_x+self.gridSize*GHOST_SIZE*(0.3+dx), screen_y -
+                             self.gridSize*GHOST_SIZE*(0.3-dy)), self.gridSize*GHOST_SIZE*0.08)
+
+    def moveGhost(self, ghost, ghostIndex, prevGhost, ghostImageParts):
+        old_x, old_y = self.to_screen(self.getPosition(prevGhost))
+        new_x, new_y = self.to_screen(self.getPosition(ghost))
+        delta = new_x - old_x, new_y - old_y
+
+        for ghostImagePart in ghostImageParts:
+            move_by(ghostImagePart, delta)
+        refresh()
+
+        if ghost.scaredTimer > 0:
+            color = SCARED_COLOR
+        else:
+            color = GHOST_COLORS[ghostIndex]
+        edit(ghostImageParts[0], ('fill', color), ('outline', color))
+        self.moveEyes(self.getPosition(ghost),
+                      self.getDirection(ghost), ghostImageParts[-4:])
+        refresh()
+
+    def getPosition(self, agentState):
+        if agentState.configuration == None:
+            return (-1000, -1000)
+        return agentState.getPosition()
+
+    def getDirection(self, agentState):
+        if agentState.configuration == None:
+            return Directions.STOP
+        return agentState.configuration.getDirection()
+
+    def finish(self):
+        end_graphics()
+
+    def to_screen(self, point):
+        (x, y) = point
+        #y = self.height - y
+        x = (x + 1)*self.gridSize
+        y = (self.height - y)*self.gridSize
+        return (x, y)
+
+    # Fixes some TK issue with off-center circles
+    def to_screen2(self, point):
+        (x, y) = point
+        #y = self.height - y
+        x = (x + 1)*self.gridSize
+        y = (self.height - y)*self.gridSize
+        return (x, y)
+
+    def drawWalls(self, wallMatrix):
+        wallColor = WALL_COLOR
+        for xNum, x in enumerate(wallMatrix):
+            if self.capture and (xNum * 2) < wallMatrix.width:
+                wallColor = TEAM_COLORS[0]
+            if self.capture and (xNum * 2) >= wallMatrix.width:
+                wallColor = TEAM_COLORS[1]
+
+            for yNum, cell in enumerate(x):
+                if cell:  # There's a wall here
+                    pos = (xNum, yNum)
+                    screen = self.to_screen(pos)
+                    screen2 = self.to_screen2(pos)
+
+                    # draw each quadrant of the square based on adjacent walls
+                    wIsWall = self.isWall(xNum-1, yNum, wallMatrix)
+                    eIsWall = self.isWall(xNum+1, yNum, wallMatrix)
+                    nIsWall = self.isWall(xNum, yNum+1, wallMatrix)
+                    sIsWall = self.isWall(xNum, yNum-1, wallMatrix)
+                    nwIsWall = self.isWall(xNum-1, yNum+1, wallMatrix)
+                    swIsWall = self.isWall(xNum-1, yNum-1, wallMatrix)
+                    neIsWall = self.isWall(xNum+1, yNum+1, wallMatrix)
+                    seIsWall = self.isWall(xNum+1, yNum-1, wallMatrix)
+
+                    # NE quadrant
+                    if (not nIsWall) and (not eIsWall):
+                        # inner circle
+                        circle(screen2, WALL_RADIUS * self.gridSize,
+                               wallColor, wallColor, (0, 91), 'arc')
+                    if (nIsWall) and (not eIsWall):
+                        # vertical line
+                        line(add(screen, (self.gridSize*WALL_RADIUS, 0)), add(screen,
+                                                                              (self.gridSize*WALL_RADIUS, self.gridSize*(-0.5)-1)), wallColor)
+                    if (not nIsWall) and (eIsWall):
+                        # horizontal line
+                        line(add(screen, (0, self.gridSize*(-1)*WALL_RADIUS)), add(screen,
+                                                                                   (self.gridSize*0.5+1, self.gridSize*(-1)*WALL_RADIUS)), wallColor)
+                    if (nIsWall) and (eIsWall) and (not neIsWall):
+                        # outer circle
+                        circle(add(screen2, (self.gridSize*2*WALL_RADIUS, self.gridSize*(-2)*WALL_RADIUS)),
+                               WALL_RADIUS * self.gridSize-1, wallColor, wallColor, (180, 271), 'arc')
+                        line(add(screen, (self.gridSize*2*WALL_RADIUS-1, self.gridSize*(-1)*WALL_RADIUS)),
+                             add(screen, (self.gridSize*0.5+1, self.gridSize*(-1)*WALL_RADIUS)), wallColor)
+                        line(add(screen, (self.gridSize*WALL_RADIUS, self.gridSize*(-2)*WALL_RADIUS+1)),
+                             add(screen, (self.gridSize*WALL_RADIUS, self.gridSize*(-0.5))), wallColor)
+
+                    # NW quadrant
+                    if (not nIsWall) and (not wIsWall):
+                        # inner circle
+                        circle(screen2, WALL_RADIUS * self.gridSize,
+                               wallColor, wallColor, (90, 181), 'arc')
+                    if (nIsWall) and (not wIsWall):
+                        # vertical line
+                        line(add(screen, (self.gridSize*(-1)*WALL_RADIUS, 0)), add(screen,
+                                                                                   (self.gridSize*(-1)*WALL_RADIUS, self.gridSize*(-0.5)-1)), wallColor)
+                    if (not nIsWall) and (wIsWall):
+                        # horizontal line
+                        line(add(screen, (0, self.gridSize*(-1)*WALL_RADIUS)), add(screen,
+                                                                                   (self.gridSize*(-0.5)-1, self.gridSize*(-1)*WALL_RADIUS)), wallColor)
+                    if (nIsWall) and (wIsWall) and (not nwIsWall):
+                        # outer circle
+                        circle(add(screen2, (self.gridSize*(-2)*WALL_RADIUS, self.gridSize*(-2)*WALL_RADIUS)),
+                               WALL_RADIUS * self.gridSize-1, wallColor, wallColor, (270, 361), 'arc')
+                        line(add(screen, (self.gridSize*(-2)*WALL_RADIUS+1, self.gridSize*(-1)*WALL_RADIUS)),
+                             add(screen, (self.gridSize*(-0.5), self.gridSize*(-1)*WALL_RADIUS)), wallColor)
+                        line(add(screen, (self.gridSize*(-1)*WALL_RADIUS, self.gridSize*(-2)*WALL_RADIUS+1)),
+                             add(screen, (self.gridSize*(-1)*WALL_RADIUS, self.gridSize*(-0.5))), wallColor)
+
+                    # SE quadrant
+                    if (not sIsWall) and (not eIsWall):
+                        # inner circle
+                        circle(screen2, WALL_RADIUS * self.gridSize,
+                               wallColor, wallColor, (270, 361), 'arc')
+                    if (sIsWall) and (not eIsWall):
+                        # vertical line
+                        line(add(screen, (self.gridSize*WALL_RADIUS, 0)), add(screen,
+                                                                              (self.gridSize*WALL_RADIUS, self.gridSize*(0.5)+1)), wallColor)
+                    if (not sIsWall) and (eIsWall):
+                        # horizontal line
+                        line(add(screen, (0, self.gridSize*(1)*WALL_RADIUS)), add(screen,
+                                                                                  (self.gridSize*0.5+1, self.gridSize*(1)*WALL_RADIUS)), wallColor)
+                    if (sIsWall) and (eIsWall) and (not seIsWall):
+                        # outer circle
+                        circle(add(screen2, (self.gridSize*2*WALL_RADIUS, self.gridSize*(2)*WALL_RADIUS)),
+                               WALL_RADIUS * self.gridSize-1, wallColor, wallColor, (90, 181), 'arc')
+                        line(add(screen, (self.gridSize*2*WALL_RADIUS-1, self.gridSize*(1)*WALL_RADIUS)),
+                             add(screen, (self.gridSize*0.5, self.gridSize*(1)*WALL_RADIUS)), wallColor)
+                        line(add(screen, (self.gridSize*WALL_RADIUS, self.gridSize*(2)*WALL_RADIUS-1)),
+                             add(screen, (self.gridSize*WALL_RADIUS, self.gridSize*(0.5))), wallColor)
+
+                    # SW quadrant
+                    if (not sIsWall) and (not wIsWall):
+                        # inner circle
+                        circle(screen2, WALL_RADIUS * self.gridSize,
+                               wallColor, wallColor, (180, 271), 'arc')
+                    if (sIsWall) and (not wIsWall):
+                        # vertical line
+                        line(add(screen, (self.gridSize*(-1)*WALL_RADIUS, 0)), add(screen,
+                                                                                   (self.gridSize*(-1)*WALL_RADIUS, self.gridSize*(0.5)+1)), wallColor)
+                    if (not sIsWall) and (wIsWall):
+                        # horizontal line
+                        line(add(screen, (0, self.gridSize*(1)*WALL_RADIUS)), add(screen,
+                                                                                  (self.gridSize*(-0.5)-1, self.gridSize*(1)*WALL_RADIUS)), wallColor)
+                    if (sIsWall) and (wIsWall) and (not swIsWall):
+                        # outer circle
+                        circle(add(screen2, (self.gridSize*(-2)*WALL_RADIUS, self.gridSize*(2)*WALL_RADIUS)),
+                               WALL_RADIUS * self.gridSize-1, wallColor, wallColor, (0, 91), 'arc')
+                        line(add(screen, (self.gridSize*(-2)*WALL_RADIUS+1, self.gridSize*(1)*WALL_RADIUS)),
+                             add(screen, (self.gridSize*(-0.5), self.gridSize*(1)*WALL_RADIUS)), wallColor)
+                        line(add(screen, (self.gridSize*(-1)*WALL_RADIUS, self.gridSize*(2)*WALL_RADIUS-1)),
+                             add(screen, (self.gridSize*(-1)*WALL_RADIUS, self.gridSize*(0.5))), wallColor)
+
+    def isWall(self, x, y, walls):
+        if x < 0 or y < 0:
+            return False
+        if x >= walls.width or y >= walls.height:
+            return False
+        return walls[x][y]
+
+    def drawFood(self, foodMatrix):
+        foodImages = []
+        color = FOOD_COLOR
+        for xNum, x in enumerate(foodMatrix):
+            if self.capture and (xNum * 2) <= foodMatrix.width:
+                color = TEAM_COLORS[0]
+            if self.capture and (xNum * 2) > foodMatrix.width:
+                color = TEAM_COLORS[1]
+            imageRow = []
+            foodImages.append(imageRow)
+            for yNum, cell in enumerate(x):
+                if cell:  # There's food here
+                    screen = self.to_screen((xNum, yNum))
+                    dot = circle(screen,
+                                 FOOD_SIZE * self.gridSize,
+                                 outlineColor=color, fillColor=color,
+                                 width=1)
+                    imageRow.append(dot)
+                else:
+                    imageRow.append(None)
+        return foodImages
+
+    def drawCapsules(self, capsules):
+        capsuleImages = {}
+        for capsule in capsules:
+            (screen_x, screen_y) = self.to_screen(capsule)
+            dot = circle((screen_x, screen_y),
+                         CAPSULE_SIZE * self.gridSize,
+                         outlineColor=CAPSULE_COLOR,
+                         fillColor=CAPSULE_COLOR,
+                         width=1)
+            capsuleImages[capsule] = dot
+        return capsuleImages
+
+    def removeFood(self, cell, foodImages):
+        x, y = cell
+        remove_from_screen(foodImages[x][y])
+
+    def removeCapsule(self, cell, capsuleImages):
+        x, y = cell
+        remove_from_screen(capsuleImages[(x, y)])
+
+    def drawExpandedCells(self, cells):
+        """
+        Draws an overlay of expanded grid positions for search agents
+        """
+        n = float(len(cells))
+        baseColor = [1.0, 0.0, 0.0]
+        self.clearExpandedCells()
+        self.expandedCells = []
+        for k, cell in enumerate(cells):
+            screenPos = self.to_screen(cell)
+            cellColor = formatColor(
+                *[(n-k) * c * .5 / n + .25 for c in baseColor])
+            block = square(screenPos,
+                           0.5 * self.gridSize,
+                           color=cellColor,
+                           filled=1, behind=2)
+            self.expandedCells.append(block)
+            if self.frameTime < 0:
+                refresh()
+
+    def clearExpandedCells(self):
+        if 'expandedCells' in dir(self) and len(self.expandedCells) > 0:
+            for cell in self.expandedCells:
+                remove_from_screen(cell)
+
+    def updateDistributions(self, distributions):
+        "Draws an agent's belief distributions"
+        # copy all distributions so we don't change their state
+        distributions = [x.copy() for x in distributions]
+        if self.distributionImages == None:
+            self.drawDistributions(self.previousState)
+        for x in range(len(self.distributionImages)):
+            for y in range(len(self.distributionImages[0])):
+                image = self.distributionImages[x][y]
+                weights = [dist[(x, y)] for dist in distributions]
+
+                if sum(weights) != 0:
+                    pass
+                # Fog of war
+                color = [0.0, 0.0, 0.0]
+                colors = GHOST_VEC_COLORS[1:]  # With Pacman
+                if self.capture:
+                    colors = GHOST_VEC_COLORS
+                for weight, gcolor in zip(weights, colors):
+                    color = [min(1.0, c + 0.95 * g * weight ** .3)
+                             for c, g in zip(color, gcolor)]
+                changeColor(image, formatColor(*color))
+        refresh()
+
+
+class FirstPersonPacmanGraphics(PacmanGraphics):
+    def __init__(self, zoom=1.0, showGhosts=True, capture=False, frameTime=0):
+        PacmanGraphics.__init__(self, zoom, frameTime=frameTime)
+        self.showGhosts = showGhosts
+        self.capture = capture
+
+    def initialize(self, state, isBlue=False):
+
+        self.isBlue = isBlue
+        PacmanGraphics.startGraphics(self, state)
+        # Initialize distribution images
+        walls = state.layout.walls
+        dist = []
+        self.layout = state.layout
+
+        # Draw the rest
+        self.distributionImages = None  # initialize lazily
+        self.drawStaticObjects(state)
+        self.drawAgentObjects(state)
+
+        # Information
+        self.previousState = state
+
+    def lookAhead(self, config, state):
+        if config.getDirection() == 'Stop':
+            return
+        else:
+            pass
+            # Draw relevant ghosts
+            allGhosts = state.getGhostStates()
+            visibleGhosts = state.getVisibleGhosts()
+            for i, ghost in enumerate(allGhosts):
+                if ghost in visibleGhosts:
+                    self.drawGhost(ghost, i)
+                else:
+                    self.currentGhostImages[i] = None
+
+    def getGhostColor(self, ghost, ghostIndex):
+        return GHOST_COLORS[ghostIndex]
+
+    def getPosition(self, ghostState):
+        if not self.showGhosts and not ghostState.isPacman and ghostState.getPosition()[1] > 1:
+            return (-1000, -1000)
+        else:
+            return PacmanGraphics.getPosition(self, ghostState)
+
+
+def add(x, y):
+    return (x[0] + y[0], x[1] + y[1])
+
+
+# Saving graphical output
+# -----------------------
+# Note: to make an animated gif from this postscript output, try the command:
+# convert -delay 7 -loop 1 -compress lzw -layers optimize frame* out.gif
+# convert is part of imagemagick (freeware)
+
+SAVE_POSTSCRIPT = False
+POSTSCRIPT_OUTPUT_DIR = 'frames'
+FRAME_NUMBER = 0
+import os
+
+
+def saveFrame():
+    "Saves the current graphical output as a postscript file"
+    global SAVE_POSTSCRIPT, FRAME_NUMBER, POSTSCRIPT_OUTPUT_DIR
+    if not SAVE_POSTSCRIPT:
+        return
+    if not os.path.exists(POSTSCRIPT_OUTPUT_DIR):
+        os.mkdir(POSTSCRIPT_OUTPUT_DIR)
+    name = os.path.join(POSTSCRIPT_OUTPUT_DIR, 'frame_%08d.ps' % FRAME_NUMBER)
+    FRAME_NUMBER += 1
+    writePostscript(name)  # writes the current canvas
diff --git a/HW2_pacman/graphicsUtils.py b/HW2_pacman/graphicsUtils.py
new file mode 100644
index 0000000..66f3cb1
--- /dev/null
+++ b/HW2_pacman/graphicsUtils.py
@@ -0,0 +1,437 @@
+import sys
+import math
+import random
+import string
+import time
+import types
+import tkinter
+import os.path
+
+_Windows = sys.platform == 'win32'  # True if on Win95/98/NT
+
+_root_window = None      # The root window for graphics output
+_canvas = None      # The canvas which holds graphics
+_canvas_xs = None      # Size of canvas object
+_canvas_ys = None
+_canvas_x = None      # Current position on canvas
+_canvas_y = None
+_canvas_col = None      # Current colour (set to black below)
+_canvas_tsize = 12
+_canvas_tserifs = 0
+
+
+def formatColor(r, g, b):
+    return '#%02x%02x%02x' % (int(r * 255), int(g * 255), int(b * 255))
+
+
+def colorToVector(color):
+    return [int(x, 16) / 256.0 for x in [color[1:3], color[3:5], color[5:7]]]
+
+
+if _Windows:
+    _canvas_tfonts = ['times new roman', 'lucida console']
+else:
+    _canvas_tfonts = ['times', 'lucidasans-24']
+    pass  # XXX need defaults here
+
+
+def sleep(secs):
+    global _root_window
+    if _root_window == None:
+        time.sleep(secs)
+    else:
+        _root_window.update_idletasks()
+        _root_window.after(int(1000 * secs), _root_window.quit)
+        _root_window.mainloop()
+
+
+def begin_graphics(width=640, height=480, color=formatColor(0, 0, 0), title=None):
+
+    global _root_window, _canvas, _canvas_x, _canvas_y, _canvas_xs, _canvas_ys, _bg_color
+
+    # Check for duplicate call
+    if _root_window is not None:
+        # Lose the window.
+        _root_window.destroy()
+
+    # Save the canvas size parameters
+    _canvas_xs, _canvas_ys = width - 1, height - 1
+    _canvas_x, _canvas_y = 0, _canvas_ys
+    _bg_color = color
+
+    # Create the root window
+    _root_window = tkinter.Tk()
+    _root_window.protocol('WM_DELETE_WINDOW', _destroy_window)
+    _root_window.title(title or 'Graphics Window')
+    _root_window.resizable(0, 0)
+
+    # Create the canvas object
+    try:
+        _canvas = tkinter.Canvas(_root_window, width=width, height=height)
+        _canvas.pack()
+        draw_background()
+        _canvas.update()
+    except:
+        _root_window = None
+        raise
+
+    # Bind to key-down and key-up events
+    _root_window.bind("", _keypress)
+    _root_window.bind("", _keyrelease)
+    _root_window.bind("", _clear_keys)
+    _root_window.bind("", _clear_keys)
+    _root_window.bind("", _leftclick)
+    _root_window.bind("", _rightclick)
+    _root_window.bind("", _rightclick)
+    _root_window.bind("", _ctrl_leftclick)
+    _clear_keys()
+
+
+_leftclick_loc = None
+_rightclick_loc = None
+_ctrl_leftclick_loc = None
+
+
+def _leftclick(event):
+    global _leftclick_loc
+    _leftclick_loc = (event.x, event.y)
+
+
+def _rightclick(event):
+    global _rightclick_loc
+    _rightclick_loc = (event.x, event.y)
+
+
+def _ctrl_leftclick(event):
+    global _ctrl_leftclick_loc
+    _ctrl_leftclick_loc = (event.x, event.y)
+
+
+def wait_for_click():
+    while True:
+        global _leftclick_loc
+        global _rightclick_loc
+        global _ctrl_leftclick_loc
+        if _leftclick_loc != None:
+            val = _leftclick_loc
+            _leftclick_loc = None
+            return val, 'left'
+        if _rightclick_loc != None:
+            val = _rightclick_loc
+            _rightclick_loc = None
+            return val, 'right'
+        if _ctrl_leftclick_loc != None:
+            val = _ctrl_leftclick_loc
+            _ctrl_leftclick_loc = None
+            return val, 'ctrl_left'
+        sleep(0.05)
+
+
+def draw_background():
+    corners = [(0, 0), (0, _canvas_ys),
+               (_canvas_xs, _canvas_ys), (_canvas_xs, 0)]
+    polygon(corners, _bg_color, fillColor=_bg_color,
+            filled=True, smoothed=False)
+
+
+def _destroy_window(event=None):
+    sys.exit(0)
+#    global _root_window
+#    _root_window.destroy()
+#    _root_window = None
+    # print "DESTROY"
+
+
+def end_graphics():
+    global _root_window, _canvas, _mouse_enabled
+    try:
+        try:
+            sleep(1)
+            if _root_window != None:
+                _root_window.destroy()
+        except SystemExit as e:
+            print('Ending graphics raised an exception:', e)
+    finally:
+        _root_window = None
+        _canvas = None
+        _mouse_enabled = 0
+        _clear_keys()
+
+
+def clear_screen(background=None):
+    global _canvas_x, _canvas_y
+    _canvas.delete('all')
+    draw_background()
+    _canvas_x, _canvas_y = 0, _canvas_ys
+
+
+def polygon(coords, outlineColor, fillColor=None, filled=1, smoothed=1, behind=0, width=1):
+    c = []
+    for coord in coords:
+        c.append(coord[0])
+        c.append(coord[1])
+    if fillColor == None:
+        fillColor = outlineColor
+    if filled == 0:
+        fillColor = ""
+    poly = _canvas.create_polygon(
+        c, outline=outlineColor, fill=fillColor, smooth=smoothed, width=width)
+    if behind > 0:
+        _canvas.tag_lower(poly, behind)  # Higher should be more visible
+    return poly
+
+
+def square(pos, r, color, filled=1, behind=0):
+    x, y = pos
+    coords = [(x - r, y - r), (x + r, y - r), (x + r, y + r), (x - r, y + r)]
+    return polygon(coords, color, color, filled, 0, behind=behind)
+
+
+def circle(pos, r, outlineColor, fillColor, endpoints=None, style='pieslice', width=2):
+    x, y = pos
+    x0, x1 = x - r - 1, x + r
+    y0, y1 = y - r - 1, y + r
+    if endpoints == None:
+        e = [0, 359]
+    else:
+        e = list(endpoints)
+    while e[0] > e[1]:
+        e[1] = e[1] + 360
+
+    return _canvas.create_arc(x0, y0, x1, y1, outline=outlineColor, fill=fillColor,
+                              extent=e[1] - e[0], start=e[0], style=style, width=width)
+
+
+def image(pos, file="../../blueghost.gif"):
+    x, y = pos
+    # img = PhotoImage(file=file)
+    return _canvas.create_image(x, y, image=tkinter.PhotoImage(file=file), anchor=tkinter.NW)
+
+
+def refresh():
+    _canvas.update_idletasks()
+
+
+def moveCircle(id, pos, r, endpoints=None):
+    global _canvas_x, _canvas_y
+
+    x, y = pos
+#    x0, x1 = x - r, x + r + 1
+#    y0, y1 = y - r, y + r + 1
+    x0, x1 = x - r - 1, x + r
+    y0, y1 = y - r - 1, y + r
+    if endpoints == None:
+        e = [0, 359]
+    else:
+        e = list(endpoints)
+    while e[0] > e[1]:
+        e[1] = e[1] + 360
+
+    if os.path.isfile('flag'):
+        edit(id, ('extent', e[1] - e[0]))
+    else:
+        edit(id, ('start', e[0]), ('extent', e[1] - e[0]))
+    move_to(id, x0, y0)
+
+
+def edit(id, *args):
+    _canvas.itemconfigure(id, **dict(args))
+
+
+def text(pos, color, contents, font='Helvetica', size=12, style='normal', anchor="nw"):
+    global _canvas_x, _canvas_y
+    x, y = pos
+    font = (font, str(size), style)
+    return _canvas.create_text(x, y, fill=color, text=contents, font=font, anchor=anchor)
+
+
+def changeText(id, newText, font=None, size=12, style='normal'):
+    _canvas.itemconfigure(id, text=newText)
+    if font != None:
+        _canvas.itemconfigure(id, font=(font, '-%d' % size, style))
+
+
+def changeColor(id, newColor):
+    _canvas.itemconfigure(id, fill=newColor)
+
+
+def line(here, there, color=formatColor(0, 0, 0), width=2):
+    x0, y0 = here[0], here[1]
+    x1, y1 = there[0], there[1]
+    return _canvas.create_line(x0, y0, x1, y1, fill=color, width=width)
+
+##############################################################################
+### Keypress handling ########################################################
+##############################################################################
+
+# We bind to key-down and key-up events.
+
+
+_keysdown = {}
+_keyswaiting = {}
+# This holds an unprocessed key release.  We delay key releases by up to
+# one call to keys_pressed() to get round a problem with auto repeat.
+_got_release = None
+
+
+def _keypress(event):
+    global _got_release
+    # remap_arrows(event)
+    _keysdown[event.keysym] = 1
+    _keyswaiting[event.keysym] = 1
+#    print event.char, event.keycode
+    _got_release = None
+
+
+def _keyrelease(event):
+    global _got_release
+    # remap_arrows(event)
+    try:
+        del _keysdown[event.keysym]
+    except:
+        pass
+    _got_release = 1
+
+
+def remap_arrows(event):
+    # TURN ARROW PRESSES INTO LETTERS (SHOULD BE IN KEYBOARD AGENT)
+    if event.char in ['a', 's', 'd', 'w']:
+        return
+    if event.keycode in [37, 101]:  # LEFT ARROW (win / x)
+        event.char = 'a'
+    if event.keycode in [38, 99]:  # UP ARROW
+        event.char = 'w'
+    if event.keycode in [39, 102]:  # RIGHT ARROW
+        event.char = 'd'
+    if event.keycode in [40, 104]:  # DOWN ARROW
+        event.char = 's'
+
+
+def _clear_keys(event=None):
+    global _keysdown, _got_release, _keyswaiting
+    _keysdown = {}
+    _keyswaiting = {}
+    _got_release = None
+
+
+def keys_pressed(d_o_e=lambda arg: _root_window.dooneevent(arg),
+                 d_w=tkinter._tkinter.DONT_WAIT):
+    d_o_e(d_w)
+    if _got_release:
+        d_o_e(d_w)
+    return list(_keysdown.keys())
+
+
+def keys_waiting():
+    global _keyswaiting
+    keys = list(_keyswaiting.keys())
+    _keyswaiting = {}
+    return keys
+
+# Block for a list of keys...
+
+
+def wait_for_keys():
+    keys = []
+    while keys == []:
+        keys = keys_pressed()
+        sleep(0.05)
+    return keys
+
+
+def remove_from_screen(x,
+                       d_o_e=lambda arg: _root_window.dooneevent(arg),
+                       d_w=tkinter._tkinter.DONT_WAIT):
+    _canvas.delete(x)
+    d_o_e(d_w)
+
+
+def _adjust_coords(coord_list, x, y):
+    for i in range(0, len(coord_list), 2):
+        coord_list[i] = coord_list[i] + x
+        coord_list[i + 1] = coord_list[i + 1] + y
+    return coord_list
+
+
+def move_to(object, x, y=None,
+            d_o_e=lambda arg: _root_window.dooneevent(arg),
+            d_w=tkinter._tkinter.DONT_WAIT):
+    if y is None:
+        try:
+            x, y = x
+        except:
+            raise Exception('incomprehensible coordinates')
+
+    horiz = True
+    newCoords = []
+    current_x, current_y = _canvas.coords(object)[0:2]  # first point
+    for coord in _canvas.coords(object):
+        if horiz:
+            inc = x - current_x
+        else:
+            inc = y - current_y
+        horiz = not horiz
+
+        newCoords.append(coord + inc)
+
+    _canvas.coords(object, *newCoords)
+    d_o_e(d_w)
+
+
+def move_by(object, x, y=None,
+            d_o_e=lambda arg: _root_window.dooneevent(arg),
+            d_w=tkinter._tkinter.DONT_WAIT, lift=False):
+    if y is None:
+        try:
+            x, y = x
+        except:
+            raise Exception('incomprehensible coordinates')
+
+    horiz = True
+    newCoords = []
+    for coord in _canvas.coords(object):
+        if horiz:
+            inc = x
+        else:
+            inc = y
+        horiz = not horiz
+
+        newCoords.append(coord + inc)
+
+    _canvas.coords(object, *newCoords)
+    d_o_e(d_w)
+    if lift:
+        _canvas.tag_raise(object)
+
+
+def writePostscript(filename):
+    "Writes the current canvas to a postscript file."
+    psfile = file(filename, 'w')
+    psfile.write(_canvas.postscript(pageanchor='sw',
+                                    y='0.c',
+                                    x='0.c'))
+    psfile.close()
+
+
+ghost_shape = [
+    (0, - 0.5),
+    (0.25, - 0.75),
+    (0.5, - 0.5),
+    (0.75, - 0.75),
+    (0.75, 0.5),
+    (0.5, 0.75),
+    (- 0.5, 0.75),
+    (- 0.75, 0.5),
+    (- 0.75, - 0.75),
+    (- 0.5, - 0.5),
+    (- 0.25, - 0.75)
+]
+
+if __name__ == '__main__':
+    begin_graphics()
+    clear_screen()
+    ghost_shape = [(x * 10 + 20, y * 10 + 20) for x, y in ghost_shape]
+    g = polygon(ghost_shape, formatColor(1, 1, 1))
+    move_to(g, (50, 50))
+    circle((150, 150), 20, formatColor(0.7, 0.3, 0.0), endpoints=[15, - 15])
+    sleep(2)
diff --git a/HW2_pacman/keyboardAgents.py b/HW2_pacman/keyboardAgents.py
new file mode 100644
index 0000000..0a925f0
--- /dev/null
+++ b/HW2_pacman/keyboardAgents.py
@@ -0,0 +1,81 @@
+from game import Agent
+from game import Directions
+import random
+
+
+class KeyboardAgent(Agent):
+    """
+    An agent controlled by the keyboard.
+    """
+    # NOTE: Arrow keys also work.
+    WEST_KEY = 'a'
+    EAST_KEY = 'd'
+    NORTH_KEY = 'w'
+    SOUTH_KEY = 's'
+    STOP_KEY = 'q'
+
+    def __init__(self, index=0):
+
+        self.lastMove = Directions.STOP
+        self.index = index
+        self.keys = []
+
+    def getAction(self, state):
+        from graphicsUtils import keys_waiting
+        from graphicsUtils import keys_pressed
+        keys = keys_waiting() + keys_pressed()
+        if keys != []:
+            self.keys = keys
+
+        legal = state.getLegalActions(self.index)
+        move = self.getMove(legal)
+
+        if move == Directions.STOP:
+            # Try to move in the same direction as before
+            if self.lastMove in legal:
+                move = self.lastMove
+
+        if (self.STOP_KEY in self.keys) and Directions.STOP in legal:
+            move = Directions.STOP
+
+        if move not in legal:
+            move = random.choice(legal)
+
+        self.lastMove = move
+        return move
+
+    def getMove(self, legal):
+        move = Directions.STOP
+        if (self.WEST_KEY in self.keys or 'Left' in self.keys) and Directions.WEST in legal:
+            move = Directions.WEST
+        if (self.EAST_KEY in self.keys or 'Right' in self.keys) and Directions.EAST in legal:
+            move = Directions.EAST
+        if (self.NORTH_KEY in self.keys or 'Up' in self.keys) and Directions.NORTH in legal:
+            move = Directions.NORTH
+        if (self.SOUTH_KEY in self.keys or 'Down' in self.keys) and Directions.SOUTH in legal:
+            move = Directions.SOUTH
+        return move
+
+
+class KeyboardAgent2(KeyboardAgent):
+    """
+    A second agent controlled by the keyboard.
+    """
+    # NOTE: Arrow keys also work.
+    WEST_KEY = 'j'
+    EAST_KEY = "l"
+    NORTH_KEY = 'i'
+    SOUTH_KEY = 'k'
+    STOP_KEY = 'u'
+
+    def getMove(self, legal):
+        move = Directions.STOP
+        if (self.WEST_KEY in self.keys) and Directions.WEST in legal:
+            move = Directions.WEST
+        if (self.EAST_KEY in self.keys) and Directions.EAST in legal:
+            move = Directions.EAST
+        if (self.NORTH_KEY in self.keys) and Directions.NORTH in legal:
+            move = Directions.NORTH
+        if (self.SOUTH_KEY in self.keys) and Directions.SOUTH in legal:
+            move = Directions.SOUTH
+        return move
diff --git a/HW2_pacman/layout.py b/HW2_pacman/layout.py
new file mode 100644
index 0000000..811ff1a
--- /dev/null
+++ b/HW2_pacman/layout.py
@@ -0,0 +1,150 @@
+from util import manhattanDistance
+from game import Grid
+import os
+import random
+from functools import reduce
+
+VISIBILITY_MATRIX_CACHE = {}
+
+
+class Layout:
+    """
+    A Layout manages the static information about the game board.
+    """
+
+    def __init__(self, layoutText):
+        self.width = len(layoutText[0])
+        self.height = len(layoutText)
+        self.walls = Grid(self.width, self.height, False)
+        self.food = Grid(self.width, self.height, False)
+        self.capsules = []
+        self.agentPositions = []
+        self.numGhosts = 0
+        self.processLayoutText(layoutText)
+        self.layoutText = layoutText
+        self.totalFood = len(self.food.asList())
+        # self.initializeVisibilityMatrix()
+
+    def getNumGhosts(self):
+        return self.numGhosts
+
+    def initializeVisibilityMatrix(self):
+        global VISIBILITY_MATRIX_CACHE
+        if reduce(str.__add__, self.layoutText) not in VISIBILITY_MATRIX_CACHE:
+            from game import Directions
+            vecs = [(-0.5, 0), (0.5, 0), (0, -0.5), (0, 0.5)]
+            dirs = [Directions.NORTH, Directions.SOUTH,
+                    Directions.WEST, Directions.EAST]
+            vis = Grid(self.width, self.height, {Directions.NORTH: set(), Directions.SOUTH: set(
+            ), Directions.EAST: set(), Directions.WEST: set(), Directions.STOP: set()})
+            for x in range(self.width):
+                for y in range(self.height):
+                    if self.walls[x][y] == False:
+                        for vec, direction in zip(vecs, dirs):
+                            dx, dy = vec
+                            nextx, nexty = x + dx, y + dy
+                            while (nextx + nexty) != int(nextx) + int(nexty) or not self.walls[int(nextx)][int(nexty)]:
+                                vis[x][y][direction].add((nextx, nexty))
+                                nextx, nexty = x + dx, y + dy
+            self.visibility = vis
+            VISIBILITY_MATRIX_CACHE[reduce(str.__add__, self.layoutText)] = vis
+        else:
+            self.visibility = VISIBILITY_MATRIX_CACHE[reduce(
+                str.__add__, self.layoutText)]
+
+    def isWall(self, pos):
+        x, col = pos
+        return self.walls[x][col]
+
+    def getRandomLegalPosition(self):
+        x = random.choice(list(range(self.width)))
+        y = random.choice(list(range(self.height)))
+        while self.isWall((x, y)):
+            x = random.choice(list(range(self.width)))
+            y = random.choice(list(range(self.height)))
+        return (x, y)
+
+    def getRandomCorner(self):
+        poses = [(1, 1), (1, self.height - 2), (self.width - 2, 1),
+                 (self.width - 2, self.height - 2)]
+        return random.choice(poses)
+
+    def getFurthestCorner(self, pacPos):
+        poses = [(1, 1), (1, self.height - 2), (self.width - 2, 1),
+                 (self.width - 2, self.height - 2)]
+        dist, pos = max([(manhattanDistance(p, pacPos), p) for p in poses])
+        return pos
+
+    def isVisibleFrom(self, ghostPos, pacPos, pacDirection):
+        row, col = [int(x) for x in pacPos]
+        return ghostPos in self.visibility[row][col][pacDirection]
+
+    def __str__(self):
+        return "\n".join(self.layoutText)
+
+    def deepCopy(self):
+        return Layout(self.layoutText[:])
+
+    def processLayoutText(self, layoutText):
+        """
+        Coordinates are flipped from the input format to the (x,y) convention here
+
+        The shape of the maze.  Each character
+        represents a different type of object.
+         % - Wall
+         . - Food
+         o - Capsule
+         G - Ghost
+         P - Pacman
+        Other characters are ignored.
+        """
+        maxY = self.height - 1
+        for y in range(self.height):
+            for x in range(self.width):
+                layoutChar = layoutText[maxY - y][x]
+                self.processLayoutChar(x, y, layoutChar)
+        self.agentPositions.sort()
+        self.agentPositions = [(i == 0, pos) for i, pos in self.agentPositions]
+
+    def processLayoutChar(self, x, y, layoutChar):
+        if layoutChar == '%':
+            self.walls[x][y] = True
+        elif layoutChar == '.':
+            self.food[x][y] = True
+        elif layoutChar == 'o':
+            self.capsules.append((x, y))
+        elif layoutChar == 'P':
+            self.agentPositions.append((0, (x, y)))
+        elif layoutChar in ['G']:
+            self.agentPositions.append((1, (x, y)))
+            self.numGhosts += 1
+        elif layoutChar in ['1', '2', '3', '4']:
+            self.agentPositions.append((int(layoutChar), (x, y)))
+            self.numGhosts += 1
+
+
+def getLayout(name, back=2):
+    if name.endswith('.lay'):
+        layout = tryToLoad('layouts/' + name)
+        if layout == None:
+            layout = tryToLoad(name)
+    else:
+        layout = tryToLoad('layouts/' + name + '.lay')
+        if layout == None:
+            layout = tryToLoad(name + '.lay')
+    if layout == None and back >= 0:
+        curdir = os.path.abspath('.')
+        os.chdir('..')
+        layout = getLayout(name, back - 1)
+        os.chdir(curdir)
+    return layout
+
+
+def tryToLoad(fullname):
+    if(not os.path.exists(fullname)):
+        return None
+    f = open(fullname)
+    try:
+        return Layout([line.strip() for line in f])
+    finally:
+        f.close()
diff --git a/HW2_pacman/layouts/capsuleClassic.lay b/HW2_pacman/layouts/capsuleClassic.lay
new file mode 100644
index 0000000..06a5c51
--- /dev/null
+++ b/HW2_pacman/layouts/capsuleClassic.lay
@@ -0,0 +1,7 @@
+%%%%%%%%%%%%%%%%%%%
+%G.       G   ....%
+%.% % %%%%%% %.%%.%
+%.%o% %   o% %.o%.%
+%.%%%.%  %%% %..%.%
+%.....  P    %..%G%
+%%%%%%%%%%%%%%%%%%%%
diff --git a/HW2_pacman/layouts/contestClassic.lay b/HW2_pacman/layouts/contestClassic.lay
new file mode 100644
index 0000000..84c8733
--- /dev/null
+++ b/HW2_pacman/layouts/contestClassic.lay
@@ -0,0 +1,9 @@
+%%%%%%%%%%%%%%%%%%%%
+%o...%........%...o%
+%.%%.%.%%..%%.%.%%.%
+%...... G GG%......%
+%.%.%%.%% %%%.%%.%.%
+%.%....% ooo%.%..%.%
+%.%.%%.% %% %.%.%%.%
+%o%......P....%....%
+%%%%%%%%%%%%%%%%%%%%
diff --git a/HW2_pacman/layouts/mediumClassic.lay b/HW2_pacman/layouts/mediumClassic.lay
new file mode 100644
index 0000000..33c5db8
--- /dev/null
+++ b/HW2_pacman/layouts/mediumClassic.lay
@@ -0,0 +1,11 @@
+%%%%%%%%%%%%%%%%%%%%
+%o...%........%....%
+%.%%.%.%%%%%%.%.%%.%
+%.%..............%.%
+%.%.%%.%%  %%.%%.%.%
+%......%G  G%......%
+%.%.%%.%%%%%%.%%.%.%
+%.%..............%.%
+%.%%.%.%%%%%%.%.%%.%
+%....%...P....%...o%
+%%%%%%%%%%%%%%%%%%%%
diff --git a/HW2_pacman/layouts/minimaxClassic.lay b/HW2_pacman/layouts/minimaxClassic.lay
new file mode 100644
index 0000000..a547397
--- /dev/null
+++ b/HW2_pacman/layouts/minimaxClassic.lay
@@ -0,0 +1,5 @@
+%%%%%%%%%
+%.P    G% 
+% %.%G%%%  
+%G    %%% 
+%%%%%%%%%
diff --git a/HW2_pacman/layouts/openClassic.lay b/HW2_pacman/layouts/openClassic.lay
new file mode 100644
index 0000000..6760b42
--- /dev/null
+++ b/HW2_pacman/layouts/openClassic.lay
@@ -0,0 +1,9 @@
+%%%%%%%%%%%%%%%%%%%%%%%%%
+%.. P  ....      ....   %
+%..  ...  ...  ...  ... %
+%..  ...  ...  ...  ... %
+%..    ....      .... G %
+%..  ...  ...  ...  ... %
+%..  ...  ...  ...  ... %
+%..    ....      ....  o%
+%%%%%%%%%%%%%%%%%%%%%%%%%
diff --git a/HW2_pacman/layouts/originalClassic.lay b/HW2_pacman/layouts/originalClassic.lay
new file mode 100644
index 0000000..b2770c5
--- /dev/null
+++ b/HW2_pacman/layouts/originalClassic.lay
@@ -0,0 +1,27 @@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%............%%............%
+%.%%%%.%%%%%.%%.%%%%%.%%%%.%
+%o%%%%.%%%%%.%%.%%%%%.%%%%o%
+%.%%%%.%%%%%.%%.%%%%%.%%%%.%
+%..........................%
+%.%%%%.%%.%%%%%%%%.%%.%%%%.%
+%.%%%%.%%.%%%%%%%%.%%.%%%%.%
+%......%%....%%....%%......%
+%%%%%%.%%%%% %% %%%%%.%%%%%%
+%%%%%%.%%%%% %% %%%%%.%%%%%%
+%%%%%%.%            %.%%%%%%
+%%%%%%.% %%%%  %%%% %.%%%%%%
+%     .  %G  GG  G%  .     %
+%%%%%%.% %%%%%%%%%% %.%%%%%%
+%%%%%%.%            %.%%%%%%
+%%%%%%.% %%%%%%%%%% %.%%%%%%
+%............%%............%
+%.%%%%.%%%%%.%%.%%%%%.%%%%.%
+%.%%%%.%%%%%.%%.%%%%%.%%%%.%
+%o..%%.......  .......%%..o%
+%%%.%%.%%.%%%%%%%%.%%.%%.%%%
+%%%.%%.%%.%%%%%%%%.%%.%%.%%%
+%......%%....%%....%%......%
+%.%%%%%%%%%%.%%.%%%%%%%%%%.%
+%.............P............%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%
diff --git a/HW2_pacman/layouts/powerClassic.lay b/HW2_pacman/layouts/powerClassic.lay
new file mode 100644
index 0000000..3f3d983
--- /dev/null
+++ b/HW2_pacman/layouts/powerClassic.lay
@@ -0,0 +1,7 @@
+%%%%%%%%%%%%%%%%%%%%
+%o....o%GGGG%o....o%
+%..%...%%  %%...%..%
+%.%o.%........%.o%.%
+%.o%.%.%%%%%%.%.%o.%
+%........P.........%
+%%%%%%%%%%%%%%%%%%%%
diff --git a/HW2_pacman/layouts/smallClassic.lay b/HW2_pacman/layouts/smallClassic.lay
new file mode 100644
index 0000000..ce6c1d9
--- /dev/null
+++ b/HW2_pacman/layouts/smallClassic.lay
@@ -0,0 +1,7 @@
+%%%%%%%%%%%%%%%%%%%%
+%......%G  G%......%
+%.%%...%%  %%...%%.%
+%.%o.%........%.o%.%
+%.%%.%.%%%%%%.%.%%.%
+%........P.........%
+%%%%%%%%%%%%%%%%%%%%
diff --git a/HW2_pacman/layouts/testClassic.lay b/HW2_pacman/layouts/testClassic.lay
new file mode 100644
index 0000000..4b3ffca
--- /dev/null
+++ b/HW2_pacman/layouts/testClassic.lay
@@ -0,0 +1,10 @@
+%%%%%
+% . %
+%.G.%
+% . %
+%. .%
+%   %
+%  .%
+%   %
+%P .%
+%%%%%
diff --git a/HW2_pacman/layouts/trappedClassic.lay b/HW2_pacman/layouts/trappedClassic.lay
new file mode 100644
index 0000000..289557f
--- /dev/null
+++ b/HW2_pacman/layouts/trappedClassic.lay
@@ -0,0 +1,5 @@
+%%%%%%%%
+%   P G%
+%G%%%%%%
+%....  %
+%%%%%%%%
diff --git a/HW2_pacman/layouts/trickyClassic.lay b/HW2_pacman/layouts/trickyClassic.lay
new file mode 100644
index 0000000..ffa156c
--- /dev/null
+++ b/HW2_pacman/layouts/trickyClassic.lay
@@ -0,0 +1,13 @@
+%%%%%%%%%%%%%%%%%%%%
+%o...%........%...o%
+%.%%.%.%%..%%.%.%%.%
+%.%.....%..%.....%.%
+%.%.%%.%%  %%.%%.%.%
+%...... GGGG%.%....%
+%.%....%%%%%%.%..%.%
+%.%....%  oo%.%..%.%
+%.%....% %%%%.%..%.%
+%.%...........%..%.%
+%.%%.%.%%%%%%.%.%%.%
+%o...%...P....%...o%
+%%%%%%%%%%%%%%%%%%%%
diff --git a/HW2_pacman/multiAgents.py b/HW2_pacman/multiAgents.py
new file mode 100644
index 0000000..d3e78db
--- /dev/null
+++ b/HW2_pacman/multiAgents.py
@@ -0,0 +1,271 @@
+from util import manhattanDistance
+from game import Directions
+import random, util
+from game import Agent
+
+class ReflexAgent(Agent):
+    """
+    A reflex agent chooses an action at each choice point by examining
+    its alternatives via a state evaluation function.
+
+    The code below is provided as a guide.  You are welcome to change
+    it in any way you see fit, so long as you don't touch our method
+    headers.
+    """
+
+    def getAction(self, gameState):
+        """
+        You do not need to change this method, but you're welcome to.
+
+        getAction chooses among the best options according to the evaluation function.
+
+        Just like in the previous project, getAction takes a GameState and returns
+        some Directions.X for some X in the set {NORTH, SOUTH, WEST, EAST, STOP}
+        """
+        # Collect legal moves and child states
+        legalMoves = gameState.getLegalActions()
+
+        # Choose one of the best actions
+        scores = [self.evaluationFunction(gameState, action) for action in legalMoves]
+        bestScore = max(scores)
+        bestIndices = [index for index in range(len(scores)) if scores[index] == bestScore]
+        chosenIndex = random.choice(bestIndices) # Pick randomly among the best
+
+        return legalMoves[chosenIndex]
+
+    def evaluationFunction(self, currentGameState, action):
+        """
+        The evaluation function takes in the current and proposed child
+        GameStates (pacman.py) and returns a number, where higher numbers are better.
+
+        The code below extracts some useful information from the state, like the
+        remaining food (newFood) and Pacman position after moving (newPos).
+        newScaredTimes holds the number of moves that each ghost will remain
+        scared because of Pacman having eaten a power pellet.
+        """
+        # Useful information you can extract from a GameState (pacman.py)
+        childGameState = currentGameState.getPacmanNextState(action)
+        newPos = childGameState.getPacmanPosition()
+        newFood = childGameState.getFood()
+        newGhostStates = childGameState.getGhostStates()
+        newScaredTimes = [ghostState.scaredTimer for ghostState in newGhostStates]
+
+        minGhostDistance = min([manhattanDistance(newPos, state.getPosition()) for state in newGhostStates])
+
+        scoreDiff = childGameState.getScore() - currentGameState.getScore()
+
+        pos = currentGameState.getPacmanPosition()
+        nearestFoodDistance = min([manhattanDistance(pos, food) for food in currentGameState.getFood().asList()])
+        newFoodsDistances = [manhattanDistance(newPos, food) for food in newFood.asList()]
+        newNearestFoodDistance = 0 if not newFoodsDistances else min(newFoodsDistances)
+        isFoodNearer = nearestFoodDistance - newNearestFoodDistance
+
+        direction = currentGameState.getPacmanState().getDirection()
+        if minGhostDistance <= 1 or action == Directions.STOP:
+            return 0
+        if scoreDiff > 0:
+            return 8
+        elif isFoodNearer > 0:
+            return 4
+        elif action == direction:
+            return 2
+        else:
+            return 1
+
+
+def scoreEvaluationFunction(currentGameState):
+    """
+    This default evaluation function just returns the score of the state.
+    The score is the same one displayed in the Pacman GUI.
+
+    This evaluation function is meant for use with adversarial search agents
+    (not reflex agents).
+    """
+    return currentGameState.getScore()
+
+
+class MultiAgentSearchAgent(Agent):
+    """
+    This class provides some common elements to all of your
+    multi-agent searchers.  Any methods defined here will be available
+    to the MinimaxPacmanAgent, AlphaBetaPacmanAgent & ExpectimaxPacmanAgent.
+
+    You *do not* need to make any changes here, but you can if you want to
+    add functionality to all your adversarial search agents.  Please do not
+    remove anything, however.
+
+    Note: this is an abstract class: one that should not be instantiated.  It's
+    only partially specified, and designed to be extended.  Agent (game.py)
+    is another abstract class.
+    """
+
+    def __init__(self, evalFn = 'scoreEvaluationFunction', depth = '2'):
+        self.index = 0 # Pacman is always agent index 0
+        self.evaluationFunction = util.lookup(evalFn, globals())
+        self.depth = int(depth)
+
+
+class MinimaxAgent(MultiAgentSearchAgent):
+    """
+    Your minimax agent (Part 1)
+    """
+
+    def getAction(self, gameState):
+        """
+        Returns the minimax action from the current gameState using self.depth
+        and self.evaluationFunction.
+
+        Here are some method calls that might be useful when implementing minimax.
+
+        gameState.getLegalActions(agentIndex):
+        Returns a list of legal actions for an agent
+        agentIndex=0 means Pacman, ghosts are >= 1
+
+        gameState.getNextState(agentIndex, action):
+        Returns the child game state after an agent takes an action
+
+        gameState.getNumAgents():
+        Returns the total number of agents in the game
+
+        gameState.isWin():
+        Returns whether or not the game state is a winning state
+
+        gameState.isLose():
+        Returns whether or not the game state is a losing state
+        """
+        # Begin your code (Part 1)
+        def minimax(s, d, agent):
+            if s.isWin() or s.isLose() or d == 0:
+                return self.evaluationFunction(s), None
+
+            nxt = (agent + 1) % s.getNumAgents()
+            d2 = d - 1 if nxt == 0 else d
+            actions = s.getLegalActions(agent)
+
+            if agent == 0:
+                best = (float('-inf'), None)
+                for a in actions:
+                    v = minimax(s.getNextState(agent, a), d2, nxt)[0]
+                    if v > best[0]:
+                        best = (v, a)
+                return best
+            else:
+                best = (float('inf'), None)
+                for a in actions:
+                    v = minimax(s.getNextState(agent, a), d2, nxt)[0]
+                    if v < best[0]:
+                        best = (v, a)
+                return best
+
+        return minimax(gameState, self.depth, 0)[1]
+        # End your code (Part 1)
+
+
+class AlphaBetaAgent(MultiAgentSearchAgent):
+    """
+    Your minimax agent with alpha-beta pruning (Part 2)
+    """
+
+    def getAction(self, gameState):
+        """
+        Returns the minimax action using self.depth and self.evaluationFunction
+        """
+        # Begin your code (Part 2)
+        def ab(s, d, agent, a, b):
+            if s.isWin() or s.isLose() or d == 0:
+                return self.evaluationFunction(s), None
+
+            nxt = (agent + 1) % s.getNumAgents()
+            d2 = d - 1 if nxt == 0 else d
+            actions = s.getLegalActions(agent)
+
+            if agent == 0:
+                best = (float('-inf'), None)
+                for act in actions:
+                    v = ab(s.getNextState(agent, act), d2, nxt, a, b)[0]
+                    if v > best[0]:
+                        best = (v, act)
+                    if best[0] > b:
+                        return best
+                    a = max(a, best[0])
+                return best
+            else:
+                best = (float('inf'), None)
+                for act in actions:
+                    v = ab(s.getNextState(agent, act), d2, nxt, a, b)[0]
+                    if v < best[0]:
+                        best = (v, act)
+                    if best[0] < a:
+                        return best
+                    b = min(b, best[0])
+                return best
+
+        return ab(gameState, self.depth, 0, float('-inf'), float('inf'))[1]
+        # End your code (Part 2)
+
+
+class ExpectimaxAgent(MultiAgentSearchAgent):
+    """
+      Your expectimax agent (Part 3)
+    """
+
+    def getAction(self, gameState):
+        """
+        Returns the expectimax action using self.depth and self.evaluationFunction
+
+        All ghosts should be modeled as choosing uniformly at random from their
+        legal moves.
+        """
+        # Begin your code (Part 3)
+        def expmax(s, d, agent):
+            if s.isWin() or s.isLose() or d == 0:
+                return self.evaluationFunction(s), None
+
+            nxt = (agent + 1) % s.getNumAgents()
+            d2 = d - 1 if nxt == 0 else d
+            actions = s.getLegalActions(agent)
+
+            if agent == 0:
+                best = (float('-inf'), None)
+                for a in actions:
+                    v = expmax(s.getNextState(agent, a), d2, nxt)[0]
+                    if v > best[0]:
+                        best = (v, a)
+                return best
+            else:
+                vals = [expmax(s.getNextState(agent, a), d2, nxt)[0] for a in actions]
+                return sum(vals) / len(vals), None
+
+        return expmax(gameState, self.depth, 0)[1]
+        # End your code (Part 3)
+
+
+def betterEvaluationFunction(currentGameState):
+    """
+    Your extreme ghost-hunting, pellet-nabbing, food-gobbling, unstoppable
+    evaluation function (Part 4).
+    """
+    # Begin your code (Part 4)
+    pos = currentGameState.getPacmanPosition()
+    foodList = currentGameState.getFood().asList()
+    ghosts = currentGameState.getGhostStates()
+
+    score = currentGameState.getScore()
+    score -= 10 * len(foodList)
+    score -= 20 * len(currentGameState.getCapsules())
+
+    if foodList:
+        score += 1.0 / min(manhattanDistance(pos, f) for f in foodList)
+
+    for g in ghosts:
+        d = manhattanDistance(pos, g.getPosition())
+        if g.scaredTimer > 0:
+            score += 200 / (d + 1)
+        else:
+            score -= 10000 / (10 ** d)
+
+    return score
+    # End your code (Part 4)
+
+# Abbreviation
+better = betterEvaluationFunction
diff --git a/HW2_pacman/multiagentTestClasses.py b/HW2_pacman/multiagentTestClasses.py
new file mode 100644
index 0000000..9854e90
--- /dev/null
+++ b/HW2_pacman/multiagentTestClasses.py
@@ -0,0 +1,563 @@
+# A minimax tree which interfaces like gameState
+#     state.getNumAgents()
+#     state.isWin()
+#     state.isLose()
+#     state.getNextState(agentIndex, action)
+#     state.getScore()
+#           used by multiAgents.scoreEvaluationFunction, which is the default
+#
+import testClasses
+import json
+
+from collections import defaultdict
+from pprint import PrettyPrinter
+pp = PrettyPrinter()
+
+from game import Agent
+from pacman import GameState
+from ghostAgents import RandomGhost, DirectionalGhost
+import random
+import math
+import traceback
+import sys
+import os
+import layout
+import pacman
+import autograder
+
+VERBOSE = False
+
+
+class MultiagentTreeState(object):
+    def __init__(self, problem, state):
+        self.problem = problem
+        self.state = state
+
+    def getNextState(self, agentIndex, action):
+        if VERBOSE:
+            print("getNextState(%s, %s, %s) -> %s" % (self.state, agentIndex,
+                                                           action, self.problem.stateToChildMap[self.state][action]))
+        child = self.problem.stateToChildMap[self.state][action]
+        self.problem.generatedStates.add(child)
+        return MultiagentTreeState(self.problem, child)
+
+    def getScore(self):
+        if VERBOSE:
+            print("getScore(%s) -> %s" %
+                  (self.state, self.problem.evaluation[self.state]))
+        if self.state not in self.problem.evaluation:
+            raise Exception(
+                'getScore() called on non-terminal state or before maximum depth achieved.')
+        return float(self.problem.evaluation[self.state])
+
+    def getLegalActions(self, agentIndex=0):
+        if VERBOSE:
+            print("getLegalActions(%s) -> %s" %
+                  (self.state, self.problem.stateToActions[self.state]))
+        # if len(self.problem.stateToActions[self.state]) == 0:
+        #    print "WARNING: getLegalActions called on leaf state %s" % (self.state,)
+        return list(self.problem.stateToActions[self.state])
+
+    def isWin(self):
+        if VERBOSE:
+            print("isWin(%s) -> %s" %
+                  (self.state, self.state in self.problem.winStates))
+        return self.state in self.problem.winStates
+
+    def isLose(self):
+        if VERBOSE:
+            print("isLose(%s) -> %s" %
+                  (self.state, self.state in self.problem.loseStates))
+        return self.state in self.problem.loseStates
+
+    def getNumAgents(self):
+        if VERBOSE:
+            print("getNumAgents(%s) -> %s" %
+                  (self.state, self.problem.numAgents))
+        return self.problem.numAgents
+
+
+class MultiagentTreeProblem(object):
+    def __init__(self, numAgents, startState, winStates, loseStates, children, evaluation):
+        self.startState = MultiagentTreeState(self, startState)
+
+        self.numAgents = numAgents
+        self.winStates = winStates
+        self.loseStates = loseStates
+        self.evaluation = evaluation
+        self.children = children
+
+        self.reset()
+
+        self.stateToChildMap = defaultdict(dict)
+        self.stateToActions = defaultdict(list)
+        for state, action, nextState in children:
+            self.stateToActions[state].append(action)
+            self.stateToChildMap[state][action] = nextState
+
+    def reset(self):
+        self.generatedStates = set([self.startState.state])
+
+
+def parseTreeProblem(testDict):
+    numAgents = int(testDict["num_agents"])
+    startState = testDict["start_state"]
+    winStates = set(testDict["win_states"].split(" "))
+    loseStates = set(testDict["lose_states"].split(" "))
+    children = []
+
+    evaluation = {}
+    for line in testDict["evaluation"].split('\n'):
+        tokens = line.split()
+        if len(tokens) == 2:
+            state, value = tokens
+            evaluation[state] = float(value)
+        else:
+            raise Exception("[parseTree] Bad evaluation line: |%s|" % (line,))
+
+    for line in testDict["children"].split('\n'):
+        tokens = line.split()
+        if len(tokens) == 3:
+            state, action, nextState = tokens
+            children.append((state, action, nextState))
+        else:
+            raise Exception("[parseTree] Bad children line: |%s|" % (line,))
+
+    return MultiagentTreeProblem(numAgents, startState, winStates, loseStates, children, evaluation)
+
+
+def run(lay, layName, pac, ghosts, disp, nGames=1, name='games'):
+    """
+    Runs a few games and outputs their statistics.
+    """
+    starttime = time.time()
+    print('*** Running %s on' % name, layName, '%d time(s).' % nGames)
+    games = pacman.runGames(lay, pac, ghosts, disp,
+                            nGames, False, catchExceptions=True, timeout=120)
+    print('*** Finished running %s on' % name, layName,
+          'after %d seconds.' % (time.time() - starttime))
+    stats = {'time': time.time() - starttime, 'wins': [g.state.isWin() for g in games].count(True), 'games': games, 'scores': [g.state.getScore() for g in games],
+             'timeouts': [g.agentTimeout for g in games].count(True), 'crashes': [g.agentCrashed for g in games].count(True)}
+    print('*** Won %d out of %d games. Average score: %f ***' %
+          (stats['wins'], len(games), sum(stats['scores']) * 1.0 / len(games)))
+    return stats
+
+
+class GradingAgent(Agent):
+    def __init__(self, seed, studentAgent, optimalActions, altDepthActions, partialPlyBugActions):
+        # save student agent and actions of refernce agents
+        self.studentAgent = studentAgent
+        self.optimalActions = optimalActions
+        self.altDepthActions = altDepthActions
+        self.partialPlyBugActions = partialPlyBugActions
+        # create fields for storing specific wrong actions
+        self.suboptimalMoves = []
+        self.wrongStatesExplored = -1
+        # boolean vectors represent types of implementation the student could have
+        self.actionsConsistentWithOptimal = [
+            True for i in range(len(optimalActions[0]))]
+        self.actionsConsistentWithAlternativeDepth = [
+            True for i in range(len(altDepthActions[0]))]
+        self.actionsConsistentWithPartialPlyBug = [
+            True for i in range(len(partialPlyBugActions[0]))]
+        # keep track of elapsed moves
+        self.stepCount = 0
+        self.seed = seed
+
+    def registerInitialState(self, state):
+        if 'registerInitialState' in dir(self.studentAgent):
+            self.studentAgent.registerInitialState(state)
+        random.seed(self.seed)
+
+    def getAction(self, state):
+        GameState.getAndResetExplored()
+        studentAction = (self.studentAgent.getAction(state),
+                         len(GameState.getAndResetExplored()))
+        optimalActions = self.optimalActions[self.stepCount]
+        altDepthActions = self.altDepthActions[self.stepCount]
+        partialPlyBugActions = self.partialPlyBugActions[self.stepCount]
+        studentOptimalAction = False
+        curRightStatesExplored = False
+        for i in range(len(optimalActions)):
+            if studentAction[0] in optimalActions[i][0]:
+                studentOptimalAction = True
+            else:
+                self.actionsConsistentWithOptimal[i] = False
+            if studentAction[1] == int(optimalActions[i][1]):
+                curRightStatesExplored = True
+        if not curRightStatesExplored and self.wrongStatesExplored < 0:
+            self.wrongStatesExplored = 1
+        for i in range(len(altDepthActions)):
+            if studentAction[0] not in altDepthActions[i]:
+                self.actionsConsistentWithAlternativeDepth[i] = False
+        for i in range(len(partialPlyBugActions)):
+            if studentAction[0] not in partialPlyBugActions[i]:
+                self.actionsConsistentWithPartialPlyBug[i] = False
+        if not studentOptimalAction:
+            self.suboptimalMoves.append(
+                (state, studentAction[0], optimalActions[0][0][0]))
+        self.stepCount += 1
+        random.seed(self.seed + self.stepCount)
+        return optimalActions[0][0][0]
+
+    def getSuboptimalMoves(self):
+        return self.suboptimalMoves
+
+    def getWrongStatesExplored(self):
+        return self.wrongStatesExplored
+
+    def checkFailure(self):
+        """
+        Return +n if have n suboptimal moves.
+        Return -1 if have only off by one depth moves.
+        Return 0 otherwise.
+        """
+        if self.wrongStatesExplored > 0:
+            return -3
+        if self.actionsConsistentWithOptimal.count(True) > 0:
+            return 0
+        elif self.actionsConsistentWithPartialPlyBug.count(True) > 0:
+            return -2
+        elif self.actionsConsistentWithAlternativeDepth.count(True) > 0:
+            return -1
+        else:
+            return len(self.suboptimalMoves)
+
+
+class PolyAgent(Agent):
+    def __init__(self, seed, multiAgents, ourPacOptions, depth):
+        # prepare our pacman agents
+        solutionAgents, alternativeDepthAgents, partialPlyBugAgents = self.construct_our_pacs(
+            multiAgents, ourPacOptions)
+        for p in solutionAgents:
+            p.depth = depth
+        for p in partialPlyBugAgents:
+            p.depth = depth
+        for p in alternativeDepthAgents[:2]:
+            p.depth = max(1, depth - 1)
+        for p in alternativeDepthAgents[2:]:
+            p.depth = depth + 1
+        self.solutionAgents = solutionAgents
+        self.alternativeDepthAgents = alternativeDepthAgents
+        self.partialPlyBugAgents = partialPlyBugAgents
+        # prepare fields for storing the results
+        self.optimalActionLists = []
+        self.alternativeDepthLists = []
+        self.partialPlyBugLists = []
+        self.seed = seed
+        self.stepCount = 0
+
+    def select(self, list, indices):
+        """
+        Return a sublist of elements given by indices in list.
+        """
+        return [list[i] for i in indices]
+
+    def construct_our_pacs(self, multiAgents, keyword_dict):
+        pacs_without_stop = [multiAgents.StaffMultiAgentSearchAgent(
+            **keyword_dict) for i in range(3)]
+        keyword_dict['keepStop'] = 'True'
+        pacs_with_stop = [multiAgents.StaffMultiAgentSearchAgent(
+            **keyword_dict) for i in range(3)]
+        keyword_dict['usePartialPlyBug'] = 'True'
+        partial_ply_bug_pacs = [
+            multiAgents.StaffMultiAgentSearchAgent(**keyword_dict)]
+        keyword_dict['keepStop'] = 'False'
+        partial_ply_bug_pacs = partial_ply_bug_pacs + \
+            [multiAgents.StaffMultiAgentSearchAgent(**keyword_dict)]
+        for pac in pacs_with_stop + pacs_without_stop + partial_ply_bug_pacs:
+            pac.verbose = False
+        ourpac = [pacs_with_stop[0], pacs_without_stop[0]]
+        alternative_depth_pacs = self.select(
+            pacs_with_stop + pacs_without_stop, [1, 4, 2, 5])
+        return (ourpac, alternative_depth_pacs, partial_ply_bug_pacs)
+
+    def registerInitialState(self, state):
+        for agent in self.solutionAgents + self.alternativeDepthAgents:
+            if 'registerInitialState' in dir(agent):
+                agent.registerInitialState(state)
+        random.seed(self.seed)
+
+    def getAction(self, state):
+        # survey agents
+        GameState.getAndResetExplored()
+        optimalActionLists = []
+        for agent in self.solutionAgents:
+            optimalActionLists.append((agent.getBestPacmanActions(
+                state)[0], len(GameState.getAndResetExplored())))
+        alternativeDepthLists = [agent.getBestPacmanActions(
+            state)[0] for agent in self.alternativeDepthAgents]
+        partialPlyBugLists = [agent.getBestPacmanActions(
+            state)[0] for agent in self.partialPlyBugAgents]
+        # record responses
+        self.optimalActionLists.append(optimalActionLists)
+        self.alternativeDepthLists.append(alternativeDepthLists)
+        self.partialPlyBugLists.append(partialPlyBugLists)
+        self.stepCount += 1
+        random.seed(self.seed + self.stepCount)
+        return optimalActionLists[0][0][0]
+
+    def getTraces(self):
+        # return traces from individual agents
+        return (self.optimalActionLists, self.alternativeDepthLists, self.partialPlyBugLists)
+
+
+class PacmanGameTreeTest(testClasses.TestCase):
+
+    def __init__(self, question, testDict):
+        super(PacmanGameTreeTest, self).__init__(question, testDict)
+        self.seed = int(self.testDict['seed'])
+        self.alg = self.testDict['alg']
+        self.layout_text = self.testDict['layout']
+        self.layout_name = self.testDict['layoutName']
+        self.depth = int(self.testDict['depth'])
+        self.max_points = int(self.testDict['max_points'])
+
+    def execute(self, grades, moduleDict, solutionDict):
+        # load student code and staff code solutions
+        multiAgents = moduleDict['multiAgents']
+        studentAgent = getattr(multiAgents, self.alg)(depth=self.depth)
+        allActions = [json.loads(x)
+                      for x in solutionDict['optimalActions'].split('\n')]
+        altDepthActions = [json.loads(
+            x) for x in solutionDict['altDepthActions'].split('\n')]
+        partialPlyBugActions = [json.loads(
+            x) for x in solutionDict['partialPlyBugActions'].split('\n')]
+        # set up game state and play a game
+        random.seed(self.seed)
+        lay = layout.Layout([l.strip() for l in self.layout_text.split('\n')])
+        pac = GradingAgent(self.seed, studentAgent, allActions,
+                           altDepthActions, partialPlyBugActions)
+        # check return codes and assign grades
+        disp = self.question.getDisplay()
+        stats = run(lay, self.layout_name, pac, [DirectionalGhost(
+            i + 1) for i in range(2)], disp, name=self.alg)
+        if stats['timeouts'] > 0:
+            self.addMessage('Agent timed out on smallClassic.  No credit')
+            return self.testFail(grades)
+        if stats['crashes'] > 0:
+            self.addMessage('Agent crashed on smallClassic.  No credit')
+            return self.testFail(grades)
+        code = pac.checkFailure()
+        if code == 0:
+            return self.testPass(grades)
+        elif code == -3:
+            if pac.getWrongStatesExplored() >= 0:
+                self.addMessage('Bug: Wrong number of states expanded.')
+                return self.testFail(grades)
+            else:
+                return self.testPass(grades)
+        elif code == -2:
+            self.addMessage('Bug: Partial Ply Bug')
+            return self.testFail(grades)
+        elif code == -1:
+            self.addMessage('Bug: Search depth off by 1')
+            return self.testFail(grades)
+        elif code > 0:
+            moves = pac.getSuboptimalMoves()
+            state, studentMove, optMove = random.choice(moves)
+            self.addMessage('Bug: Suboptimal moves')
+            self.addMessage('State:%s\nStudent Move:%s\nOptimal Move:%s' % (
+                state, studentMove, optMove))
+            return self.testFail(grades)
+
+    def writeList(self, handle, name, list):
+        handle.write('%s: """\n' % name)
+        for l in list:
+            handle.write('%s\n' % json.dumps(l))
+        handle.write('"""\n')
+
+    def writeSolution(self, moduleDict, filePath):
+        # load module, set seed, create ghosts and macman, run game
+        multiAgents = moduleDict['multiAgents']
+        random.seed(self.seed)
+        lay = layout.Layout([l.strip() for l in self.layout_text.split('\n')])
+        if self.alg == 'ExpectimaxAgent':
+            ourPacOptions = {'expectimax': 'True'}
+        elif self.alg == 'AlphaBetaAgent':
+            ourPacOptions = {'alphabeta': 'True'}
+        else:
+            ourPacOptions = {}
+        pac = PolyAgent(self.seed, multiAgents, ourPacOptions, self.depth)
+        disp = self.question.getDisplay()
+        run(lay, self.layout_name, pac, [DirectionalGhost(
+            i + 1) for i in range(2)], disp, name=self.alg)
+        (optimalActions, altDepthActions, partialPlyBugActions) = pac.getTraces()
+        # recover traces and record to file
+        handle = open(filePath, 'w')
+        self.writeList(handle, 'optimalActions', optimalActions)
+        self.writeList(handle, 'altDepthActions', altDepthActions)
+        self.writeList(handle, 'partialPlyBugActions', partialPlyBugActions)
+        handle.close()
+
+
+class GraphGameTreeTest(testClasses.TestCase):
+
+    def __init__(self, question, testDict):
+        super(GraphGameTreeTest, self).__init__(question, testDict)
+        self.problem = parseTreeProblem(testDict)
+        self.alg = self.testDict['alg']
+        self.diagram = self.testDict['diagram'].split('\n')
+        self.depth = int(self.testDict['depth'])
+
+    def solveProblem(self, multiAgents):
+        self.problem.reset()
+        studentAgent = getattr(multiAgents, self.alg)(depth=self.depth)
+        action = studentAgent.getAction(self.problem.startState)
+        generated = self.problem.generatedStates
+        return action, " ".join([str(s) for s in sorted(generated)])
+
+    def addDiagram(self):
+        self.addMessage('Tree:')
+        for line in self.diagram:
+            self.addMessage(line)
+
+    def execute(self, grades, moduleDict, solutionDict):
+        multiAgents = moduleDict['multiAgents']
+        goldAction = solutionDict['action']
+        goldGenerated = solutionDict['generated']
+        action, generated = self.solveProblem(multiAgents)
+
+        fail = False
+        if action != goldAction:
+            self.addMessage('Incorrect move for depth=%s' % (self.depth,))
+            self.addMessage(
+                '    Student move: %s\n    Optimal move: %s' % (action, goldAction))
+            fail = True
+
+        if generated != goldGenerated:
+            self.addMessage(
+                'Incorrect generated nodes for depth=%s' % (self.depth,))
+            self.addMessage('    Student generated nodes: %s\n    Correct generated nodes: %s' % (
+                generated, goldGenerated))
+            fail = True
+
+        if fail:
+            self.addDiagram()
+            return self.testFail(grades)
+        else:
+            return self.testPass(grades)
+
+    def writeSolution(self, moduleDict, filePath):
+        multiAgents = moduleDict['multiAgents']
+        action, generated = self.solveProblem(multiAgents)
+        with open(filePath, 'w') as handle:
+            handle.write('# This is the solution file for %s.\n' % self.path)
+            handle.write('action: "%s"\n' % (action,))
+            handle.write('generated: "%s"\n' % (generated,))
+        return True
+
+
+import time
+from util import TimeoutFunction
+
+
+class EvalAgentTest(testClasses.TestCase):
+
+    def __init__(self, question, testDict):
+        super(EvalAgentTest, self).__init__(question, testDict)
+        self.layoutName = testDict['layoutName']
+        self.agentName = testDict['agentName']
+        self.ghosts = eval(testDict['ghosts'])
+        self.maxTime = int(testDict['maxTime'])
+        self.seed = int(testDict['randomSeed'])
+        self.numGames = int(testDict['numGames'])
+
+        self.scoreMinimum = int(
+            testDict['scoreMinimum']) if 'scoreMinimum' in testDict else None
+        self.nonTimeoutMinimum = int(
+            testDict['nonTimeoutMinimum']) if 'nonTimeoutMinimum' in testDict else None
+        self.winsMinimum = int(
+            testDict['winsMinimum']) if 'winsMinimum' in testDict else None
+
+        self.scoreThresholds = [int(s) for s in testDict.get(
+            'scoreThresholds', '').split()]
+        self.nonTimeoutThresholds = [int(s) for s in testDict.get(
+            'nonTimeoutThresholds', '').split()]
+        self.winsThresholds = [int(s) for s in testDict.get(
+            'winsThresholds', '').split()]
+
+        self.maxPoints = sum([len(t) for t in [
+                             self.scoreThresholds, self.nonTimeoutThresholds, self.winsThresholds]])
+        self.agentArgs = testDict.get('agentArgs', '')
+
+    def execute(self, grades, moduleDict, solutionDict):
+        startTime = time.time()
+
+        agentType = getattr(moduleDict['multiAgents'], self.agentName)
+        agentOpts = pacman.parseAgentArgs(
+            self.agentArgs) if self.agentArgs != '' else {}
+        agent = agentType(**agentOpts)
+
+        lay = layout.getLayout(self.layoutName, 3)
+
+        disp = self.question.getDisplay()
+
+        random.seed(self.seed)
+        games = pacman.runGames(lay, agent, self.ghosts, disp, self.numGames,
+                                False, catchExceptions=True, timeout=self.maxTime)
+        totalTime = time.time() - startTime
+
+        stats = {'time': totalTime, 'wins': [g.state.isWin() for g in games].count(True),
+                 'games': games, 'scores': [g.state.getScore() for g in games],
+                 'timeouts': [g.agentTimeout for g in games].count(True), 'crashes': [g.agentCrashed for g in games].count(True)}
+
+        averageScore = sum(stats['scores']) / float(len(stats['scores']))
+        nonTimeouts = self.numGames - stats['timeouts']
+        wins = stats['wins']
+
+        def gradeThreshold(value, minimum, thresholds, weight, name):
+            points = 0
+            passed = (minimum == None) or (value >= minimum)
+            if passed:
+                for t in thresholds:
+                    if value >= t:
+                        points += weight
+            return (passed, points, value, minimum, thresholds, weight, name)
+
+        results = [gradeThreshold(averageScore, self.scoreMinimum, self.scoreThresholds, 2, "average score"),
+                   gradeThreshold(nonTimeouts, self.nonTimeoutMinimum,
+                                  self.nonTimeoutThresholds, 1, "games not timed out"),
+                   gradeThreshold(wins, self.winsMinimum, self.winsThresholds, 1, "wins")]
+
+        totalPoints = 0
+        for passed, points, value, minimum, thresholds, weight, name in results:
+            if minimum == None and len(thresholds) == 0:
+                continue
+
+            # print passed, points, value, minimum, thresholds, name
+            totalPoints += points
+            if not passed:
+                assert points == 0
+                self.addMessage(
+                    "%s %s (fail: below minimum value %s)" % (value, name, minimum))
+            else:
+                self.addMessage("%s %s (%s of %s points)" %
+                                (value, name, points, len(thresholds) * weight))
+
+            if minimum != None:
+                self.addMessage("    Grading scheme:")
+                self.addMessage("     < %s:  fail" % (minimum,))
+                if len(thresholds) == 0 or minimum != thresholds[0]:
+                    self.addMessage("    >= %s:  0 points" % (minimum,))
+                for idx, threshold in enumerate(thresholds):
+                    self.addMessage("    >= %s:  %s points" %
+                                    (threshold, (idx+1) * weight))
+            elif len(thresholds) > 0:
+                self.addMessage("    Grading scheme:")
+                self.addMessage("     < %s:  0 points" % (thresholds[0],))
+                for idx, threshold in enumerate(thresholds):
+                    self.addMessage("    >= %s:  %s points" %
+                                    (threshold, (idx+1) * weight))
+
+        if any([not passed for passed, _, _, _, _, _, _ in results]):
+            totalPoints = 0
+
+        return self.testPartial(grades, totalPoints, self.maxPoints)
+
+    def writeSolution(self, moduleDict, filePath):
+        handle = open(filePath, 'w')
+        handle.write('# This is the solution file for %s.\n' % self.path)
+        handle.write('# File intentionally blank.\n')
+        handle.close()
+        return True
diff --git a/HW2_pacman/pacman.py b/HW2_pacman/pacman.py
new file mode 100644
index 0000000..6eb1c9b
--- /dev/null
+++ b/HW2_pacman/pacman.py
@@ -0,0 +1,730 @@
+"""
+Pacman.py holds the logic for the classic pacman game along with the main
+code to run a game.  This file is divided into three sections:
+
+  (i)  Your interface to the pacman world:
+          Pacman is a complex environment.  You probably don't want to
+          read through all of the code we wrote to make the game runs
+          correctly.  This section contains the parts of the code
+          that you will need to understand in order to complete the
+          project.  There is also some code in game.py that you should
+          understand.
+
+  (ii)  The hidden secrets of pacman:
+          This section contains all of the logic code that the pacman
+          environment uses to decide who can move where, who dies when
+          things collide, etc.  You shouldn't need to read this section
+          of code, but you can if you want.
+
+  (iii) Framework to start a game:
+          The final section contains the code for reading the command
+          you use to set up the game, then starting up a new game, along with
+          linking in all the external parts (agent functions, graphics).
+          Check this section out to see all the options available to you.
+
+To play your first game, type 'python pacman.py' from the command line.
+The keys are 'a', 's', 'd', and 'w' to move (or arrow keys).  Have fun!
+"""
+from game import GameStateData
+from game import Game
+from game import Directions
+from game import Actions
+from util import nearestPoint
+from util import manhattanDistance
+import util
+import layout
+import sys
+import types
+import time
+import random
+import os
+
+###################################################
+# YOUR INTERFACE TO THE PACMAN WORLD: A GameState #
+###################################################
+
+
+class GameState:
+    """
+    A GameState specifies the full game state, including the food, capsules,
+    agent configurations and score changes.
+
+    GameStates are used by the Game object to capture the actual state of the game and
+    can be used by agents to reason about the game.
+
+    Much of the information in a GameState is stored in a GameStateData object.  We
+    strongly suggest that you access that data via the accessor methods below rather
+    than referring to the GameStateData object directly.
+
+    Note that in classic Pacman, Pacman is always agent 0.
+    """
+
+    ####################################################
+    # Accessor methods: use these to access state data #
+    ####################################################
+
+    # static variable keeps track of which states have had getLegalActions called
+    explored = set()
+
+    def getAndResetExplored():
+        tmp = GameState.explored.copy()
+        GameState.explored = set()
+        return tmp
+    getAndResetExplored = staticmethod(getAndResetExplored)
+
+    def getLegalActions(self, agentIndex=0):
+        """
+        Returns the legal actions for the agent specified.
+        """
+#        GameState.explored.add(self)
+        if self.isWin() or self.isLose():
+            return []
+
+        if agentIndex == 0:  # Pacman is moving
+            return PacmanRules.getLegalActions(self)
+        else:
+            return GhostRules.getLegalActions(self, agentIndex)
+
+    def getNextState(self, agentIndex, action):
+        """
+        Returns the child state after the specified agent takes the action.
+        """
+        # Check that children exist
+        if self.isWin() or self.isLose():
+            raise Exception('Can\'t generate a child of a terminal state.')
+
+        # Copy current state
+        state = GameState(self)
+
+        # Let agent's logic deal with its action's effects on the board
+        if agentIndex == 0:  # Pacman is moving
+            state.data._eaten = [False for i in range(state.getNumAgents())]
+            PacmanRules.applyAction(state, action)
+        else:                # A ghost is moving
+            GhostRules.applyAction(state, action, agentIndex)
+
+        # Time passes
+        if agentIndex == 0:
+            state.data.scoreChange += -TIME_PENALTY  # Penalty for waiting around
+        else:
+            GhostRules.decrementTimer(state.data.agentStates[agentIndex])
+
+        # Resolve multi-agent effects
+        GhostRules.checkDeath(state, agentIndex)
+
+        # Book keeping
+        state.data._agentMoved = agentIndex
+        state.data.score += state.data.scoreChange
+        GameState.explored.add(self)
+        GameState.explored.add(state)
+        return state
+
+    def getLegalPacmanActions(self):
+        return self.getLegalActions(0)
+
+    def getPacmanNextState(self, action):
+        """
+        Generates the child state after the specified pacman move
+        """
+        return self.getNextState(0, action)
+
+    def getPacmanState(self):
+        """
+        Returns an AgentState object for pacman (in game.py)
+
+        state.pos gives the current position
+        state.direction gives the travel vector
+        """
+        return self.data.agentStates[0].copy()
+
+    def getPacmanPosition(self):
+        return self.data.agentStates[0].getPosition()
+
+    def getGhostStates(self):
+        return self.data.agentStates[1:]
+
+    def getGhostState(self, agentIndex):
+        if agentIndex == 0 or agentIndex >= self.getNumAgents():
+            raise Exception("Invalid index passed to getGhostState")
+        return self.data.agentStates[agentIndex]
+
+    def getGhostPosition(self, agentIndex):
+        if agentIndex == 0:
+            raise Exception("Pacman's index passed to getGhostPosition")
+        return self.data.agentStates[agentIndex].getPosition()
+
+    def getGhostPositions(self):
+        return [s.getPosition() for s in self.getGhostStates()]
+
+    def getNumAgents(self):
+        return len(self.data.agentStates)
+
+    def getScore(self):
+        return float(self.data.score)
+
+    def getCapsules(self):
+        """
+        Returns a list of positions (x,y) of the remaining capsules.
+        """
+        return self.data.capsules
+
+    def getNumFood(self):
+        return self.data.food.count()
+
+    def getFood(self):
+        """
+        Returns a Grid of boolean food indicator variables.
+
+        Grids can be accessed via list notation, so to check
+        if there is food at (x,y), just call
+
+        currentFood = state.getFood()
+        if currentFood[x][y] == True: ...
+        """
+        return self.data.food
+
+    def getWalls(self):
+        """
+        Returns a Grid of boolean wall indicator variables.
+
+        Grids can be accessed via list notation, so to check
+        if there is a wall at (x,y), just call
+
+        walls = state.getWalls()
+        if walls[x][y] == True: ...
+        """
+        return self.data.layout.walls
+
+    def hasFood(self, x, y):
+        return self.data.food[x][y]
+
+    def hasWall(self, x, y):
+        return self.data.layout.walls[x][y]
+
+    def isLose(self):
+        return self.data._lose
+
+    def isWin(self):
+        return self.data._win
+
+    #############################################
+    #             Helper methods:               #
+    # You shouldn't need to call these directly #
+    #############################################
+
+    def __init__(self, prevState=None):
+        """
+        Generates a new state by copying information from its predecessor.
+        """
+        if prevState != None:  # Initial state
+            self.data = GameStateData(prevState.data)
+        else:
+            self.data = GameStateData()
+
+    def deepCopy(self):
+        state = GameState(self)
+        state.data = self.data.deepCopy()
+        return state
+
+    def __eq__(self, other):
+        """
+        Allows two states to be compared.
+        """
+        return hasattr(other, 'data') and self.data == other.data
+
+    def __hash__(self):
+        """
+        Allows states to be keys of dictionaries.
+        """
+        return hash(self.data)
+
+    def __str__(self):
+
+        return str(self.data)
+
+    def initialize(self, layout, numGhostAgents=1000):
+        """
+        Creates an initial game state from a layout array (see layout.py).
+        """
+        self.data.initialize(layout, numGhostAgents)
+
+############################################################################
+#                     THE HIDDEN SECRETS OF PACMAN                         #
+#                                                                          #
+# You shouldn't need to look through the code in this section of the file. #
+############################################################################
+
+
+SCARED_TIME = 40    # Moves ghosts are scared
+COLLISION_TOLERANCE = 0.7  # How close ghosts must be to Pacman to kill
+TIME_PENALTY = 1  # Number of points lost each round
+
+
+class ClassicGameRules:
+    """
+    These game rules manage the control flow of a game, deciding when
+    and how the game starts and ends.
+    """
+
+    def __init__(self, timeout=30):
+        self.timeout = timeout
+
+    def newGame(self, layout, pacmanAgent, ghostAgents, display, quiet=False, catchExceptions=False):
+        agents = [pacmanAgent] + ghostAgents[:layout.getNumGhosts()]
+        initState = GameState()
+        initState.initialize(layout, len(ghostAgents))
+        game = Game(agents, display, self, catchExceptions=catchExceptions)
+        game.state = initState
+        self.initialState = initState.deepCopy()
+        self.quiet = quiet
+        return game
+
+    def process(self, state, game):
+        """
+        Checks to see whether it is time to end the game.
+        """
+        if state.isWin():
+            self.win(state, game)
+        if state.isLose():
+            self.lose(state, game)
+
+    def win(self, state, game):
+        if not self.quiet:
+            print("Pacman emerges victorious! Score: %d" % state.data.score)
+        game.gameOver = True
+
+    def lose(self, state, game):
+        if not self.quiet:
+            print("Pacman died! Score: %d" % state.data.score)
+        game.gameOver = True
+
+    def getProgress(self, game):
+        return float(game.state.getNumFood()) / self.initialState.getNumFood()
+
+    def agentCrash(self, game, agentIndex):
+        if agentIndex == 0:
+            print("Pacman crashed")
+        else:
+            print("A ghost crashed")
+
+    def getMaxTotalTime(self, agentIndex):
+        return self.timeout
+
+    def getMaxStartupTime(self, agentIndex):
+        return self.timeout
+
+    def getMoveWarningTime(self, agentIndex):
+        return self.timeout
+
+    def getMoveTimeout(self, agentIndex):
+        return self.timeout
+
+    def getMaxTimeWarnings(self, agentIndex):
+        return 0
+
+
+class PacmanRules:
+    """
+    These functions govern how pacman interacts with his environment under
+    the classic game rules.
+    """
+    PACMAN_SPEED = 1
+
+    def getLegalActions(state):
+        """
+        Returns a list of possible actions.
+        """
+        return Actions.getPossibleActions(state.getPacmanState().configuration, state.data.layout.walls)
+    getLegalActions = staticmethod(getLegalActions)
+
+    def applyAction(state, action):
+        """
+        Edits the state to reflect the results of the action.
+        """
+        legal = PacmanRules.getLegalActions(state)
+        if action not in legal:
+            raise Exception("Illegal action " + str(action))
+
+        pacmanState = state.data.agentStates[0]
+
+        # Update Configuration
+        vector = Actions.directionToVector(action, PacmanRules.PACMAN_SPEED)
+        pacmanState.configuration = pacmanState.configuration.getNextState(
+            vector)
+
+        # Eat
+        next = pacmanState.configuration.getPosition()
+        nearest = nearestPoint(next)
+        if manhattanDistance(nearest, next) <= 0.5:
+            # Remove food
+            PacmanRules.consume(nearest, state)
+    applyAction = staticmethod(applyAction)
+
+    def consume(position, state):
+        x, y = position
+        # Eat food
+        if state.data.food[x][y]:
+            state.data.scoreChange += 10
+            state.data.food = state.data.food.copy()
+            state.data.food[x][y] = False
+            state.data._foodEaten = position
+            # TODO: cache numFood?
+            numFood = state.getNumFood()
+            if numFood == 0 and not state.data._lose:
+                state.data.scoreChange += 500
+                state.data._win = True
+        # Eat capsule
+        if(position in state.getCapsules()):
+            state.data.capsules.remove(position)
+            state.data._capsuleEaten = position
+            # Reset all ghosts' scared timers
+            for index in range(1, len(state.data.agentStates)):
+                state.data.agentStates[index].scaredTimer = SCARED_TIME
+    consume = staticmethod(consume)
+
+
+class GhostRules:
+    """
+    These functions dictate how ghosts interact with their environment.
+    """
+    GHOST_SPEED = 1.0
+
+    def getLegalActions(state, ghostIndex):
+        """
+        Ghosts cannot stop, and cannot turn around unless they
+        reach a dead end, but can turn 90 degrees at intersections.
+        """
+        conf = state.getGhostState(ghostIndex).configuration
+        possibleActions = Actions.getPossibleActions(
+            conf, state.data.layout.walls)
+        reverse = Actions.reverseDirection(conf.direction)
+        if Directions.STOP in possibleActions:
+            possibleActions.remove(Directions.STOP)
+        if reverse in possibleActions and len(possibleActions) > 1:
+            possibleActions.remove(reverse)
+        return possibleActions
+    getLegalActions = staticmethod(getLegalActions)
+
+    def applyAction(state, action, ghostIndex):
+
+        legal = GhostRules.getLegalActions(state, ghostIndex)
+        if action not in legal:
+            raise Exception("Illegal ghost action " + str(action))
+
+        ghostState = state.data.agentStates[ghostIndex]
+        speed = GhostRules.GHOST_SPEED
+        if ghostState.scaredTimer > 0:
+            speed /= 2.0
+        vector = Actions.directionToVector(action, speed)
+        ghostState.configuration = ghostState.configuration.getNextState(
+            vector)
+    applyAction = staticmethod(applyAction)
+
+    def decrementTimer(ghostState):
+        timer = ghostState.scaredTimer
+        if timer == 1:
+            ghostState.configuration.pos = nearestPoint(
+                ghostState.configuration.pos)
+        ghostState.scaredTimer = max(0, timer - 1)
+    decrementTimer = staticmethod(decrementTimer)
+
+    def checkDeath(state, agentIndex):
+        pacmanPosition = state.getPacmanPosition()
+        if agentIndex == 0:  # Pacman just moved; Anyone can kill him
+            for index in range(1, len(state.data.agentStates)):
+                ghostState = state.data.agentStates[index]
+                ghostPosition = ghostState.configuration.getPosition()
+                if GhostRules.canKill(pacmanPosition, ghostPosition):
+                    GhostRules.collide(state, ghostState, index)
+        else:
+            ghostState = state.data.agentStates[agentIndex]
+            ghostPosition = ghostState.configuration.getPosition()
+            if GhostRules.canKill(pacmanPosition, ghostPosition):
+                GhostRules.collide(state, ghostState, agentIndex)
+    checkDeath = staticmethod(checkDeath)
+
+    def collide(state, ghostState, agentIndex):
+        if ghostState.scaredTimer > 0:
+            state.data.scoreChange += 200
+            GhostRules.placeGhost(state, ghostState)
+            ghostState.scaredTimer = 0
+            # Added for first-person
+            state.data._eaten[agentIndex] = True
+        else:
+            if not state.data._win:
+                state.data.scoreChange -= 500
+                state.data._lose = True
+    collide = staticmethod(collide)
+
+    def canKill(pacmanPosition, ghostPosition):
+        return manhattanDistance(ghostPosition, pacmanPosition) <= COLLISION_TOLERANCE
+    canKill = staticmethod(canKill)
+
+    def placeGhost(state, ghostState):
+        ghostState.configuration = ghostState.start
+    placeGhost = staticmethod(placeGhost)
+
+#############################
+# FRAMEWORK TO START A GAME #
+#############################
+
+
+def default(str):
+    return str + ' [Default: %default]'
+
+
+def parseAgentArgs(str):
+    if str == None:
+        return {}
+    pieces = str.split(',')
+    opts = {}
+    for p in pieces:
+        if '=' in p:
+            key, val = p.split('=')
+        else:
+            key, val = p, 1
+        opts[key] = val
+    return opts
+
+
+def readCommand(argv):
+    """
+    Processes the command used to run pacman from the command line.
+    """
+    from optparse import OptionParser
+    usageStr = """
+    USAGE:      python pacman.py 
+    EXAMPLES:   (1) python pacman.py
+                    - starts an interactive game
+                (2) python pacman.py --layout smallClassic --zoom 2
+                OR  python pacman.py -l smallClassic -z 2
+                    - starts an interactive game on a smaller board, zoomed in
+    """
+    parser = OptionParser(usageStr)
+
+    parser.add_option('-n', '--numGames', dest='numGames', type='int',
+                      help=default('the number of GAMES to play'), metavar='GAMES', default=1)
+    parser.add_option('-l', '--layout', dest='layout',
+                      help=default(
+                          'the LAYOUT_FILE from which to load the map layout'),
+                      metavar='LAYOUT_FILE', default='mediumClassic')
+    parser.add_option('-p', '--pacman', dest='pacman',
+                      help=default(
+                          'the agent TYPE in the pacmanAgents module to use'),
+                      metavar='TYPE', default='KeyboardAgent')
+    parser.add_option('-t', '--textGraphics', action='store_true', dest='textGraphics',
+                      help='Display output as text only', default=False)
+    parser.add_option('-q', '--quietTextGraphics', action='store_true', dest='quietGraphics',
+                      help='Generate minimal output and no graphics', default=False)
+    parser.add_option('-g', '--ghosts', dest='ghost',
+                      help=default(
+                          'the ghost agent TYPE in the ghostAgents module to use'),
+                      metavar='TYPE', default='RandomGhost')
+    parser.add_option('-k', '--numghosts', type='int', dest='numGhosts',
+                      help=default('The maximum number of ghosts to use'), default=4)
+    parser.add_option('-z', '--zoom', type='float', dest='zoom',
+                      help=default('Zoom the size of the graphics window'), default=1.0)
+    parser.add_option('-f', '--fixRandomSeed', action='store_true', dest='fixRandomSeed',
+                      help='Fixes the random seed to always play the same game', default=False)
+    parser.add_option('-r', '--recordActions', action='store_true', dest='record',
+                      help='Writes game histories to a file (named by the time they were played)', default=False)
+    parser.add_option('--replay', dest='gameToReplay',
+                      help='A recorded game file (pickle) to replay', default=None)
+    parser.add_option('-a', '--agentArgs', dest='agentArgs',
+                      help='Comma separated values sent to agent. e.g. "opt1=val1,opt2,opt3=val3"')
+    parser.add_option('-x', '--numTraining', dest='numTraining', type='int',
+                      help=default('How many episodes are training (suppresses output)'), default=0)
+    parser.add_option('--frameTime', dest='frameTime', type='float',
+                      help=default('Time to delay between frames; <0 means keyboard'), default=0.1)
+    parser.add_option('-c', '--catchExceptions', action='store_true', dest='catchExceptions',
+                      help='Turns on exception handling and timeouts during games', default=False)
+    parser.add_option('--timeout', dest='timeout', type='int',
+                      help=default('Maximum length of time an agent can spend computing in a single game'), default=30)
+
+    options, otherjunk = parser.parse_args(argv)
+    if len(otherjunk) != 0:
+        raise Exception('Command line input not understood: ' + str(otherjunk))
+    args = dict()
+
+    # Fix the random seed
+    if options.fixRandomSeed:
+        random.seed('cs188')
+
+    # Choose a layout
+    args['layout'] = layout.getLayout(options.layout)
+    if args['layout'] == None:
+        raise Exception("The layout " + options.layout + " cannot be found")
+
+    # Choose a Pacman agent
+    noKeyboard = options.gameToReplay == None and (
+        options.textGraphics or options.quietGraphics)
+    pacmanType = loadAgent(options.pacman, noKeyboard)
+    agentOpts = parseAgentArgs(options.agentArgs)
+    if options.numTraining > 0:
+        args['numTraining'] = options.numTraining
+        if 'numTraining' not in agentOpts:
+            agentOpts['numTraining'] = options.numTraining
+    pacman = pacmanType(**agentOpts)  # Instantiate Pacman with agentArgs
+    args['pacman'] = pacman
+
+    # Don't display training games
+    if 'numTrain' in agentOpts:
+        options.numQuiet = int(agentOpts['numTrain'])
+        options.numIgnore = int(agentOpts['numTrain'])
+
+    # Choose a ghost agent
+    ghostType = loadAgent(options.ghost, noKeyboard)
+    args['ghosts'] = [ghostType(i+1) for i in range(options.numGhosts)]
+
+    # Choose a display format
+    if options.quietGraphics:
+        import textDisplay
+        args['display'] = textDisplay.NullGraphics()
+    elif options.textGraphics:
+        import textDisplay
+        textDisplay.SLEEP_TIME = options.frameTime
+        args['display'] = textDisplay.PacmanGraphics()
+    else:
+        import graphicsDisplay
+        args['display'] = graphicsDisplay.PacmanGraphics(
+            options.zoom, frameTime=options.frameTime)
+    args['numGames'] = options.numGames
+    args['record'] = options.record
+    args['catchExceptions'] = options.catchExceptions
+    args['timeout'] = options.timeout
+
+    # Special case: recorded games don't use the runGames method or args structure
+    if options.gameToReplay != None:
+        print('Replaying recorded game %s.' % options.gameToReplay)
+        import pickle
+        f = open(options.gameToReplay)
+        try:
+            recorded = pickle.load(f)
+        finally:
+            f.close()
+        recorded['display'] = args['display']
+        replayGame(**recorded)
+        sys.exit(0)
+
+    return args
+
+
+def loadAgent(pacman, nographics):
+    # Looks through all pythonPath Directories for the right module,
+    pythonPathStr = os.path.expandvars("$PYTHONPATH")
+    if pythonPathStr.find(';') == -1:
+        pythonPathDirs = pythonPathStr.split(':')
+    else:
+        pythonPathDirs = pythonPathStr.split(';')
+    pythonPathDirs.append('.')
+
+    for moduleDir in pythonPathDirs:
+        if not os.path.isdir(moduleDir):
+            continue
+        moduleNames = [f for f in os.listdir(
+            moduleDir) if f.endswith('gents.py')]
+        for modulename in moduleNames:
+            try:
+                module = __import__(modulename[:-3])
+            except ImportError:
+                continue
+            if pacman in dir(module):
+                if nographics and modulename == 'keyboardAgents.py':
+                    raise Exception(
+                        'Using the keyboard requires graphics (not text display)')
+                return getattr(module, pacman)
+    raise Exception('The agent ' + pacman +
+                    ' is not specified in any *Agents.py.')
+
+
+def replayGame(layout, actions, display):
+    import pacmanAgents
+    import ghostAgents
+    rules = ClassicGameRules()
+    agents = [pacmanAgents.GreedyAgent()] + [ghostAgents.RandomGhost(i+1)
+                                             for i in range(layout.getNumGhosts())]
+    game = rules.newGame(layout, agents[0], agents[1:], display)
+    state = game.state
+    display.initialize(state.data)
+
+    for action in actions:
+            # Execute the action
+        state = state.getNextState(*action)
+        # Change the display
+        display.update(state.data)
+        # Allow for game specific conditions (winning, losing, etc.)
+        rules.process(state, game)
+
+    display.finish()
+
+
+def runGames(layout, pacman, ghosts, display, numGames, record, numTraining=0, catchExceptions=False, timeout=30):
+    import __main__
+    __main__.__dict__['_display'] = display
+
+    rules = ClassicGameRules(timeout)
+    games = []
+
+    # --- 1. Add start timer here ---
+    startTime = time.time()
+
+    for i in range(numGames):
+        beQuiet = i < numTraining
+        if beQuiet:
+                # Suppress output and graphics
+            import textDisplay
+            gameDisplay = textDisplay.NullGraphics()
+            rules.quiet = True
+        else:
+            gameDisplay = display
+            rules.quiet = False
+        game = rules.newGame(layout, pacman, ghosts,
+                             gameDisplay, beQuiet, catchExceptions)
+        game.run()
+        if not beQuiet:
+            games.append(game)
+
+        if record:
+            import pickle
+            fname = ('recorded-game-%d' % (i + 1)) + \
+                '-'.join([str(t) for t in time.localtime()[1:6]])
+            f = file(fname, 'w')
+            components = {'layout': layout, 'actions': game.moveHistory}
+            pickle.dump(components, f)
+            f.close()
+
+    # --- 2. Calculate the total time before calculating the total score ---
+    totalTime = time.time() - startTime
+
+    if (numGames-numTraining) > 0:
+        scores = [game.state.getScore() for game in games]
+        wins = [game.state.isWin() for game in games]
+        winRate = wins.count(True) / float(len(wins))
+        
+        print('Scores:       ', ', '.join([str(score) for score in scores]))
+        print('Record:       ', ', '.join(
+            [['Loss', 'Win'][int(w)] for w in wins]))
+        print('Average Score:', sum(scores) / float(len(scores)))
+        print('Win Rate:      %d/%d (%.2f)' %
+              (wins.count(True), len(wins), winRate))
+        # --- 3. Output total execution time ---
+        print('Total Time:    %.2f seconds' % totalTime)
+
+    return games
+
+
+if __name__ == '__main__':
+    """
+    The main function called when pacman.py is run
+    from the command line:
+
+    > python pacman.py
+
+    See the usage string for more details.
+
+    > python pacman.py --help
+    """
+    args = readCommand(sys.argv[1:])  # Get game components based on input
+    runGames(**args)
+
+    pass
diff --git a/HW2_pacman/pacmanAgents.py b/HW2_pacman/pacmanAgents.py
new file mode 100644
index 0000000..9a9520a
--- /dev/null
+++ b/HW2_pacman/pacmanAgents.py
@@ -0,0 +1,49 @@
+from pacman import Directions
+from game import Agent
+import random
+import game
+import util
+
+
+class LeftTurnAgent(game.Agent):
+    "An agent that turns left at every opportunity"
+
+    def getAction(self, state):
+        legal = state.getLegalPacmanActions()
+        current = state.getPacmanState().configuration.direction
+        if current == Directions.STOP:
+            current = Directions.NORTH
+        left = Directions.LEFT[current]
+        if left in legal:
+            return left
+        if current in legal:
+            return current
+        if Directions.RIGHT[current] in legal:
+            return Directions.RIGHT[current]
+        if Directions.LEFT[left] in legal:
+            return Directions.LEFT[left]
+        return Directions.STOP
+
+
+class GreedyAgent(Agent):
+    def __init__(self, evalFn="scoreEvaluation"):
+        self.evaluationFunction = util.lookup(evalFn, globals())
+        assert self.evaluationFunction != None
+
+    def getAction(self, state):
+        # Generate candidate actions
+        legal = state.getLegalPacmanActions()
+        if Directions.STOP in legal:
+            legal.remove(Directions.STOP)
+
+        children = [(state.getNextState(0, action), action)
+                      for action in legal]
+        scored = [(self.evaluationFunction(state), action)
+                  for state, action in children]
+        bestScore = max(scored)[0]
+        bestActions = [pair[1] for pair in scored if pair[0] == bestScore]
+        return random.choice(bestActions)
+
+
+def scoreEvaluation(state):
+    return state.getScore()
diff --git a/HW2_pacman/projectParams.py b/HW2_pacman/projectParams.py
new file mode 100644
index 0000000..edd5960
--- /dev/null
+++ b/HW2_pacman/projectParams.py
@@ -0,0 +1,4 @@
+STUDENT_CODE_DEFAULT = 'multiAgents.py'
+PROJECT_TEST_CLASSES = 'multiagentTestClasses.py'
+PROJECT_NAME = 'Project 2: Multiagent search'
+BONUS_PIC = False
diff --git a/HW2_pacman/testClasses.py b/HW2_pacman/testClasses.py
new file mode 100644
index 0000000..9790f8a
--- /dev/null
+++ b/HW2_pacman/testClasses.py
@@ -0,0 +1,189 @@
+import inspect
+import re
+import sys
+
+
+# Class which models a question in a project.  Note that questions have a
+# maximum number of points they are worth, and are composed of a series of
+# test cases
+class Question(object):
+
+    def raiseNotDefined(self):
+        print('Method not implemented: %s' % inspect.stack()[1][3])
+        sys.exit(1)
+
+    def __init__(self, questionDict, display):
+        self.maxPoints = int(questionDict['max_points'])
+        self.testCases = []
+        self.display = display
+
+    def getDisplay(self):
+        return self.display
+
+    def getMaxPoints(self):
+        return self.maxPoints
+
+    # Note that 'thunk' must be a function which accepts a single argument,
+    # namely a 'grading' object
+    def addTestCase(self, testCase, thunk):
+        self.testCases.append((testCase, thunk))
+
+    def execute(self, grades):
+        self.raiseNotDefined()
+
+# Question in which all test cases must be passed in order to receive credit
+class PassAllTestsQuestion(Question):
+
+    def execute(self, grades):
+        # TODO: is this the right way to use grades?  The autograder doesn't seem to use it.
+        testsFailed = False
+        grades.assignZeroCredit()
+        for _, f in self.testCases:
+            if not f(grades):
+                testsFailed = True
+        if testsFailed:
+            grades.fail("Tests failed.")
+        else:
+            grades.assignFullCredit()
+
+
+class ExtraCreditPassAllTestsQuestion(Question):
+    def __init__(self, questionDict, display):
+        Question.__init__(self, questionDict, display)
+        self.extraPoints = int(questionDict['extra_points'])
+
+    def execute(self, grades):
+        # TODO: is this the right way to use grades?  The autograder doesn't seem to use it.
+        testsFailed = False
+        grades.assignZeroCredit()
+        for _, f in self.testCases:
+            if not f(grades):
+                testsFailed = True
+        if testsFailed:
+            grades.fail("Tests failed.")
+        else:
+            grades.assignFullCredit()
+            grades.addPoints(self.extraPoints)
+
+# Question in which predict credit is given for test cases with a ``points'' property.
+# All other tests are mandatory and must be passed.
+class HackedPartialCreditQuestion(Question):
+
+    def execute(self, grades):
+        # TODO: is this the right way to use grades?  The autograder doesn't seem to use it.
+        grades.assignZeroCredit()
+
+        points = 0
+        passed = True
+        for testCase, f in self.testCases:
+            testResult = f(grades)
+            if "points" in testCase.testDict:
+                if testResult:
+                    points += float(testCase.testDict["points"])
+            else:
+                passed = passed and testResult
+
+        # FIXME: Below terrible hack to match q3's logic
+        if int(points) == self.maxPoints and not passed:
+            grades.assignZeroCredit()
+        else:
+            grades.addPoints(int(points))
+
+
+class Q6PartialCreditQuestion(Question):
+    """Fails any test which returns False, otherwise doesn't effect the grades object.
+    Partial credit tests will add the required points."""
+
+    def execute(self, grades):
+        grades.assignZeroCredit()
+
+        results = []
+        for _, f in self.testCases:
+            results.append(f(grades))
+        if False in results:
+            grades.assignZeroCredit()
+
+
+class PartialCreditQuestion(Question):
+    """Fails any test which returns False, otherwise doesn't effect the grades object.
+    Partial credit tests will add the required points."""
+
+    def execute(self, grades):
+        grades.assignZeroCredit()
+
+        for _, f in self.testCases:
+            if not f(grades):
+                grades.assignZeroCredit()
+                grades.fail("Tests failed.")
+                return False
+
+
+class NumberPassedQuestion(Question):
+    """Grade is the number of test cases passed."""
+
+    def execute(self, grades):
+        grades.addPoints([f(grades) for _, f in self.testCases].count(True))
+
+
+# Template modeling a generic test case
+class TestCase(object):
+
+    def raiseNotDefined(self):
+        print('Method not implemented: %s' % inspect.stack()[1][3])
+        sys.exit(1)
+
+    def getPath(self):
+        return self.path
+
+    def __init__(self, question, testDict):
+        self.question = question
+        self.testDict = testDict
+        self.path = testDict['path']
+        self.messages = []
+
+    def __str__(self):
+        self.raiseNotDefined()
+
+    def execute(self, grades, moduleDict, solutionDict):
+        self.raiseNotDefined()
+
+    def writeSolution(self, moduleDict, filePath):
+        self.raiseNotDefined()
+        return True
+
+    # Tests should call the following messages for grading
+    # to ensure a uniform format for test output.
+    #
+    # TODO: this is hairy, but we need to fix grading.py's interface
+    # to get a nice hierarchical project - question - test structure,
+    # then these should be moved into Question proper.
+    def testPass(self, grades):
+        grades.addMessage('PASS: %s' % (self.path,))
+        for line in self.messages:
+            grades.addMessage('    %s' % (line,))
+        return True
+
+    def testFail(self, grades):
+        grades.addMessage('FAIL: %s' % (self.path,))
+        for line in self.messages:
+            grades.addMessage('    %s' % (line,))
+        return False
+
+    # This should really be question level?
+    def testPartial(self, grades, points, maxPoints):
+        grades.addPoints(points)
+        # extraCredit = max(0, points - maxPoints)
+        # regularCredit = points - extraCredit
+
+        # grades.addMessage('%s: %s (%s of %s points)' % (
+        #     "PASS" if points >= maxPoints else "FAIL", self.path, regularCredit, maxPoints))
+        # if extraCredit > 0:
+        #     grades.addMessage('EXTRA CREDIT: %s points' % (extraCredit,))
+
+        for line in self.messages:
+            grades.addMessage('    %s' % (line,))
+
+        return True
+
+    def addMessage(self, message):
+        self.messages.extend(message.split('\n'))
diff --git a/HW2_pacman/testParser.py b/HW2_pacman/testParser.py
new file mode 100644
index 0000000..cb8764f
--- /dev/null
+++ b/HW2_pacman/testParser.py
@@ -0,0 +1,72 @@
+import re
+import sys
+
+
+class TestParser(object):
+
+    def __init__(self, path):
+        # save the path to the test file
+        self.path = path
+
+    def removeComments(self, rawlines):
+        # remove any portion of a line following a '#' symbol
+        fixed_lines = []
+        for l in rawlines:
+            idx = l.find('#')
+            if idx == -1:
+                fixed_lines.append(l)
+            else:
+                fixed_lines.append(l[0:idx])
+        return '\n'.join(fixed_lines)
+
+    def parse(self):
+        # read in the test case and remove comments
+        test = {}
+        with open(self.path) as handle:
+            raw_lines = handle.read().split('\n')
+
+        test_text = self.removeComments(raw_lines)
+        test['__raw_lines__'] = raw_lines
+        test['path'] = self.path
+        test['__emit__'] = []
+        lines = test_text.split('\n')
+        i = 0
+        # read a property in each loop cycle
+        while(i < len(lines)):
+            # skip blank lines
+            if re.match('\A\s*\Z', lines[i]):
+                test['__emit__'].append(("raw", raw_lines[i]))
+                i += 1
+                continue
+            m = re.match('\A([^"]*?):\s*"([^"]*)"\s*\Z', lines[i])
+            if m:
+                test[m.group(1)] = m.group(2)
+                test['__emit__'].append(("oneline", m.group(1)))
+                i += 1
+                continue
+            m = re.match('\A([^"]*?):\s*"""\s*\Z', lines[i])
+            if m:
+                msg = []
+                i += 1
+                while(not re.match('\A\s*"""\s*\Z', lines[i])):
+                    msg.append(raw_lines[i])
+                    i += 1
+                test[m.group(1)] = '\n'.join(msg)
+                test['__emit__'].append(("multiline", m.group(1)))
+                i += 1
+                continue
+            print('error parsing test file: %s' % self.path)
+            sys.exit(1)
+        return test
+
+
+def emitTestDict(testDict, handle):
+    for kind, data in testDict['__emit__']:
+        if kind == "raw":
+            handle.write(data + "\n")
+        elif kind == "oneline":
+            handle.write('%s: "%s"\n' % (data, testDict[data]))
+        elif kind == "multiline":
+            handle.write('%s: """\n%s\n"""\n' % (data, testDict[data]))
+        else:
+            raise Exception("Bad __emit__")
diff --git a/HW2_pacman/test_cases/CONFIG b/HW2_pacman/test_cases/CONFIG
new file mode 100644
index 0000000..d62c994
--- /dev/null
+++ b/HW2_pacman/test_cases/CONFIG
@@ -0,0 +1 @@
+order: "part1 part2 part3 part4"
diff --git a/HW2_pacman/test_cases/part1/0-eval-function-lose-states-1.solution b/HW2_pacman/test_cases/part1/0-eval-function-lose-states-1.solution
new file mode 100644
index 0000000..d0b6eed
--- /dev/null
+++ b/HW2_pacman/test_cases/part1/0-eval-function-lose-states-1.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q2/0-eval-function-lose-states-1.test.
+action: "Left"
+generated: "lose1 lose2 root"
diff --git a/HW2_pacman/test_cases/part1/0-eval-function-lose-states-1.test b/HW2_pacman/test_cases/part1/0-eval-function-lose-states-1.test
new file mode 100644
index 0000000..fba4ac5
--- /dev/null
+++ b/HW2_pacman/test_cases/part1/0-eval-function-lose-states-1.test
@@ -0,0 +1,30 @@
+class: "GraphGameTreeTest"
+alg: "MinimaxAgent"
+depth: "2"
+
+diagram: """
+        root
+       /    \
+    lose1   lose2
+      1       0
+
+If your algorithm is returning a different
+action, make sure you are calling the
+evaluation function on losing states.
+"""
+num_agents: "2"
+
+start_state: "root"
+win_states: ""
+lose_states: "lose1 lose2"
+
+children: """
+root Left lose1
+root Right lose2
+"""
+
+evaluation: """
+lose1 1.0
+lose2 0.0
+"""
+
diff --git a/HW2_pacman/test_cases/part1/0-eval-function-lose-states-2.solution b/HW2_pacman/test_cases/part1/0-eval-function-lose-states-2.solution
new file mode 100644
index 0000000..df68452
--- /dev/null
+++ b/HW2_pacman/test_cases/part1/0-eval-function-lose-states-2.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q2/0-eval-function-lose-states-2.test.
+action: "Right"
+generated: "lose1 lose2 root"
diff --git a/HW2_pacman/test_cases/part1/0-eval-function-lose-states-2.test b/HW2_pacman/test_cases/part1/0-eval-function-lose-states-2.test
new file mode 100644
index 0000000..ec22e91
--- /dev/null
+++ b/HW2_pacman/test_cases/part1/0-eval-function-lose-states-2.test
@@ -0,0 +1,30 @@
+class: "GraphGameTreeTest"
+alg: "MinimaxAgent"
+depth: "2"
+
+diagram: """
+        root
+       /    \
+    lose1   lose2
+      0       1
+
+If your algorithm is returning a different
+action, make sure you are calling the
+evaluation function on losing states.
+"""
+num_agents: "2"
+
+start_state: "root"
+win_states: ""
+lose_states: "lose1 lose2"
+
+children: """
+root Left lose1
+root Right lose2
+"""
+
+evaluation: """
+lose1 0.0
+lose2 1.0
+"""
+
diff --git a/HW2_pacman/test_cases/part1/0-eval-function-win-states-1.solution b/HW2_pacman/test_cases/part1/0-eval-function-win-states-1.solution
new file mode 100644
index 0000000..0254142
--- /dev/null
+++ b/HW2_pacman/test_cases/part1/0-eval-function-win-states-1.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q2/0-eval-function-win-states-1.test.
+action: "Left"
+generated: "root win1 win2"
diff --git a/HW2_pacman/test_cases/part1/0-eval-function-win-states-1.test b/HW2_pacman/test_cases/part1/0-eval-function-win-states-1.test
new file mode 100644
index 0000000..d7c6802
--- /dev/null
+++ b/HW2_pacman/test_cases/part1/0-eval-function-win-states-1.test
@@ -0,0 +1,30 @@
+class: "GraphGameTreeTest"
+alg: "MinimaxAgent"
+depth: "2"
+
+diagram: """
+        root
+       /    \
+    win1     win2
+      1       0
+
+If your algorithm is returning a different
+action, make sure you are calling the
+evaluation function on winning states.
+"""
+num_agents: "2"
+
+start_state: "root"
+win_states: "win1 win2"
+lose_states: ""
+
+children: """
+root Left win1
+root Right win2
+"""
+
+evaluation: """
+win1 1.0
+win2 0.0
+"""
+
diff --git a/HW2_pacman/test_cases/part1/0-eval-function-win-states-2.solution b/HW2_pacman/test_cases/part1/0-eval-function-win-states-2.solution
new file mode 100644
index 0000000..f21c04a
--- /dev/null
+++ b/HW2_pacman/test_cases/part1/0-eval-function-win-states-2.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q2/0-eval-function-win-states-2.test.
+action: "Right"
+generated: "root win1 win2"
diff --git a/HW2_pacman/test_cases/part1/0-eval-function-win-states-2.test b/HW2_pacman/test_cases/part1/0-eval-function-win-states-2.test
new file mode 100644
index 0000000..01865d4
--- /dev/null
+++ b/HW2_pacman/test_cases/part1/0-eval-function-win-states-2.test
@@ -0,0 +1,30 @@
+class: "GraphGameTreeTest"
+alg: "MinimaxAgent"
+depth: "2"
+
+diagram: """
+        root
+       /    \
+    win1    win2
+      0      1
+
+If your algorithm is returning a different
+action, make sure you are calling the
+evaluation function on winning states.
+"""
+num_agents: "2"
+
+start_state: "root"
+win_states: "win1 win2"
+lose_states: ""
+
+children: """
+root Left win1
+root Right win2
+"""
+
+evaluation: """
+win1 0.0
+win2 1.0
+"""
+
diff --git a/HW2_pacman/test_cases/part1/0-lecture-6-tree.solution b/HW2_pacman/test_cases/part1/0-lecture-6-tree.solution
new file mode 100644
index 0000000..3c6a74d
--- /dev/null
+++ b/HW2_pacman/test_cases/part1/0-lecture-6-tree.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q2/0-lecture-6-tree.test.
+action: "Center"
+generated: "A B C D E F G H I max min1 min2 min3"
diff --git a/HW2_pacman/test_cases/part1/0-lecture-6-tree.test b/HW2_pacman/test_cases/part1/0-lecture-6-tree.test
new file mode 100644
index 0000000..a4b0f8e
--- /dev/null
+++ b/HW2_pacman/test_cases/part1/0-lecture-6-tree.test
@@ -0,0 +1,50 @@
+class: "GraphGameTreeTest"
+alg: "MinimaxAgent"
+depth: "2"
+
+#  Tree from lecture 6 slides
+diagram: """
+           max
+      /-/   |   \--\
+     /      |       \
+    /       |        \
+ min1      min2      min3
+  /|\      /|\       /|\ 
+ / | \    / | \     / | \
+A  B  C  D  E  F   G  H  I  
+3 12  8  5  4  6  14  1  11
+"""
+
+num_agents: "2"
+
+start_state: "max"
+win_states: "A B C D E F G H I"
+lose_states: ""
+
+children: """
+max Left min1
+max Center min2
+max Right min3
+min1 Left A
+min1 Center B
+min1 Right C
+min2 Left D
+min2 Center E
+min2 Right F
+min3 Left G
+min3 Center H
+min3 Right I
+"""
+
+
+evaluation: """
+A 3.0
+B 12.0
+C 8.0
+D 5.0
+E 4.0
+F 6.0
+G 14.0
+H 1.0
+I 11.0
+"""
diff --git a/HW2_pacman/test_cases/part1/0-small-tree.solution b/HW2_pacman/test_cases/part1/0-small-tree.solution
new file mode 100644
index 0000000..f381f9a
--- /dev/null
+++ b/HW2_pacman/test_cases/part1/0-small-tree.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q2/0-small-tree.test.
+action: "pacLeft"
+generated: "A B C D deeper minLeft minRight root"
diff --git a/HW2_pacman/test_cases/part1/0-small-tree.test b/HW2_pacman/test_cases/part1/0-small-tree.test
new file mode 100644
index 0000000..6cd8cef
--- /dev/null
+++ b/HW2_pacman/test_cases/part1/0-small-tree.test
@@ -0,0 +1,36 @@
+class: "GraphGameTreeTest"
+alg: "MinimaxAgent"
+depth: "3"
+
+diagram: """
+        root
+       /    \
+ minLeft  minRight
+  / \       /    \
+ A   B     C   deeper
+ 4   3     2     |
+                 D
+               1000
+"""
+num_agents: "2"
+
+start_state: "root"
+win_states: "A C"
+lose_states: "B D"
+
+children: """
+root pacLeft minLeft
+root pacRight minRight
+minLeft gLeft A
+minLeft gRight B
+minRight gLeft C
+minRight gRight deeper
+deeper pacLeft D
+"""
+
+evaluation: """
+A 4.0
+B 3.0
+C 2.0
+D 1000.0
+"""
diff --git a/HW2_pacman/test_cases/part1/1-1-minmax.solution b/HW2_pacman/test_cases/part1/1-1-minmax.solution
new file mode 100644
index 0000000..3ac7510
--- /dev/null
+++ b/HW2_pacman/test_cases/part1/1-1-minmax.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q2/1-1-minmax.test.
+action: "Left"
+generated: "a b1 b2 c1 c2 cx d1 d2 d3 d4 dx"
diff --git a/HW2_pacman/test_cases/part1/1-1-minmax.test b/HW2_pacman/test_cases/part1/1-1-minmax.test
new file mode 100644
index 0000000..06d5e36
--- /dev/null
+++ b/HW2_pacman/test_cases/part1/1-1-minmax.test
@@ -0,0 +1,47 @@
+class: "GraphGameTreeTest"
+alg: "MinimaxAgent"
+depth: "3"
+
+diagram: """
+            /-----a------\
+           /              \
+          /                \
+        b1                  b2
+      /    \                 |
+   c1        c2             cx
+  /  \      /  \             |
+ d1   d2  d3   d4           dx
+-3    -9  10    6         -3.01
+
+a - max
+b - min
+c - max
+
+Note that the minimax value of b1 is -3.
+"""
+num_agents: "2"
+
+start_state: "a"
+win_states: "d1 d2 d3 d4 dx"
+lose_states: ""
+
+children: """
+a Left b1
+a Right b2
+b1 Left c1
+b1 Right c2
+b2 Down cx
+c1 Left d1
+c1 Right d2
+c2 Left d3
+c2 Right d4
+cx Down dx
+"""
+
+evaluation: """
+d1 -3.0
+d2 -9.0
+d3 10.0
+d4 6.0
+dx -3.01
+"""
diff --git a/HW2_pacman/test_cases/part1/1-2-minmax.solution b/HW2_pacman/test_cases/part1/1-2-minmax.solution
new file mode 100644
index 0000000..e40e3de
--- /dev/null
+++ b/HW2_pacman/test_cases/part1/1-2-minmax.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q2/1-2-minmax.test.
+action: "Right"
+generated: "a b1 b2 c1 c2 cx d1 d2 d3 d4 dx"
diff --git a/HW2_pacman/test_cases/part1/1-2-minmax.test b/HW2_pacman/test_cases/part1/1-2-minmax.test
new file mode 100644
index 0000000..5fc8df2
--- /dev/null
+++ b/HW2_pacman/test_cases/part1/1-2-minmax.test
@@ -0,0 +1,47 @@
+class: "GraphGameTreeTest"
+alg: "MinimaxAgent"
+depth: "3"
+
+diagram: """
+            /-----a------\
+           /              \
+          /                \
+        b1                  b2
+      /    \                 |
+   c1        c2             cx
+  /  \      /  \             |
+ d1   d2  d3   d4           dx
+-3    -9  10    6         -2.99
+
+a - max
+b - min
+c - max
+
+Note that the minimax value of b1 is -3.
+"""
+num_agents: "2"
+
+start_state: "a"
+win_states: "d1 d2 d3 d4 dx"
+lose_states: ""
+
+children: """
+a Left b1
+a Right b2
+b1 Left c1
+b1 Right c2
+b2 Down cx
+c1 Left d1
+c1 Right d2
+c2 Left d3
+c2 Right d4
+cx Down dx
+"""
+
+evaluation: """
+d1 -3.0
+d2 -9.0
+d3 10.0
+d4 6.0
+dx -2.99
+"""
diff --git a/HW2_pacman/test_cases/part1/1-3-minmax.solution b/HW2_pacman/test_cases/part1/1-3-minmax.solution
new file mode 100644
index 0000000..513961c
--- /dev/null
+++ b/HW2_pacman/test_cases/part1/1-3-minmax.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q2/1-3-minmax.test.
+action: "Left"
+generated: "a b1 b2 c3 c4 cx d5 d6 d7 d8 dx"
diff --git a/HW2_pacman/test_cases/part1/1-3-minmax.test b/HW2_pacman/test_cases/part1/1-3-minmax.test
new file mode 100644
index 0000000..0f4df68
--- /dev/null
+++ b/HW2_pacman/test_cases/part1/1-3-minmax.test
@@ -0,0 +1,47 @@
+class: "GraphGameTreeTest"
+alg: "MinimaxAgent"
+depth: "3"
+
+diagram: """
+            /-----a------\
+           /              \
+          /                \
+        b1                  b2
+         |                /    \
+        cx             c3        c4
+         |            /   \     /   \
+        dx           d5   d6   d7   d8
+       4.01          4    -7   0    5
+
+a - max
+b - min
+c - max
+
+Note that the minimax value of b2 is 4.
+"""
+num_agents: "2"
+
+start_state: "a"
+win_states: "d1 d2 d3 d4 d5 d6 d7 d8 dx"
+lose_states: ""
+
+children: """
+a Left b1
+a Right b2
+b1 Down cx
+b2 Left c3
+b2 Right c4
+c3 Left d5
+c3 Right d6
+c4 Left d7
+c4 Right d8
+cx Down dx
+"""
+
+evaluation: """
+d5 4.0
+d6 -7.0
+d7 0.0
+d8 5.0
+dx 4.01
+"""
diff --git a/HW2_pacman/test_cases/part1/1-4-minmax.solution b/HW2_pacman/test_cases/part1/1-4-minmax.solution
new file mode 100644
index 0000000..1ae4c0f
--- /dev/null
+++ b/HW2_pacman/test_cases/part1/1-4-minmax.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q2/1-4-minmax.test.
+action: "Right"
+generated: "a b1 b2 c3 c4 cx d5 d6 d7 d8 dx"
diff --git a/HW2_pacman/test_cases/part1/1-4-minmax.test b/HW2_pacman/test_cases/part1/1-4-minmax.test
new file mode 100644
index 0000000..9ac8314
--- /dev/null
+++ b/HW2_pacman/test_cases/part1/1-4-minmax.test
@@ -0,0 +1,47 @@
+class: "GraphGameTreeTest"
+alg: "MinimaxAgent"
+depth: "3"
+
+diagram: """
+            /-----a------\
+           /              \
+          /                \
+        b1                  b2
+         |                /    \
+        cx             c3        c4
+         |            /   \     /   \
+        dx           d5   d6   d7   d8
+       3.99          4    -7   0    5
+
+a - max
+b - min
+c - max
+
+Note that the minimax value of b2 is 4.
+"""
+num_agents: "2"
+
+start_state: "a"
+win_states: "d1 d2 d3 d4 d5 d6 d7 d8 dx"
+lose_states: ""
+
+children: """
+a Left b1
+a Right b2
+b1 Down cx
+b2 Left c3
+b2 Right c4
+c3 Left d5
+c3 Right d6
+c4 Left d7
+c4 Right d8
+cx Down dx
+"""
+
+evaluation: """
+d5 4.0
+d6 -7.0
+d7 0.0
+d8 5.0
+dx 3.99
+"""
diff --git a/HW2_pacman/test_cases/part1/1-5-minmax.solution b/HW2_pacman/test_cases/part1/1-5-minmax.solution
new file mode 100644
index 0000000..0553ca7
--- /dev/null
+++ b/HW2_pacman/test_cases/part1/1-5-minmax.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q2/1-5-minmax.test.
+action: "Right"
+generated: "A B C D E F G H Z a b1 b2 c1 c2 cx d1 d2 d3 d4 dx"
diff --git a/HW2_pacman/test_cases/part1/1-5-minmax.test b/HW2_pacman/test_cases/part1/1-5-minmax.test
new file mode 100644
index 0000000..93e0818
--- /dev/null
+++ b/HW2_pacman/test_cases/part1/1-5-minmax.test
@@ -0,0 +1,75 @@
+class: "GraphGameTreeTest"
+alg: "MinimaxAgent"
+depth: "4"
+
+diagram: """
+             /-----a------\
+            /              \
+           /                \
+         b1                  b2
+       /    \                |
+    c1        c2             cx
+   /  \      /  \            |
+  d1   d2  d3   d4           dx
+ / \  / \  / \  / \          |
+ A B  C D  E F  G H          Z
+-3 13 5 9 10 3 -6 8        3.01
+
+a - max
+b - min
+c - max
+d - min
+
+Note the minimax value of b1 is 3.
+"""
+num_agents: "2"
+
+start_state: "a"
+win_states: "A B C D E F G H I J K L M N O P Z"
+lose_states: ""
+
+children: """
+a Left b1
+a Right b2
+b1 Left c1
+b1 Right c2
+b2 Down cx
+c1 Left d1
+c1 Right d2
+c2 Left d3
+c2 Right d4
+c3 Left d5
+c3 Right d6
+c4 Left d7
+c4 Right d8
+cx Down dx
+d1 Left A
+d1 Right B
+d2 Left C
+d2 Right D
+d3 Left E
+d3 Right F
+d4 Left G
+d4 Right H
+d5 Left I
+d5 Right J
+d6 Left K
+d6 Right L
+d7 Left M
+d7 Right N
+d8 Left O
+d8 Right P
+dx Down Z
+"""
+
+evaluation: """
+A -3.0
+B 13.0
+C 5.0
+D 9.0
+E 10.0
+F 3.0
+G -6.0
+H 8.0
+Z 3.01
+"""
diff --git a/HW2_pacman/test_cases/part1/1-6-minmax.solution b/HW2_pacman/test_cases/part1/1-6-minmax.solution
new file mode 100644
index 0000000..f25e068
--- /dev/null
+++ b/HW2_pacman/test_cases/part1/1-6-minmax.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q2/1-6-minmax.test.
+action: "Left"
+generated: "A B C D E F G H Z a b1 b2 c1 c2 cx d1 d2 d3 d4 dx"
diff --git a/HW2_pacman/test_cases/part1/1-6-minmax.test b/HW2_pacman/test_cases/part1/1-6-minmax.test
new file mode 100644
index 0000000..3af1e5c
--- /dev/null
+++ b/HW2_pacman/test_cases/part1/1-6-minmax.test
@@ -0,0 +1,75 @@
+class: "GraphGameTreeTest"
+alg: "MinimaxAgent"
+depth: "4"
+
+diagram: """
+             /-----a------\
+            /              \
+           /                \
+         b1                  b2
+       /    \                |
+    c1        c2             cx
+   /  \      /  \            |
+  d1   d2  d3   d4           dx
+ / \  / \  / \  / \          |
+ A B  C D  E F  G H          Z
+-3 13 5 9 10 3 -6 8        2.99
+
+a - max
+b - min
+c - max
+d - min
+
+Note the minimax value of b1 is 3.
+"""
+num_agents: "2"
+
+start_state: "a"
+win_states: "A B C D E F G H I J K L M N O P Z"
+lose_states: ""
+
+children: """
+a Left b1
+a Right b2
+b1 Left c1
+b1 Right c2
+b2 Down cx
+c1 Left d1
+c1 Right d2
+c2 Left d3
+c2 Right d4
+c3 Left d5
+c3 Right d6
+c4 Left d7
+c4 Right d8
+cx Down dx
+d1 Left A
+d1 Right B
+d2 Left C
+d2 Right D
+d3 Left E
+d3 Right F
+d4 Left G
+d4 Right H
+d5 Left I
+d5 Right J
+d6 Left K
+d6 Right L
+d7 Left M
+d7 Right N
+d8 Left O
+d8 Right P
+dx Down Z
+"""
+
+evaluation: """
+A -3.0
+B 13.0
+C 5.0
+D 9.0
+E 10.0
+F 3.0
+G -6.0
+H 8.0
+Z 2.99
+"""
diff --git a/HW2_pacman/test_cases/part1/1-7-minmax.solution b/HW2_pacman/test_cases/part1/1-7-minmax.solution
new file mode 100644
index 0000000..fd801a8
--- /dev/null
+++ b/HW2_pacman/test_cases/part1/1-7-minmax.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q2/1-7-minmax.test.
+action: "Left"
+generated: "I J K L M N O P Z a b1 b2 c3 c4 cx d5 d6 d7 d8 dx"
diff --git a/HW2_pacman/test_cases/part1/1-7-minmax.test b/HW2_pacman/test_cases/part1/1-7-minmax.test
new file mode 100644
index 0000000..6c5474a
--- /dev/null
+++ b/HW2_pacman/test_cases/part1/1-7-minmax.test
@@ -0,0 +1,75 @@
+class: "GraphGameTreeTest"
+alg: "MinimaxAgent"
+depth: "4"
+
+diagram: """
+            /-----a------\
+           /              \
+          /                \
+        b1                  b2
+        |                 /    \
+        cx             c3        c4
+        |             /   \     /   \
+        dx           d5   d6   d7   d8
+        |           / \  / \  / \  / \ 
+        Z           I J  K L  M N  O P
+     -1.99        -1 -9  4 7  2 5 -3 -2
+
+a - max
+b - min
+c - min
+d - max
+
+Note that the minimax value of b2 is -2
+"""
+num_agents: "3"
+
+start_state: "a"
+win_states: "A B C D E F G H I J K L M N O P Z"
+lose_states: ""
+
+children: """
+a Left b1
+a Right b2
+b1 Down cx
+b2 Left c3
+b2 Right c4
+c1 Left d1
+c1 Right d2
+c2 Left d3
+c2 Right d4
+c3 Left d5
+c3 Right d6
+c4 Left d7
+c4 Right d8
+cx Down dx
+d1 Left A
+d1 Right B
+d2 Left C
+d2 Right D
+d3 Left E
+d3 Right F
+d4 Left G
+d4 Right H
+d5 Left I
+d5 Right J
+d6 Left K
+d6 Right L
+d7 Left M
+d7 Right N
+d8 Left O
+d8 Right P
+dx Down Z
+"""
+
+evaluation: """
+I -1.0
+J -9.0
+K 4.0
+L 7.0
+M 2.0
+N 5.0
+O -3.0
+P -2.0
+Z -1.99
+"""
diff --git a/HW2_pacman/test_cases/part1/1-8-minmax.solution b/HW2_pacman/test_cases/part1/1-8-minmax.solution
new file mode 100644
index 0000000..80c7ebe
--- /dev/null
+++ b/HW2_pacman/test_cases/part1/1-8-minmax.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q2/1-8-minmax.test.
+action: "Right"
+generated: "I J K L M N O P Z a b1 b2 c3 c4 cx d5 d6 d7 d8 dx"
diff --git a/HW2_pacman/test_cases/part1/1-8-minmax.test b/HW2_pacman/test_cases/part1/1-8-minmax.test
new file mode 100644
index 0000000..6883664
--- /dev/null
+++ b/HW2_pacman/test_cases/part1/1-8-minmax.test
@@ -0,0 +1,75 @@
+class: "GraphGameTreeTest"
+alg: "MinimaxAgent"
+depth: "4"
+
+diagram: """
+            /-----a------\
+           /              \
+          /                \
+        b1                  b2
+        |                 /    \
+        cx             c3        c4
+        |             /   \     /   \
+        dx           d5   d6   d7   d8 
+        |           / \  / \  / \  / \ 
+        Z           I J  K L  M N  O P
+     -2.01        -1 -9  4 7  2 5 -3 -2
+
+a - max
+b - min
+c - min
+d - max
+
+Note that the minimax value of b2 is -2.01
+"""
+num_agents: "3"
+
+start_state: "a"
+win_states: "A B C D E F G H I J K L M N O P Z"
+lose_states: ""
+
+children: """
+a Left b1
+a Right b2
+b1 Down cx
+b2 Left c3
+b2 Right c4
+c1 Left d1
+c1 Right d2
+c2 Left d3
+c2 Right d4
+c3 Left d5
+c3 Right d6
+c4 Left d7
+c4 Right d8
+cx Down dx
+d1 Left A
+d1 Right B
+d2 Left C
+d2 Right D
+d3 Left E
+d3 Right F
+d4 Left G
+d4 Right H
+d5 Left I
+d5 Right J
+d6 Left K
+d6 Right L
+d7 Left M
+d7 Right N
+d8 Left O
+d8 Right P
+dx Down Z
+"""
+
+evaluation: """
+I -1.0
+J -9.0
+K 4.0
+L 7.0
+M 2.0
+N 5.0
+O -3.0
+P -2.0
+Z -2.01
+"""
diff --git a/HW2_pacman/test_cases/part1/2-1a-vary-depth.solution b/HW2_pacman/test_cases/part1/2-1a-vary-depth.solution
new file mode 100644
index 0000000..9dd1708
--- /dev/null
+++ b/HW2_pacman/test_cases/part1/2-1a-vary-depth.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q2/2-1a-vary-depth.test.
+action: "Left"
+generated: "a b1 b2 c1 c2 cx"
diff --git a/HW2_pacman/test_cases/part1/2-1a-vary-depth.test b/HW2_pacman/test_cases/part1/2-1a-vary-depth.test
new file mode 100644
index 0000000..aaba3c2
--- /dev/null
+++ b/HW2_pacman/test_cases/part1/2-1a-vary-depth.test
@@ -0,0 +1,52 @@
+class: "GraphGameTreeTest"
+alg: "MinimaxAgent"
+depth: "1"
+
+diagram: """
+            /-----a------\
+           /              \
+          /                \
+        b1                  b2
+      /    \                 |
+-4 c1        c2 9           cx -4.01
+  /  \      /  \             |
+ d1   d2  d3   d4           dx
+-3    -9  10    6         -4.01
+
+a - max
+b - min
+c - max
+
+Note that the minimax value of b1 is -3, but the depth=1 limited value is -4.
+The values next to c1, c2, and cx are the values of the evaluation function, not
+necessarily the correct minimax backup.
+"""
+num_agents: "2"
+
+start_state: "a"
+win_states: "d1 d2 d3 d4 dx"
+lose_states: ""
+
+children: """
+a Left b1
+a Right b2
+b1 Left c1
+b1 Right c2
+b2 Down cx
+c1 Left d1
+c1 Right d2
+c2 Left d3
+c2 Right d4
+cx Down dx
+"""
+
+evaluation: """
+c1 -4.0
+c2 9.0
+cx -4.01
+d1 -3.0
+d2 -9.0
+d3 10.0
+d4 6.0
+dx -4.01
+"""
diff --git a/HW2_pacman/test_cases/part1/2-1b-vary-depth.solution b/HW2_pacman/test_cases/part1/2-1b-vary-depth.solution
new file mode 100644
index 0000000..a824e44
--- /dev/null
+++ b/HW2_pacman/test_cases/part1/2-1b-vary-depth.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q2/2-1b-vary-depth.test.
+action: "Left"
+generated: "a b1 b2 c1 c2 cx d1 d2 d3 d4 dx"
diff --git a/HW2_pacman/test_cases/part1/2-1b-vary-depth.test b/HW2_pacman/test_cases/part1/2-1b-vary-depth.test
new file mode 100644
index 0000000..f9a79c3
--- /dev/null
+++ b/HW2_pacman/test_cases/part1/2-1b-vary-depth.test
@@ -0,0 +1,52 @@
+class: "GraphGameTreeTest"
+alg: "MinimaxAgent"
+depth: "2"
+
+diagram: """
+            /-----a------\
+           /              \
+          /                \
+        b1                  b2
+      /    \                 |
+-4 c1        c2 9           cx -4.01
+  /  \      /  \             |
+ d1   d2  d3   d4           dx
+-3    -9  10    6         -4.01
+
+a - max
+b - min
+c - max
+
+Note that the minimax value of b1 is -3, but the depth=1 limited value is -4.
+The values next to c1, c2, and cx are the values of the evaluation function, not
+necessarily the correct minimax backup.
+"""
+num_agents: "2"
+
+start_state: "a"
+win_states: "d1 d2 d3 d4 dx"
+lose_states: ""
+
+children: """
+a Left b1
+a Right b2
+b1 Left c1
+b1 Right c2
+b2 Down cx
+c1 Left d1
+c1 Right d2
+c2 Left d3
+c2 Right d4
+cx Down dx
+"""
+
+evaluation: """
+c1 -4.0
+c2 9.0
+cx -4.01
+d1 -3.0
+d2 -9.0
+d3 10.0
+d4 6.0
+dx -4.01
+"""
diff --git a/HW2_pacman/test_cases/part1/2-2a-vary-depth.solution b/HW2_pacman/test_cases/part1/2-2a-vary-depth.solution
new file mode 100644
index 0000000..b4b0e98
--- /dev/null
+++ b/HW2_pacman/test_cases/part1/2-2a-vary-depth.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q2/2-2a-vary-depth.test.
+action: "Right"
+generated: "a b1 b2 c1 c2 cx"
diff --git a/HW2_pacman/test_cases/part1/2-2a-vary-depth.test b/HW2_pacman/test_cases/part1/2-2a-vary-depth.test
new file mode 100644
index 0000000..093522b
--- /dev/null
+++ b/HW2_pacman/test_cases/part1/2-2a-vary-depth.test
@@ -0,0 +1,52 @@
+class: "GraphGameTreeTest"
+alg: "MinimaxAgent"
+depth: "1"
+
+diagram: """
+            /-----a------\
+           /              \
+          /                \
+        b1                  b2
+      /    \                 |
+-4 c1        c2 9           cx -3.99
+  /  \      /  \             |
+ d1   d2  d3   d4           dx
+-3    -9  10    6         -3.99
+
+a - max
+b - min
+c - max
+
+Note that the minimax value of b1 is -3, but the depth=1 limited value is -4.
+The values next to c1, c2, and cx are the values of the evaluation function, not
+necessarily the correct minimax backup.
+"""
+num_agents: "2"
+
+start_state: "a"
+win_states: "d1 d2 d3 d4 dx"
+lose_states: ""
+
+children: """
+a Left b1
+a Right b2
+b1 Left c1
+b1 Right c2
+b2 Down cx
+c1 Left d1
+c1 Right d2
+c2 Left d3
+c2 Right d4
+cx Down dx
+"""
+
+evaluation: """
+c1 -4.0
+c2 9.0
+cx -3.99
+d1 -3.0
+d2 -9.0
+d3 10.0
+d4 6.0
+dx -3.99
+"""
diff --git a/HW2_pacman/test_cases/part1/2-2b-vary-depth.solution b/HW2_pacman/test_cases/part1/2-2b-vary-depth.solution
new file mode 100644
index 0000000..94e2089
--- /dev/null
+++ b/HW2_pacman/test_cases/part1/2-2b-vary-depth.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q2/2-2b-vary-depth.test.
+action: "Left"
+generated: "a b1 b2 c1 c2 cx d1 d2 d3 d4 dx"
diff --git a/HW2_pacman/test_cases/part1/2-2b-vary-depth.test b/HW2_pacman/test_cases/part1/2-2b-vary-depth.test
new file mode 100644
index 0000000..3478e0f
--- /dev/null
+++ b/HW2_pacman/test_cases/part1/2-2b-vary-depth.test
@@ -0,0 +1,52 @@
+class: "GraphGameTreeTest"
+alg: "MinimaxAgent"
+depth: "2"
+
+diagram: """
+            /-----a------\
+           /              \
+          /                \
+        b1                  b2
+      /    \                 |
+-4 c1        c2 9           cx -3.99
+  /  \      /  \             |
+ d1   d2  d3   d4           dx
+-3    -9  10    6         -3.99
+
+a - max
+b - min
+c - max
+
+Note that the minimax value of b1 is -3, but the depth=1 limited value is -4.
+The values next to c1, c2, and cx are the values of the evaluation function, not
+necessarily the correct minimax backup.
+"""
+num_agents: "2"
+
+start_state: "a"
+win_states: "d1 d2 d3 d4 dx"
+lose_states: ""
+
+children: """
+a Left b1
+a Right b2
+b1 Left c1
+b1 Right c2
+b2 Down cx
+c1 Left d1
+c1 Right d2
+c2 Left d3
+c2 Right d4
+cx Down dx
+"""
+
+evaluation: """
+c1 -4.0
+c2 9.0
+cx -3.99
+d1 -3.0
+d2 -9.0
+d3 10.0
+d4 6.0
+dx -3.99
+"""
diff --git a/HW2_pacman/test_cases/part1/2-3a-vary-depth.solution b/HW2_pacman/test_cases/part1/2-3a-vary-depth.solution
new file mode 100644
index 0000000..1bab661
--- /dev/null
+++ b/HW2_pacman/test_cases/part1/2-3a-vary-depth.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q2/2-3a-vary-depth.test.
+action: "Left"
+generated: "a b1 b2 c3 c4 cx"
diff --git a/HW2_pacman/test_cases/part1/2-3a-vary-depth.test b/HW2_pacman/test_cases/part1/2-3a-vary-depth.test
new file mode 100644
index 0000000..6fb311f
--- /dev/null
+++ b/HW2_pacman/test_cases/part1/2-3a-vary-depth.test
@@ -0,0 +1,52 @@
+class: "GraphGameTreeTest"
+alg: "MinimaxAgent"
+depth: "1"
+
+diagram: """
+            /-----a------\
+           /              \
+          /                \
+        b1                  b2
+         |                /    \
+ 5.01   cx          8  c3        c4   5
+         |            /   \     /   \
+        dx           d5   d6   d7   d8
+       5.01          4    -7   0    5
+
+a - max
+b - min
+c - max
+
+Note that the minimax value of b1 is 4, but the depth=1 limited value is 5.
+The values next to c3, c4, and cx are the values of the evaluation function, not
+necessarily the correct minimax backup.
+"""
+num_agents: "2"
+
+start_state: "a"
+win_states: "d1 d2 d3 d4 d5 d6 d7 d8 dx"
+lose_states: ""
+
+children: """
+a Left b1
+a Right b2
+b1 Down cx
+b2 Left c3
+b2 Right c4
+c3 Left d5
+c3 Right d6
+c4 Left d7
+c4 Right d8
+cx Down dx
+"""
+
+evaluation: """
+c3 8.0
+c4 5.0
+cx 5.01
+d5 4.0
+d6 -7.0
+d7 0.0
+d8 5.0
+dx 5.01
+"""
diff --git a/HW2_pacman/test_cases/part1/2-3b-vary-depth.solution b/HW2_pacman/test_cases/part1/2-3b-vary-depth.solution
new file mode 100644
index 0000000..fb389ec
--- /dev/null
+++ b/HW2_pacman/test_cases/part1/2-3b-vary-depth.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q2/2-3b-vary-depth.test.
+action: "Left"
+generated: "a b1 b2 c3 c4 cx d5 d6 d7 d8 dx"
diff --git a/HW2_pacman/test_cases/part1/2-3b-vary-depth.test b/HW2_pacman/test_cases/part1/2-3b-vary-depth.test
new file mode 100644
index 0000000..e4acbb0
--- /dev/null
+++ b/HW2_pacman/test_cases/part1/2-3b-vary-depth.test
@@ -0,0 +1,52 @@
+class: "GraphGameTreeTest"
+alg: "MinimaxAgent"
+depth: "2"
+
+diagram: """
+            /-----a------\
+           /              \
+          /                \
+        b1                  b2
+         |                /    \
+ 5.01   cx          8  c3        c4   5
+         |            /   \     /   \
+        dx           d5   d6   d7   d8
+       5.01          4    -7   0    5
+
+a - max
+b - min
+c - max
+
+Note that the minimax value of b1 is 4, but the depth=1 limited value is 5.
+The values next to c3, c4, and cx are the values of the evaluation function, not
+necessarily the correct minimax backup.
+"""
+num_agents: "2"
+
+start_state: "a"
+win_states: "d1 d2 d3 d4 d5 d6 d7 d8 dx"
+lose_states: ""
+
+children: """
+a Left b1
+a Right b2
+b1 Down cx
+b2 Left c3
+b2 Right c4
+c3 Left d5
+c3 Right d6
+c4 Left d7
+c4 Right d8
+cx Down dx
+"""
+
+evaluation: """
+c3 8.0
+c4 5.0
+cx 5.01
+d5 4.0
+d6 -7.0
+d7 0.0
+d8 5.0
+dx 5.01
+"""
diff --git a/HW2_pacman/test_cases/part1/2-4a-vary-depth.solution b/HW2_pacman/test_cases/part1/2-4a-vary-depth.solution
new file mode 100644
index 0000000..815147d
--- /dev/null
+++ b/HW2_pacman/test_cases/part1/2-4a-vary-depth.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q2/2-4a-vary-depth.test.
+action: "Right"
+generated: "a b1 b2 c3 c4 cx"
diff --git a/HW2_pacman/test_cases/part1/2-4a-vary-depth.test b/HW2_pacman/test_cases/part1/2-4a-vary-depth.test
new file mode 100644
index 0000000..1b0b885
--- /dev/null
+++ b/HW2_pacman/test_cases/part1/2-4a-vary-depth.test
@@ -0,0 +1,52 @@
+class: "GraphGameTreeTest"
+alg: "MinimaxAgent"
+depth: "1"
+
+diagram: """
+            /-----a------\
+           /              \
+          /                \
+        b1                  b2
+         |                /    \
+ 4.99   cx          8  c3        c4   5
+         |            /   \     /   \
+        dx           d5   d6   d7   d8
+       4.99          4    -7   0    5
+
+a - max
+b - min
+c - max
+
+Note that the minimax value of b1 is 4, but the depth=1 limited value is 5.
+The values next to c3, c4, and cx are the values of the evaluation function, not
+necessarily the correct minimax backup.
+"""
+num_agents: "2"
+
+start_state: "a"
+win_states: "d1 d2 d3 d4 d5 d6 d7 d8 dx"
+lose_states: ""
+
+children: """
+a Left b1
+a Right b2
+b1 Down cx
+b2 Left c3
+b2 Right c4
+c3 Left d5
+c3 Right d6
+c4 Left d7
+c4 Right d8
+cx Down dx
+"""
+
+evaluation: """
+c3 8.0
+c4 5.0
+cx 4.99
+d5 4.0
+d6 -7.0
+d7 0.0
+d8 5.0
+dx 4.99
+"""
diff --git a/HW2_pacman/test_cases/part1/2-4b-vary-depth.solution b/HW2_pacman/test_cases/part1/2-4b-vary-depth.solution
new file mode 100644
index 0000000..3b12519
--- /dev/null
+++ b/HW2_pacman/test_cases/part1/2-4b-vary-depth.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q2/2-4b-vary-depth.test.
+action: "Left"
+generated: "a b1 b2 c3 c4 cx d5 d6 d7 d8 dx"
diff --git a/HW2_pacman/test_cases/part1/2-4b-vary-depth.test b/HW2_pacman/test_cases/part1/2-4b-vary-depth.test
new file mode 100644
index 0000000..f0426b2
--- /dev/null
+++ b/HW2_pacman/test_cases/part1/2-4b-vary-depth.test
@@ -0,0 +1,52 @@
+class: "GraphGameTreeTest"
+alg: "MinimaxAgent"
+depth: "2"
+
+diagram: """
+            /-----a------\
+           /              \
+          /                \
+        b1                  b2
+         |                /    \
+ 4.99   cx          8  c3        c4   5
+         |            /   \     /   \
+        dx           d5   d6   d7   d8
+       4.99          4    -7   0    5
+
+a - max
+b - min
+c - max
+
+Note that the minimax value of b1 is 4, but the depth=1 limited value is 5.
+The values next to c3, c4, and cx are the values of the evaluation function, not
+necessarily the correct minimax backup.
+"""
+num_agents: "2"
+
+start_state: "a"
+win_states: "d1 d2 d3 d4 d5 d6 d7 d8 dx"
+lose_states: ""
+
+children: """
+a Left b1
+a Right b2
+b1 Down cx
+b2 Left c3
+b2 Right c4
+c3 Left d5
+c3 Right d6
+c4 Left d7
+c4 Right d8
+cx Down dx
+"""
+
+evaluation: """
+c3 8.0
+c4 5.0
+cx 4.99
+d5 4.0
+d6 -7.0
+d7 0.0
+d8 5.0
+dx 4.99
+"""
diff --git a/HW2_pacman/test_cases/part1/2-one-ghost-3level.solution b/HW2_pacman/test_cases/part1/2-one-ghost-3level.solution
new file mode 100644
index 0000000..f7b10fb
--- /dev/null
+++ b/HW2_pacman/test_cases/part1/2-one-ghost-3level.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q2/2-one-ghost-3level.test.
+action: "Left"
+generated: "a b1 b2 c1 c2 c3 c4 d1 d2 d3 d4 d5 d6 d7 d8"
diff --git a/HW2_pacman/test_cases/part1/2-one-ghost-3level.test b/HW2_pacman/test_cases/part1/2-one-ghost-3level.test
new file mode 100644
index 0000000..cd365a3
--- /dev/null
+++ b/HW2_pacman/test_cases/part1/2-one-ghost-3level.test
@@ -0,0 +1,52 @@
+class: "GraphGameTreeTest"
+alg: "MinimaxAgent"
+depth: "3"
+
+diagram: """
+            /-----a------\
+           /              \
+          /                \
+        b1                  b2
+      /    \              /    \
+   c1        c2        c3        c4
+  /  \      /  \      /   \     /   \
+ d1   d2  d3   d4    d5   d6   d7   d8
+ 3    9   10   6     4    7    0    5
+
+a - max
+b - min
+c - max
+"""
+num_agents: "2"
+
+start_state: "a"
+win_states: "d1 d2 d3 d4 d5 d6 d7 d8"
+lose_states: ""
+
+children: """
+a Left b1
+a Right b2
+b1 Left c1
+b1 Right c2
+b2 Left c3
+b2 Right c4
+c1 Left d1
+c1 Right d2
+c2 Left d3
+c2 Right d4
+c3 Left d5
+c3 Right d6
+c4 Left d7
+c4 Right d8
+"""
+
+evaluation: """
+d1 3.0
+d2 9.0
+d3 10.0
+d4 6.0
+d5 4.0
+d6 7.0
+d7 0.0
+d8 5.0
+"""
diff --git a/HW2_pacman/test_cases/part1/3-one-ghost-4level.solution b/HW2_pacman/test_cases/part1/3-one-ghost-4level.solution
new file mode 100644
index 0000000..5fcb2c5
--- /dev/null
+++ b/HW2_pacman/test_cases/part1/3-one-ghost-4level.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q2/3-one-ghost-4level.test.
+action: "Left"
+generated: "A B C D E F G H I J K L M N O P a b1 b2 c1 c2 c3 c4 d1 d2 d3 d4 d5 d6 d7 d8"
diff --git a/HW2_pacman/test_cases/part1/3-one-ghost-4level.test b/HW2_pacman/test_cases/part1/3-one-ghost-4level.test
new file mode 100644
index 0000000..8138030
--- /dev/null
+++ b/HW2_pacman/test_cases/part1/3-one-ghost-4level.test
@@ -0,0 +1,79 @@
+class: "GraphGameTreeTest"
+alg: "MinimaxAgent"
+depth: "4"
+
+diagram: """
+            /-----a------\
+           /              \
+          /                \
+        b1                  b2
+      /    \              /    \
+   c1        c2        c3        c4
+  /  \      /  \      /   \     /   \
+ d1   d2  d3   d4    d5   d6   d7   d8
+/ \  / \  / \  / \   / \  / \  / \  / \ 
+A B  C D  E F  G H   I J  K L  M N  O P
+3 13 5 9 10 11 6 8   1 0  4 7 12 15 2 14
+
+a - max
+b - min
+c - max
+d - min
+"""
+num_agents: "2"
+
+start_state: "a"
+win_states: "A B C D E F G H I J K L M N O P"
+lose_states: ""
+
+children: """
+a Left b1
+a Right b2
+b1 Left c1
+b1 Right c2
+b2 Left c3
+b2 Right c4
+c1 Left d1
+c1 Right d2
+c2 Left d3
+c2 Right d4
+c3 Left d5
+c3 Right d6
+c4 Left d7
+c4 Right d8
+d1 Left A
+d1 Right B
+d2 Left C
+d2 Right D
+d3 Left E
+d3 Right F
+d4 Left G
+d4 Right H
+d5 Left I
+d5 Right J
+d6 Left K
+d6 Right L
+d7 Left M
+d7 Right N
+d8 Left O
+d8 Right P
+"""
+
+evaluation: """
+A 3.0
+B 13.0
+C 5.0
+D 9.0
+E 10.0
+F 11.0
+G 6.0
+H 8.0
+I 1.0
+J 0.0
+K 4.0
+L 7.0
+M 12.0
+N 15.0
+O 2.0
+P 14.0
+"""
diff --git a/HW2_pacman/test_cases/part1/4-two-ghosts-3level.solution b/HW2_pacman/test_cases/part1/4-two-ghosts-3level.solution
new file mode 100644
index 0000000..36a2326
--- /dev/null
+++ b/HW2_pacman/test_cases/part1/4-two-ghosts-3level.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q2/4-two-ghosts-3level.test.
+action: "Left"
+generated: "a b1 b2 c1 c2 c3 c4 d1 d2 d3 d4 d5 d6 d7 d8"
diff --git a/HW2_pacman/test_cases/part1/4-two-ghosts-3level.test b/HW2_pacman/test_cases/part1/4-two-ghosts-3level.test
new file mode 100644
index 0000000..39576ee
--- /dev/null
+++ b/HW2_pacman/test_cases/part1/4-two-ghosts-3level.test
@@ -0,0 +1,52 @@
+class: "GraphGameTreeTest"
+alg: "MinimaxAgent"
+depth: "3"
+
+diagram: """
+            /-----a------\
+           /              \
+          /                \
+        b1                  b2
+      /    \              /    \
+   c1        c2        c3        c4
+  /  \      /  \      /   \     /   \
+ d1   d2  d3   d4    d5   d6   d7   d8
+ 3    9   10   6     4    7    0    5
+
+a - max
+b - min
+c - min
+"""
+num_agents: "3"
+
+start_state: "a"
+win_states: "d1 d2 d3 d4 d5 d6 d7 d8"
+lose_states: ""
+
+children: """
+a Left b1
+a Right b2
+b1 Left c1
+b1 Right c2
+b2 Left c3
+b2 Right c4
+c1 Left d1
+c1 Right d2
+c2 Left d3
+c2 Right d4
+c3 Left d5
+c3 Right d6
+c4 Left d7
+c4 Right d8
+"""
+
+evaluation: """
+d1 3.0
+d2 9.0
+d3 10.0
+d4 6.0
+d5 4.0
+d6 7.0
+d7 0.0
+d8 5.0
+"""
diff --git a/HW2_pacman/test_cases/part1/5-two-ghosts-4level.solution b/HW2_pacman/test_cases/part1/5-two-ghosts-4level.solution
new file mode 100644
index 0000000..3164ec0
--- /dev/null
+++ b/HW2_pacman/test_cases/part1/5-two-ghosts-4level.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q2/5-two-ghosts-4level.test.
+action: "Left"
+generated: "A B C D E F G H I J K L M N O P a b1 b2 c1 c2 c3 c4 d1 d2 d3 d4 d5 d6 d7 d8"
diff --git a/HW2_pacman/test_cases/part1/5-two-ghosts-4level.test b/HW2_pacman/test_cases/part1/5-two-ghosts-4level.test
new file mode 100644
index 0000000..767041d
--- /dev/null
+++ b/HW2_pacman/test_cases/part1/5-two-ghosts-4level.test
@@ -0,0 +1,79 @@
+class: "GraphGameTreeTest"
+alg: "MinimaxAgent"
+depth: "4"
+
+diagram: """
+            /-----a------\
+           /              \
+          /                \
+        b1                  b2
+      /    \              /    \
+   c1        c2        c3        c4
+  /  \      /  \      /   \     /   \
+ d1   d2  d3   d4    d5   d6   d7   d8
+/ \  / \  / \  / \   / \  / \  / \  / \ 
+A B  C D  E F  G H   I J  K L  M N  O P
+3 13 5 9 10 11 6 8   1 0  4 7 12 15 2 14
+
+a - max
+b - min
+c - min
+d - max
+"""
+num_agents: "3"
+
+start_state: "a"
+win_states: "A B C D E F G H I J K L M N O P"
+lose_states: ""
+
+children: """
+a Left b1
+a Right b2
+b1 Left c1
+b1 Right c2
+b2 Left c3
+b2 Right c4
+c1 Left d1
+c1 Right d2
+c2 Left d3
+c2 Right d4
+c3 Left d5
+c3 Right d6
+c4 Left d7
+c4 Right d8
+d1 Left A
+d1 Right B
+d2 Left C
+d2 Right D
+d3 Left E
+d3 Right F
+d4 Left G
+d4 Right H
+d5 Left I
+d5 Right J
+d6 Left K
+d6 Right L
+d7 Left M
+d7 Right N
+d8 Left O
+d8 Right P
+"""
+
+evaluation: """
+A 3.0
+B 13.0
+C 5.0
+D 9.0
+E 10.0
+F 11.0
+G 6.0
+H 8.0
+I 1.0
+J 0.0
+K 4.0
+L 7.0
+M 12.0
+N 15.0
+O 2.0
+P 14.0
+"""
diff --git a/HW2_pacman/test_cases/part1/6-tied-root.solution b/HW2_pacman/test_cases/part1/6-tied-root.solution
new file mode 100644
index 0000000..61918b0
--- /dev/null
+++ b/HW2_pacman/test_cases/part1/6-tied-root.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q2/6-tied-root.test.
+action: "Left"
+generated: "A B C max min1 min2"
diff --git a/HW2_pacman/test_cases/part1/6-tied-root.test b/HW2_pacman/test_cases/part1/6-tied-root.test
new file mode 100644
index 0000000..804a913
--- /dev/null
+++ b/HW2_pacman/test_cases/part1/6-tied-root.test
@@ -0,0 +1,31 @@
+class: "GraphGameTreeTest"
+alg: "MinimaxAgent"
+depth: "3"
+
+diagram: """
+    max
+   /   \
+min1    min2
+ |      /  \
+ A      B   C
+10     10   0
+"""
+num_agents: "2"
+
+start_state: "max"
+win_states: "A B"
+lose_states: "C"
+
+children: """
+max Left min1
+max Right min2
+min1 Down A
+min2 Left B
+min2 Right C
+"""
+
+evaluation: """
+A 10.0
+B 10.0
+C 0.0
+"""
diff --git a/HW2_pacman/test_cases/part1/7-1a-check-depth-one-ghost.solution b/HW2_pacman/test_cases/part1/7-1a-check-depth-one-ghost.solution
new file mode 100644
index 0000000..0b7f01b
--- /dev/null
+++ b/HW2_pacman/test_cases/part1/7-1a-check-depth-one-ghost.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q2/7-1a-check-depth-one-ghost.test.
+action: "Left"
+generated: "a b1 b2 b3 c1 c2 c3"
diff --git a/HW2_pacman/test_cases/part1/7-1a-check-depth-one-ghost.test b/HW2_pacman/test_cases/part1/7-1a-check-depth-one-ghost.test
new file mode 100644
index 0000000..1c9a757
--- /dev/null
+++ b/HW2_pacman/test_cases/part1/7-1a-check-depth-one-ghost.test
@@ -0,0 +1,83 @@
+class: "GraphGameTreeTest"
+alg: "MinimaxAgent"
+depth: "1"
+
+diagram: """
+            a
+      /-/   |   \--\
+     /      |       \
+  0 b1    0 b2      b3 8
+    |       |        |
+ 10 c1    0 c2      c3 8
+    |       |        |
+  0 d1    0 d2      d3 8
+    |       |        |
+  0 e1   10 e2      e3 8
+    |       |        |
+  0 f1    0 f2      f3 8
+    |       |        |
+    g1      g2      g3
+    0       0        8
+
+a - max
+b - min
+c - max
+d - min
+e - max
+f - min
+
+At depth 1, the evaluation function is called at level c,
+so Left should be returned. If your algorithm is returning a
+different action, check how you implemented your depth.
+"""
+
+num_agents: "2"
+
+start_state: "a"
+win_states: "g1 g2 g3"
+lose_states: ""
+
+children: """
+a Left b1
+a Center b2
+a Right b3
+b1 Center c1
+b2 Center c2
+b3 Center c3
+c1 Center d1
+c2 Center d2
+c3 Center d3
+d1 Center e1
+d2 Center e2
+d3 Center e3
+e1 Center f1
+e2 Center f2
+e3 Center f3
+f1 Center g1
+f2 Center g2
+f3 Center g3
+"""
+
+
+evaluation: """
+b1 0.0
+b2 0.0
+b3 8.0
+c1 10.0
+c2 0.0
+c3 8.0
+d1 0.0
+d2 0.0
+d3 8.0
+e1 0.0
+e2 10.0
+e3 8.0
+f1 0.0
+f2 0.0
+f3 8.0
+g1 0.0
+g2 0.0
+g3 8.0
+"""
+
+
diff --git a/HW2_pacman/test_cases/part1/7-1b-check-depth-one-ghost.solution b/HW2_pacman/test_cases/part1/7-1b-check-depth-one-ghost.solution
new file mode 100644
index 0000000..e7e3c6f
--- /dev/null
+++ b/HW2_pacman/test_cases/part1/7-1b-check-depth-one-ghost.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q2/7-1b-check-depth-one-ghost.test.
+action: "Center"
+generated: "a b1 b2 b3 c1 c2 c3 d1 d2 d3 e1 e2 e3"
diff --git a/HW2_pacman/test_cases/part1/7-1b-check-depth-one-ghost.test b/HW2_pacman/test_cases/part1/7-1b-check-depth-one-ghost.test
new file mode 100644
index 0000000..150e101
--- /dev/null
+++ b/HW2_pacman/test_cases/part1/7-1b-check-depth-one-ghost.test
@@ -0,0 +1,83 @@
+class: "GraphGameTreeTest"
+alg: "MinimaxAgent"
+depth: "2"
+
+diagram: """
+            a
+      /-/   |   \--\
+     /      |       \
+  0 b1    0 b2      b3 8
+    |       |        |
+ 10 c1    0 c2      c3 8
+    |       |        |
+  0 d1    0 d2      d3 8
+    |       |        |
+  0 e1   10 e2      e3 8
+    |       |        |
+  0 f1    0 f2      f3 8
+    |       |        |
+    g1      g2      g3
+    0       0        8
+
+a - max
+b - min
+c - max
+d - min
+e - max
+f - min
+
+At depth 2, the evaluation function is called at level e,
+so Center should be returned. If your algorithm is returning a
+different action, check how you implemented your depth.
+"""
+
+num_agents: "2"
+
+start_state: "a"
+win_states: "g1 g2 g3"
+lose_states: ""
+
+children: """
+a Left b1
+a Center b2
+a Right b3
+b1 Center c1
+b2 Center c2
+b3 Center c3
+c1 Center d1
+c2 Center d2
+c3 Center d3
+d1 Center e1
+d2 Center e2
+d3 Center e3
+e1 Center f1
+e2 Center f2
+e3 Center f3
+f1 Center g1
+f2 Center g2
+f3 Center g3
+"""
+
+
+evaluation: """
+b1 0.0
+b2 0.0
+b3 8.0
+c1 10.0
+c2 0.0
+c3 8.0
+d1 0.0
+d2 0.0
+d3 8.0
+e1 0.0
+e2 10.0
+e3 8.0
+f1 0.0
+f2 0.0
+f3 8.0
+g1 0.0
+g2 0.0
+g3 8.0
+"""
+
+
diff --git a/HW2_pacman/test_cases/part1/7-1c-check-depth-one-ghost.solution b/HW2_pacman/test_cases/part1/7-1c-check-depth-one-ghost.solution
new file mode 100644
index 0000000..188854d
--- /dev/null
+++ b/HW2_pacman/test_cases/part1/7-1c-check-depth-one-ghost.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q2/7-1c-check-depth-one-ghost.test.
+action: "Right"
+generated: "a b1 b2 b3 c1 c2 c3 d1 d2 d3 e1 e2 e3 f1 f2 f3 g1 g2 g3"
diff --git a/HW2_pacman/test_cases/part1/7-1c-check-depth-one-ghost.test b/HW2_pacman/test_cases/part1/7-1c-check-depth-one-ghost.test
new file mode 100644
index 0000000..170698f
--- /dev/null
+++ b/HW2_pacman/test_cases/part1/7-1c-check-depth-one-ghost.test
@@ -0,0 +1,83 @@
+class: "GraphGameTreeTest"
+alg: "MinimaxAgent"
+depth: "3"
+
+diagram: """
+            a
+      /-/   |   \--\
+     /      |       \
+  0 b1    0 b2      b3 8
+    |       |        |
+ 10 c1    0 c2      c3 8
+    |       |        |
+  0 d1    0 d2      d3 8
+    |       |        |
+  0 e1   10 e2      e3 8
+    |       |        |
+  0 f1    0 f2      f3 8
+    |       |        |
+    g1      g2      g3
+    0       0        8
+
+a - max
+b - min
+c - max
+d - min
+e - max
+f - min
+
+At depth 3, the evaluation function is called at level g,
+so Right should be returned. If your algorithm is returning a
+different action, check how you implemented your depth.
+"""
+
+num_agents: "2"
+
+start_state: "a"
+win_states: "g1 g2 g3"
+lose_states: ""
+
+children: """
+a Left b1
+a Center b2
+a Right b3
+b1 Center c1
+b2 Center c2
+b3 Center c3
+c1 Center d1
+c2 Center d2
+c3 Center d3
+d1 Center e1
+d2 Center e2
+d3 Center e3
+e1 Center f1
+e2 Center f2
+e3 Center f3
+f1 Center g1
+f2 Center g2
+f3 Center g3
+"""
+
+
+evaluation: """
+b1 0.0
+b2 0.0
+b3 8.0
+c1 10.0
+c2 0.0
+c3 8.0
+d1 0.0
+d2 0.0
+d3 8.0
+e1 0.0
+e2 10.0
+e3 8.0
+f1 0.0
+f2 0.0
+f3 8.0
+g1 0.0
+g2 0.0
+g3 8.0
+"""
+
+
diff --git a/HW2_pacman/test_cases/part1/7-2a-check-depth-two-ghosts.solution b/HW2_pacman/test_cases/part1/7-2a-check-depth-two-ghosts.solution
new file mode 100644
index 0000000..649825a
--- /dev/null
+++ b/HW2_pacman/test_cases/part1/7-2a-check-depth-two-ghosts.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q2/7-2a-check-depth-two-ghosts.test.
+action: "Left"
+generated: "a b1 b2 b3 c1 c2 c3 d1 d2 d3"
diff --git a/HW2_pacman/test_cases/part1/7-2a-check-depth-two-ghosts.test b/HW2_pacman/test_cases/part1/7-2a-check-depth-two-ghosts.test
new file mode 100644
index 0000000..ad1081f
--- /dev/null
+++ b/HW2_pacman/test_cases/part1/7-2a-check-depth-two-ghosts.test
@@ -0,0 +1,110 @@
+class: "GraphGameTreeTest"
+alg: "MinimaxAgent"
+depth: "1"
+
+diagram: """
+            a
+      /-/   |   \--\
+     /      |       \
+  0 b1    0 b2      b3 8
+    |       |        |
+  0 c1    0 c2      c3 8
+    |       |        |
+ 10 d1    0 d2      d3 8
+    |       |        |
+  0 e1    0 e2      e3 8
+    |       |        |
+  0 f1    0 f2      f3 8
+    |       |        |
+  0 g1   10 g2      g3 8
+    |       |        |
+  0 h1    0 h2      h3 8
+    |       |        |
+  0 i1    0 i2      i3 8
+    |       |        |
+    j1      j2      j3
+    0       0        8
+
+a - max
+b - min
+c - min
+d - max
+e - min
+f - min
+g - max
+h - min
+i - min
+
+At depth 1, the evaluation function is called at level d,
+so Left should be returned. If your algorithm is returning a
+different action, check how you implemented your depth.
+"""
+
+num_agents: "3"
+
+start_state: "a"
+win_states: "j1 j2 j3"
+lose_states: ""
+
+children: """
+a Left b1
+a Center b2
+a Right b3
+b1 Center c1
+b2 Center c2
+b3 Center c3
+c1 Center d1
+c2 Center d2
+c3 Center d3
+d1 Center e1
+d2 Center e2
+d3 Center e3
+e1 Center f1
+e2 Center f2
+e3 Center f3
+f1 Center g1
+f2 Center g2
+f3 Center g3
+g1 Center h1
+g2 Center h2
+g3 Center h3
+h1 Center i1
+h2 Center i2
+h3 Center i3
+i1 Center j1
+i2 Center j2
+i3 Center j3
+"""
+
+
+evaluation: """
+b1 0.0
+b2 0.0
+b3 8.0
+c1 0.0
+c2 0.0
+c3 8.0
+d1 10.0
+d2 0.0
+d3 8.0
+e1 0.0
+e2 0.0
+e3 8.0
+f1 0.0
+f2 0.0
+f3 8.0
+g1 0.0
+g2 10.0
+g3 8.0
+h1 0.0
+h2 0.0
+h3 8.0
+i1 0.0
+i2 0.0
+i3 8.0
+j1 0.0
+j2 0.0
+j3 8.0
+"""
+
+
diff --git a/HW2_pacman/test_cases/part1/7-2b-check-depth-two-ghosts.solution b/HW2_pacman/test_cases/part1/7-2b-check-depth-two-ghosts.solution
new file mode 100644
index 0000000..440eaf8
--- /dev/null
+++ b/HW2_pacman/test_cases/part1/7-2b-check-depth-two-ghosts.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q2/7-2b-check-depth-two-ghosts.test.
+action: "Center"
+generated: "a b1 b2 b3 c1 c2 c3 d1 d2 d3 e1 e2 e3 f1 f2 f3 g1 g2 g3"
diff --git a/HW2_pacman/test_cases/part1/7-2b-check-depth-two-ghosts.test b/HW2_pacman/test_cases/part1/7-2b-check-depth-two-ghosts.test
new file mode 100644
index 0000000..3962f51
--- /dev/null
+++ b/HW2_pacman/test_cases/part1/7-2b-check-depth-two-ghosts.test
@@ -0,0 +1,110 @@
+class: "GraphGameTreeTest"
+alg: "MinimaxAgent"
+depth: "2"
+
+diagram: """
+            a
+      /-/   |   \--\
+     /      |       \
+  0 b1    0 b2      b3 8
+    |       |        |
+  0 c1    0 c2      c3 8
+    |       |        |
+ 10 d1    0 d2      d3 8
+    |       |        |
+  0 e1    0 e2      e3 8
+    |       |        |
+  0 f1    0 f2      f3 8
+    |       |        |
+  0 g1   10 g2      g3 8
+    |       |        |
+  0 h1    0 h2      h3 8
+    |       |        |
+  0 i1    0 i2      i3 8
+    |       |        |
+    j1      j2      j3
+    0       0        8
+
+a - max
+b - min
+c - min
+d - max
+e - min
+f - min
+g - max
+h - min
+i - min
+
+At depth 2, the evaluation function is called at level g,
+so Center should be returned. If your algorithm is returning
+a different action, check how you implemented your depth.
+"""
+
+num_agents: "3"
+
+start_state: "a"
+win_states: "j1 j2 j3"
+lose_states: ""
+
+children: """
+a Left b1
+a Center b2
+a Right b3
+b1 Center c1
+b2 Center c2
+b3 Center c3
+c1 Center d1
+c2 Center d2
+c3 Center d3
+d1 Center e1
+d2 Center e2
+d3 Center e3
+e1 Center f1
+e2 Center f2
+e3 Center f3
+f1 Center g1
+f2 Center g2
+f3 Center g3
+g1 Center h1
+g2 Center h2
+g3 Center h3
+h1 Center i1
+h2 Center i2
+h3 Center i3
+i1 Center j1
+i2 Center j2
+i3 Center j3
+"""
+
+
+evaluation: """
+b1 0.0
+b2 0.0
+b3 8.0
+c1 0.0
+c2 0.0
+c3 8.0
+d1 10.0
+d2 0.0
+d3 8.0
+e1 0.0
+e2 0.0
+e3 8.0
+f1 0.0
+f2 0.0
+f3 8.0
+g1 0.0
+g2 10.0
+g3 8.0
+h1 0.0
+h2 0.0
+h3 8.0
+i1 0.0
+i2 0.0
+i3 8.0
+j1 0.0
+j2 0.0
+j3 8.0
+"""
+
+
diff --git a/HW2_pacman/test_cases/part1/7-2c-check-depth-two-ghosts.solution b/HW2_pacman/test_cases/part1/7-2c-check-depth-two-ghosts.solution
new file mode 100644
index 0000000..fb146d8
--- /dev/null
+++ b/HW2_pacman/test_cases/part1/7-2c-check-depth-two-ghosts.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q2/7-2c-check-depth-two-ghosts.test.
+action: "Right"
+generated: "a b1 b2 b3 c1 c2 c3 d1 d2 d3 e1 e2 e3 f1 f2 f3 g1 g2 g3 h1 h2 h3 i1 i2 i3 j1 j2 j3"
diff --git a/HW2_pacman/test_cases/part1/7-2c-check-depth-two-ghosts.test b/HW2_pacman/test_cases/part1/7-2c-check-depth-two-ghosts.test
new file mode 100644
index 0000000..7f7a84b
--- /dev/null
+++ b/HW2_pacman/test_cases/part1/7-2c-check-depth-two-ghosts.test
@@ -0,0 +1,110 @@
+class: "GraphGameTreeTest"
+alg: "MinimaxAgent"
+depth: "3"
+
+diagram: """
+            a
+      /-/   |   \--\
+     /      |       \
+  0 b1    0 b2      b3 8
+    |       |        |
+  0 c1    0 c2      c3 8
+    |       |        |
+ 10 d1    0 d2      d3 8
+    |       |        |
+  0 e1    0 e2      e3 8
+    |       |        |
+  0 f1    0 f2      f3 8
+    |       |        |
+  0 g1   10 g2      g3 8
+    |       |        |
+  0 h1    0 h2      h3 8
+    |       |        |
+  0 i1    0 i2      i3 8
+    |       |        |
+    j1      j2      j3
+    0       0        8
+
+a - max
+b - min
+c - min
+d - max
+e - min
+f - min
+g - max
+h - min
+i - min
+
+At depth 3, the evaluation function is called at level j,
+so Right should be returned. If your algorithm is returning
+a different action, check how you implemented your depth.
+"""
+
+num_agents: "3"
+
+start_state: "a"
+win_states: "j1 j2 j3"
+lose_states: ""
+
+children: """
+a Left b1
+a Center b2
+a Right b3
+b1 Center c1
+b2 Center c2
+b3 Center c3
+c1 Center d1
+c2 Center d2
+c3 Center d3
+d1 Center e1
+d2 Center e2
+d3 Center e3
+e1 Center f1
+e2 Center f2
+e3 Center f3
+f1 Center g1
+f2 Center g2
+f3 Center g3
+g1 Center h1
+g2 Center h2
+g3 Center h3
+h1 Center i1
+h2 Center i2
+h3 Center i3
+i1 Center j1
+i2 Center j2
+i3 Center j3
+"""
+
+
+evaluation: """
+b1 0.0
+b2 0.0
+b3 8.0
+c1 0.0
+c2 0.0
+c3 8.0
+d1 10.0
+d2 0.0
+d3 8.0
+e1 0.0
+e2 0.0
+e3 8.0
+f1 0.0
+f2 0.0
+f3 8.0
+g1 0.0
+g2 10.0
+g3 8.0
+h1 0.0
+h2 0.0
+h3 8.0
+i1 0.0
+i2 0.0
+i3 8.0
+j1 0.0
+j2 0.0
+j3 8.0
+"""
+
+
diff --git a/HW2_pacman/test_cases/part1/8-pacman-game.solution b/HW2_pacman/test_cases/part1/8-pacman-game.solution
new file mode 100644
index 0000000..4ee19d8
--- /dev/null
+++ b/HW2_pacman/test_cases/part1/8-pacman-game.solution
@@ -0,0 +1,444 @@
+optimalActions: """
+[[["West", "East"], 59], [["West", "East"], 35]]
+[[["West"], 190], [["West"], 127]]
+[[["West"], 190], [["West"], 135]]
+[[["West", "North"], 120], [["West", "North"], 82]]
+[[["West"], 77], [["West"], 57]]
+[[["West", "North"], 143], [["West", "North"], 97]]
+[[["West"], 155], [["West"], 110]]
+[[["West"], 40], [["West"], 27]]
+[[["North"], 64], [["North"], 43]]
+[[["North"], 85], [["North"], 57]]
+[[["North"], 106], [["North"], 71]]
+[[["North"], 97], [["North"], 65]]
+[[["Stop", "East"], 154], [["East"], 103]]
+[[["East"], 156], [["East"], 101]]
+[[["West"], 30], [["West"], 17]]
+[[["South"], 15], [["South"], 9]]
+[[["South"], 15], [["South"], 9]]
+[[["South"], 15], [["South"], 9]]
+[[["South"], 15], [["South"], 9]]
+[[["East"], 15], [["East"], 9]]
+[[["East"], 15], [["East"], 9]]
+[[["East"], 18], [["East"], 12]]
+[[["North"], 29], [["North"], 18]]
+[[["North"], 50], [["North"], 31]]
+[[["West"], 55], [["West"], 36]]
+[[["East"], 29], [["East"], 16]]
+[[["North"], 89], [["North"], 61]]
+[[["East", "North"], 161], [["East", "North"], 121]]
+[[["East", "North"], 221], [["East", "North"], 166]]
+[[["North", "South"], 105], [["North", "South"], 77]]
+[[["West"], 69], [["West"], 51]]
+[[["West"], 94], [["West"], 69]]
+[[["West", "Stop"], 57], [["West"], 42]]
+[[["West", "Stop", "East"], 69], [["West", "East"], 49]]
+[[["West", "Stop", "East"], 61], [["West", "East"], 41]]
+[[["Stop", "East", "South"], 55], [["East", "South"], 37]]
+[[["Stop", "East", "South"], 28], [["East", "South"], 19]]
+[[["Stop", "East", "South"], 34], [["East", "South"], 23]]
+[[["Stop", "East", "South"], 55], [["East", "South"], 37]]
+[[["Stop", "East", "South"], 55], [["East", "South"], 37]]
+[[["Stop", "East", "South"], 61], [["East", "South"], 41]]
+[[["Stop", "East", "South"], 85], [["East", "South"], 57]]
+[[["Stop", "East", "South"], 64], [["East", "South"], 43]]
+[[["Stop", "East", "South"], 61], [["East", "South"], 41]]
+[[["Stop", "East", "South"], 61], [["East", "South"], 41]]
+[[["Stop", "East", "South"], 85], [["East", "South"], 57]]
+[[["Stop", "East", "South"], 102], [["East", "South"], 67]]
+[[["Stop", "South"], 23], [["South"], 13]]
+[[["South"], 15], [["South"], 9]]
+[[["South"], 15], [["South"], 9]]
+[[["South"], 15], [["South"], 9]]
+[[["South"], 15], [["South"], 9]]
+[[["East"], 15], [["East"], 9]]
+[[["East"], 15], [["East"], 9]]
+[[["East"], 18], [["East"], 12]]
+[[["East", "North"], 29], [["East", "North"], 18]]
+[[["East"], 38], [["East"], 22]]
+[[["North"], 29], [["North"], 18]]
+[[["North"], 38], [["North"], 22]]
+[[["East"], 33], [["East"], 22]]
+[[["East"], 37], [["East"], 18]]
+[[["East"], 18], [["East"], 12]]
+[[["East"], 37], [["East"], 26]]
+[[["East"], 69], [["East"], 41]]
+[[["East"], 56], [["East"], 26]]
+[[["East"], 44], [["East"], 29]]
+[[["North", "South"], 83], [["North", "South"], 52]]
+[[["East", "North"], 121], [["East", "North"], 74]]
+[[["East", "North"], 97], [["East", "North"], 73]]
+[[["North", "South"], 173], [["North", "South"], 130]]
+[[["West", "East"], 90], [["West", "East"], 66]]
+[[["West", "Stop", "East"], 161], [["West", "East"], 118]]
+[[["Stop", "East", "South"], 58], [["East", "South"], 43]]
+[[["Stop", "East"], 120], [["South"], 85]]
+[[["East"], 78], [["East"], 45]]
+[[["West"], 77], [["West"], 42]]
+[[["South"], 83], [["South"], 48]]
+[[["South"], 49], [["South"], 37]]
+[[["South"], 185], [["South"], 104]]
+[[["South"], 68], [["South"], 41]]
+[[["West"], 30], [["West"], 18]]
+[[["West"], 56], [["West"], 29]]
+[[["West"], 14], [["West"], 10]]
+[[["West"], 20], [["West"], 14]]
+[[["West"], 13], [["West"], 9]]
+[[["West"], 13], [["West"], 9]]
+[[["West"], 16], [["West"], 12]]
+[[["West", "North"], 30], [["West", "North"], 20]]
+[[["West"], 38], [["West"], 23]]
+[[["West", "Stop", "East", "North"], 70], [["West", "East", "North"], 46]]
+[[["West", "Stop", "East"], 128], [["West", "East"], 89]]
+[[["West", "Stop", "East"], 31], [["West", "East"], 20]]
+[[["Stop", "East", "North"], 69], [["East", "North"], 45]]
+[[["Stop", "North"], 58], [["North"], 31]]
+[[["North"], 34], [["North"], 19]]
+[[["North"], 30], [["North"], 17]]
+[[["North"], 19], [["North"], 11]]
+[[["North"], 34], [["North"], 19]]
+[[["East"], 30], [["East"], 17]]
+[[["East"], 19], [["East"], 11]]
+[[["East"], 44], [["East"], 29]]
+[[["East", "South"], 87], [["East", "South"], 60]]
+[[["East", "South"], 108], [["East", "South"], 62]]
+[[["South"], 120], [["South"], 61]]
+[[["North", "South"], 209], [["North", "South"], 132]]
+[[["West"], 108], [["West"], 60]]
+[[["West", "Stop", "East", "South"], 83], [["West", "East", "South"], 61]]
+[[["West", "Stop", "East", "South"], 90], [["West", "East", "South"], 66]]
+[[["West", "Stop", "East"], 134], [["West", "East"], 95]]
+[[["West", "Stop", "East"], 82], [["West", "East"], 55]]
+[[["Stop", "East", "South"], 142], [["East", "South"], 95]]
+[[["Stop", "East", "South"], 98], [["East", "South"], 65]]
+[[["Stop", "East", "South"], 128], [["East", "South"], 86]]
+[[["Stop", "East", "South"], 82], [["East", "South"], 55]]
+[[["Stop", "East", "South"], 85], [["East", "South"], 57]]
+[[["Stop", "East", "South"], 190], [["East", "South"], 127]]
+[[["Stop", "East", "South"], 158], [["East", "South"], 103]]
+[[["Stop", "South"], 50], [["South"], 27]]
+[[["South"], 30], [["South"], 17]]
+[[["South"], 15], [["South"], 9]]
+[[["South"], 15], [["South"], 9]]
+[[["South"], 15], [["South"], 9]]
+[[["East"], 15], [["East"], 9]]
+[[["East"], 15], [["East"], 9]]
+[[["East"], 18], [["East"], 12]]
+[[["East", "North"], 29], [["East", "North"], 18]]
+[[["East"], 37], [["East"], 22]]
+[[["East", "North"], 41], [["East", "North"], 24]]
+[[["East"], 59], [["East"], 29]]
+[[["East"], 19], [["East"], 11]]
+[[["East"], 26], [["East"], 15]]
+[[["East"], 15], [["East"], 9]]
+[[["East"], 15], [["East"], 9]]
+[[["East"], 18], [["East"], 12]]
+[[["East"], 29], [["East"], 18]]
+[[["East"], 37], [["East"], 22]]
+[[["East", "North"], 41], [["East", "North"], 24]]
+[[["East"], 59], [["East"], 29]]
+[[["East"], 19], [["East"], 11]]
+[[["North"], 26], [["North"], 15]]
+[[["North"], 19], [["North"], 11]]
+[[["North"], 30], [["North"], 17]]
+[[["North"], 34], [["North"], 19]]
+[[["West"], 34], [["West"], 19]]
+[[["West"], 25], [["West"], 13]]
+[[["West", "Stop", "East"], 7], [["West", "East"], 3]]
+"""
+altDepthActions: """
+[["West", "East"], ["West", "East"], ["West", "East"], ["West", "East"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["West", "North"], ["West", "North"], ["West", "North"], ["West", "North"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["West", "North"], ["West", "North"], ["West", "North"], ["West", "North"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["North"], ["North"], ["Stop", "North"], ["North"]]
+[["East"], ["East"], ["Stop", "East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["North"], ["North"], ["West"], ["West"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["East", "North"], ["East", "North"], ["East", "North"], ["East", "North"]]
+[["East", "North"], ["East", "North"], ["East", "North"], ["East", "North"]]
+[["North", "South"], ["North", "South"], ["North"], ["North"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["West"], ["West"], ["West", "Stop"], ["West"]]
+[["West"], ["West"], ["West", "Stop", "East", "South"], ["West", "East", "South"]]
+[["West", "Stop", "East"], ["West", "East"], ["West", "Stop", "East"], ["West", "East"]]
+[["West", "Stop", "East"], ["West", "East"], ["West", "Stop", "East"], ["West", "East"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "South"], ["South"], ["Stop", "South"], ["South"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East", "North"], ["East", "North"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["North", "South"], ["North", "South"], ["South"], ["South"]]
+[["East", "North"], ["East", "North"], ["East", "North"], ["East", "North"]]
+[["East", "North"], ["East", "North"], ["East", "North"], ["East", "North"]]
+[["North", "South"], ["North", "South"], ["North"], ["North"]]
+[["West", "East"], ["West", "East"], ["East"], ["East"]]
+[["West"], ["West"], ["East"], ["East"]]
+[["Stop", "East", "South"], ["East", "South"], ["East"], ["East"]]
+[["Stop", "East"], ["East"], ["Stop", "East"], ["South"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["West", "East"], ["West", "East"], ["West"], ["West"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["West", "North"], ["West", "North"], ["West", "North"], ["West", "North"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["West", "Stop", "East", "North"], ["West", "East", "North"], ["West", "Stop", "East", "North"], ["West", "East", "North"]]
+[["West", "Stop", "East"], ["West", "East"], ["West", "Stop", "East"], ["West", "East"]]
+[["West", "Stop", "East"], ["West", "East"], ["West", "Stop", "East"], ["West", "East"]]
+[["Stop", "East", "North"], ["East", "North"], ["Stop", "East", "North"], ["East", "North"]]
+[["Stop", "North"], ["North"], ["Stop", "North"], ["North"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East", "South"], ["East", "South"], ["East", "South"], ["East", "South"]]
+[["East", "South"], ["East", "South"], ["East", "South"], ["East", "South"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["North", "South"], ["North", "South"], ["North", "South"], ["North", "South"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["West", "Stop", "East", "South"], ["West", "East", "South"], ["West", "Stop", "East", "South"], ["West", "East", "South"]]
+[["West", "Stop", "East", "South"], ["West", "East", "South"], ["West", "Stop", "East", "South"], ["West", "East", "South"]]
+[["West", "Stop", "East"], ["West", "East"], ["West", "Stop", "East"], ["West", "East"]]
+[["West", "Stop", "East"], ["West", "East"], ["West", "Stop", "East"], ["West", "East"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "South"], ["South"], ["Stop", "South"], ["South"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East", "North"], ["East", "North"], ["East", "North"], ["East", "North"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East", "North"], ["East", "North"], ["East", "North"], ["East", "North"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East", "North"], ["East", "North"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["West", "Stop", "East"], ["West", "East"], ["West", "Stop", "East"], ["West", "East"]]
+"""
+partialPlyBugActions: """
+[["West", "East"], ["West", "East"]]
+[["West"], ["West"]]
+[["West"], ["West"]]
+[["West", "North"], ["West", "North"]]
+[["West"], ["West"]]
+[["West", "North"], ["West", "North"]]
+[["West"], ["West"]]
+[["West"], ["West"]]
+[["North"], ["North"]]
+[["North"], ["North"]]
+[["North"], ["North"]]
+[["North"], ["North"]]
+[["East"], ["East"]]
+[["Stop", "East"], ["East"]]
+[["West"], ["West"]]
+[["South"], ["South"]]
+[["South"], ["South"]]
+[["South"], ["South"]]
+[["South"], ["South"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["North"], ["North"]]
+[["North"], ["North"]]
+[["West"], ["West"]]
+[["East"], ["East"]]
+[["North"], ["North"]]
+[["East", "North"], ["East", "North"]]
+[["East", "North"], ["East", "North"]]
+[["North", "South"], ["North", "South"]]
+[["West"], ["West"]]
+[["West"], ["West"]]
+[["West", "Stop"], ["West"]]
+[["West", "Stop", "East"], ["West", "East"]]
+[["West", "Stop", "East"], ["West", "East"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "South"], ["South"]]
+[["South"], ["South"]]
+[["South"], ["South"]]
+[["South"], ["South"]]
+[["South"], ["South"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East", "North"], ["East", "North"]]
+[["East"], ["East"]]
+[["North"], ["North"]]
+[["North"], ["North"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["North", "South"], ["North", "South"]]
+[["East", "North"], ["East", "North"]]
+[["East", "North"], ["East", "North"]]
+[["North", "South"], ["North", "South"]]
+[["West", "East"], ["West", "East"]]
+[["West", "Stop", "East"], ["West", "East"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East"], ["East"]]
+[["East"], ["East"]]
+[["West"], ["West"]]
+[["South"], ["South"]]
+[["South"], ["South"]]
+[["South"], ["South"]]
+[["South"], ["South"]]
+[["West"], ["West"]]
+[["West"], ["West"]]
+[["West"], ["West"]]
+[["West"], ["West"]]
+[["West"], ["West"]]
+[["West"], ["West"]]
+[["West"], ["West"]]
+[["West", "North"], ["West", "North"]]
+[["West"], ["West"]]
+[["West", "Stop", "East", "North"], ["West", "East", "North"]]
+[["West", "Stop", "East"], ["West", "East"]]
+[["West", "Stop", "East"], ["West", "East"]]
+[["Stop", "East", "North"], ["East", "North"]]
+[["Stop", "North"], ["North"]]
+[["North"], ["North"]]
+[["North"], ["North"]]
+[["North"], ["North"]]
+[["North"], ["North"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East", "South"], ["East", "South"]]
+[["East", "South"], ["East", "South"]]
+[["South"], ["South"]]
+[["North", "South"], ["North", "South"]]
+[["West"], ["West"]]
+[["West", "Stop", "East", "South"], ["West", "East", "South"]]
+[["West", "Stop", "East", "South"], ["West", "East", "South"]]
+[["West", "Stop", "East"], ["West", "East"]]
+[["West", "Stop", "East"], ["West", "East"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "South"], ["South"]]
+[["South"], ["South"]]
+[["South"], ["South"]]
+[["South"], ["South"]]
+[["South"], ["South"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East", "North"], ["East", "North"]]
+[["East"], ["East"]]
+[["East", "North"], ["East", "North"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East", "North"], ["East", "North"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["North"], ["North"]]
+[["North"], ["North"]]
+[["North"], ["North"]]
+[["North"], ["North"]]
+[["West"], ["West"]]
+[["West"], ["West"]]
+[["West", "Stop", "East"], ["West", "East"]]
+"""
diff --git a/HW2_pacman/test_cases/part1/8-pacman-game.test b/HW2_pacman/test_cases/part1/8-pacman-game.test
new file mode 100644
index 0000000..de9dc20
--- /dev/null
+++ b/HW2_pacman/test_cases/part1/8-pacman-game.test
@@ -0,0 +1,19 @@
+class: "PacmanGameTreeTest"
+alg: "MinimaxAgent"
+seed: "0"
+depth: "2"
+max_points: "20"
+
+# The following specifies the layout to be used 
+layoutName: "smallClassic"
+layout: """
+%%%%%%%%%%%%%%%%%%%%
+%......%G  G%......%
+%.%%...%%  %%...%%.%
+%.%o.%........%.o%.%
+%.%%.%.%%%%%%.%.%%.%
+%........P.........%
+%%%%%%%%%%%%%%%%%%%%
+"""
+
+
diff --git a/HW2_pacman/test_cases/part1/CONFIG b/HW2_pacman/test_cases/part1/CONFIG
new file mode 100644
index 0000000..4e8cecf
--- /dev/null
+++ b/HW2_pacman/test_cases/part1/CONFIG
@@ -0,0 +1,2 @@
+max_points: "10"
+class: "PassAllTestsQuestion"
diff --git a/HW2_pacman/test_cases/part2/0-eval-function-lose-states-1.solution b/HW2_pacman/test_cases/part2/0-eval-function-lose-states-1.solution
new file mode 100644
index 0000000..7d48add
--- /dev/null
+++ b/HW2_pacman/test_cases/part2/0-eval-function-lose-states-1.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q3/0-eval-function-lose-states-1.test.
+action: "Left"
+generated: "lose1 lose2 root"
diff --git a/HW2_pacman/test_cases/part2/0-eval-function-lose-states-1.test b/HW2_pacman/test_cases/part2/0-eval-function-lose-states-1.test
new file mode 100644
index 0000000..a3992c7
--- /dev/null
+++ b/HW2_pacman/test_cases/part2/0-eval-function-lose-states-1.test
@@ -0,0 +1,30 @@
+class: "GraphGameTreeTest"
+alg: "AlphaBetaAgent"
+depth: "2"
+
+diagram: """
+        root
+       /    \
+    lose1   lose2
+      1       0
+
+If your algorithm is returning a different
+action, make sure you are calling the
+evaluation function on losing states.
+"""
+num_agents: "2"
+
+start_state: "root"
+win_states: ""
+lose_states: "lose1 lose2"
+
+children: """
+root Left lose1
+root Right lose2
+"""
+
+evaluation: """
+lose1 1.0
+lose2 0.0
+"""
+
diff --git a/HW2_pacman/test_cases/part2/0-eval-function-lose-states-2.solution b/HW2_pacman/test_cases/part2/0-eval-function-lose-states-2.solution
new file mode 100644
index 0000000..cc0f8f7
--- /dev/null
+++ b/HW2_pacman/test_cases/part2/0-eval-function-lose-states-2.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q3/0-eval-function-lose-states-2.test.
+action: "Right"
+generated: "lose1 lose2 root"
diff --git a/HW2_pacman/test_cases/part2/0-eval-function-lose-states-2.test b/HW2_pacman/test_cases/part2/0-eval-function-lose-states-2.test
new file mode 100644
index 0000000..0c37224
--- /dev/null
+++ b/HW2_pacman/test_cases/part2/0-eval-function-lose-states-2.test
@@ -0,0 +1,30 @@
+class: "GraphGameTreeTest"
+alg: "AlphaBetaAgent"
+depth: "2"
+
+diagram: """
+        root
+       /    \
+    lose1   lose2
+      0       1
+
+If your algorithm is returning a different
+action, make sure you are calling the
+evaluation function on losing states.
+"""
+num_agents: "2"
+
+start_state: "root"
+win_states: ""
+lose_states: "lose1 lose2"
+
+children: """
+root Left lose1
+root Right lose2
+"""
+
+evaluation: """
+lose1 0.0
+lose2 1.0
+"""
+
diff --git a/HW2_pacman/test_cases/part2/0-eval-function-win-states-1.solution b/HW2_pacman/test_cases/part2/0-eval-function-win-states-1.solution
new file mode 100644
index 0000000..7734b36
--- /dev/null
+++ b/HW2_pacman/test_cases/part2/0-eval-function-win-states-1.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q3/0-eval-function-win-states-1.test.
+action: "Left"
+generated: "root win1 win2"
diff --git a/HW2_pacman/test_cases/part2/0-eval-function-win-states-1.test b/HW2_pacman/test_cases/part2/0-eval-function-win-states-1.test
new file mode 100644
index 0000000..527ec19
--- /dev/null
+++ b/HW2_pacman/test_cases/part2/0-eval-function-win-states-1.test
@@ -0,0 +1,30 @@
+class: "GraphGameTreeTest"
+alg: "AlphaBetaAgent"
+depth: "2"
+
+diagram: """
+        root
+       /    \
+    win1     win2
+      1       0
+
+If your algorithm is returning a different
+action, make sure you are calling the
+evaluation function on winning states.
+"""
+num_agents: "2"
+
+start_state: "root"
+win_states: "win1 win2"
+lose_states: ""
+
+children: """
+root Left win1
+root Right win2
+"""
+
+evaluation: """
+win1 1.0
+win2 0.0
+"""
+
diff --git a/HW2_pacman/test_cases/part2/0-eval-function-win-states-2.solution b/HW2_pacman/test_cases/part2/0-eval-function-win-states-2.solution
new file mode 100644
index 0000000..7e479db
--- /dev/null
+++ b/HW2_pacman/test_cases/part2/0-eval-function-win-states-2.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q3/0-eval-function-win-states-2.test.
+action: "Right"
+generated: "root win1 win2"
diff --git a/HW2_pacman/test_cases/part2/0-eval-function-win-states-2.test b/HW2_pacman/test_cases/part2/0-eval-function-win-states-2.test
new file mode 100644
index 0000000..d69e0ab
--- /dev/null
+++ b/HW2_pacman/test_cases/part2/0-eval-function-win-states-2.test
@@ -0,0 +1,30 @@
+class: "GraphGameTreeTest"
+alg: "AlphaBetaAgent"
+depth: "2"
+
+diagram: """
+        root
+       /    \
+    win1    win2
+      0      1
+
+If your algorithm is returning a different
+action, make sure you are calling the
+evaluation function on winning states.
+"""
+num_agents: "2"
+
+start_state: "root"
+win_states: "win1 win2"
+lose_states: ""
+
+children: """
+root Left win1
+root Right win2
+"""
+
+evaluation: """
+win1 0.0
+win2 1.0
+"""
+
diff --git a/HW2_pacman/test_cases/part2/0-lecture-6-tree.solution b/HW2_pacman/test_cases/part2/0-lecture-6-tree.solution
new file mode 100644
index 0000000..c4a91ad
--- /dev/null
+++ b/HW2_pacman/test_cases/part2/0-lecture-6-tree.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q3/0-lecture-6-tree.test.
+action: "Center"
+generated: "A B C D E F G H max min1 min2 min3"
diff --git a/HW2_pacman/test_cases/part2/0-lecture-6-tree.test b/HW2_pacman/test_cases/part2/0-lecture-6-tree.test
new file mode 100644
index 0000000..a203b64
--- /dev/null
+++ b/HW2_pacman/test_cases/part2/0-lecture-6-tree.test
@@ -0,0 +1,50 @@
+class: "GraphGameTreeTest"
+alg: "AlphaBetaAgent"
+depth: "2"
+
+#  Tree from lecture 6 slides
+diagram: """
+           max
+      /-/   |   \--\
+     /      |       \
+    /       |        \
+ min1      min2      min3
+  /|\      /|\       /|\ 
+ / | \    / | \     / | \
+A  B  C  D  E  F   G  H  I  
+3 12  8  5  4  6  14  1  11
+"""
+
+num_agents: "2"
+
+start_state: "max"
+win_states: "A B C D E F G H I"
+lose_states: ""
+
+children: """
+max Left min1
+max Center min2
+max Right min3
+min1 Left A
+min1 Center B
+min1 Right C
+min2 Left D
+min2 Center E
+min2 Right F
+min3 Left G
+min3 Center H
+min3 Right I
+"""
+
+
+evaluation: """
+A 3.0
+B 12.0
+C 8.0
+D 5.0
+E 4.0
+F 6.0
+G 14.0
+H 1.0
+I 11.0
+"""
diff --git a/HW2_pacman/test_cases/part2/0-small-tree.solution b/HW2_pacman/test_cases/part2/0-small-tree.solution
new file mode 100644
index 0000000..e940986
--- /dev/null
+++ b/HW2_pacman/test_cases/part2/0-small-tree.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q3/0-small-tree.test.
+action: "pacLeft"
+generated: "A B C minLeft minRight root"
diff --git a/HW2_pacman/test_cases/part2/0-small-tree.test b/HW2_pacman/test_cases/part2/0-small-tree.test
new file mode 100644
index 0000000..968e5ec
--- /dev/null
+++ b/HW2_pacman/test_cases/part2/0-small-tree.test
@@ -0,0 +1,36 @@
+class: "GraphGameTreeTest"
+alg: "AlphaBetaAgent"
+depth: "3"
+
+diagram: """
+        root
+       /    \
+ minLeft  minRight
+  / \       /    \
+ A   B     C   deeper
+ 4   3     2     |
+                 D
+               1000
+"""
+num_agents: "2"
+
+start_state: "root"
+win_states: "A C"
+lose_states: "B D"
+
+children: """
+root pacLeft minLeft
+root pacRight minRight
+minLeft gLeft A
+minLeft gRight B
+minRight gLeft C
+minRight gRight deeper
+deeper pacLeft D
+"""
+
+evaluation: """
+A 4.0
+B 3.0
+C 2.0
+D 1000.0
+"""
diff --git a/HW2_pacman/test_cases/part2/1-1-minmax.solution b/HW2_pacman/test_cases/part2/1-1-minmax.solution
new file mode 100644
index 0000000..2834b29
--- /dev/null
+++ b/HW2_pacman/test_cases/part2/1-1-minmax.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q3/1-1-minmax.test.
+action: "Left"
+generated: "a b1 b2 c1 c2 cx d1 d2 d3 dx"
diff --git a/HW2_pacman/test_cases/part2/1-1-minmax.test b/HW2_pacman/test_cases/part2/1-1-minmax.test
new file mode 100644
index 0000000..5ca0a7c
--- /dev/null
+++ b/HW2_pacman/test_cases/part2/1-1-minmax.test
@@ -0,0 +1,47 @@
+class: "GraphGameTreeTest"
+alg: "AlphaBetaAgent"
+depth: "3"
+
+diagram: """
+            /-----a------\
+           /              \
+          /                \
+        b1                  b2
+      /    \                 |
+   c1        c2             cx
+  /  \      /  \             |
+ d1   d2  d3   d4           dx
+-3    -9  10    6         -3.01
+
+a - max
+b - min
+c - max
+
+Note that the minimax value of b1 is -3.
+"""
+num_agents: "2"
+
+start_state: "a"
+win_states: "d1 d2 d3 d4 dx"
+lose_states: ""
+
+children: """
+a Left b1
+a Right b2
+b1 Left c1
+b1 Right c2
+b2 Down cx
+c1 Left d1
+c1 Right d2
+c2 Left d3
+c2 Right d4
+cx Down dx
+"""
+
+evaluation: """
+d1 -3.0
+d2 -9.0
+d3 10.0
+d4 6.0
+dx -3.01
+"""
diff --git a/HW2_pacman/test_cases/part2/1-2-minmax.solution b/HW2_pacman/test_cases/part2/1-2-minmax.solution
new file mode 100644
index 0000000..8c17bcf
--- /dev/null
+++ b/HW2_pacman/test_cases/part2/1-2-minmax.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q3/1-2-minmax.test.
+action: "Right"
+generated: "a b1 b2 c1 c2 cx d1 d2 d3 dx"
diff --git a/HW2_pacman/test_cases/part2/1-2-minmax.test b/HW2_pacman/test_cases/part2/1-2-minmax.test
new file mode 100644
index 0000000..e9983da
--- /dev/null
+++ b/HW2_pacman/test_cases/part2/1-2-minmax.test
@@ -0,0 +1,47 @@
+class: "GraphGameTreeTest"
+alg: "AlphaBetaAgent"
+depth: "3"
+
+diagram: """
+            /-----a------\
+           /              \
+          /                \
+        b1                  b2
+      /    \                 |
+   c1        c2             cx
+  /  \      /  \             |
+ d1   d2  d3   d4           dx
+-3    -9  10    6         -2.99
+
+a - max
+b - min
+c - max
+
+Note that the minimax value of b1 is -3.
+"""
+num_agents: "2"
+
+start_state: "a"
+win_states: "d1 d2 d3 d4 dx"
+lose_states: ""
+
+children: """
+a Left b1
+a Right b2
+b1 Left c1
+b1 Right c2
+b2 Down cx
+c1 Left d1
+c1 Right d2
+c2 Left d3
+c2 Right d4
+cx Down dx
+"""
+
+evaluation: """
+d1 -3.0
+d2 -9.0
+d3 10.0
+d4 6.0
+dx -2.99
+"""
diff --git a/HW2_pacman/test_cases/part2/1-3-minmax.solution b/HW2_pacman/test_cases/part2/1-3-minmax.solution
new file mode 100644
index 0000000..827cdbd
--- /dev/null
+++ b/HW2_pacman/test_cases/part2/1-3-minmax.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q3/1-3-minmax.test.
+action: "Left"
+generated: "a b1 b2 c3 cx d5 d6 dx"
diff --git a/HW2_pacman/test_cases/part2/1-3-minmax.test b/HW2_pacman/test_cases/part2/1-3-minmax.test
new file mode 100644
index 0000000..5ed0bae
--- /dev/null
+++ b/HW2_pacman/test_cases/part2/1-3-minmax.test
@@ -0,0 +1,47 @@
+class: "GraphGameTreeTest"
+alg: "AlphaBetaAgent"
+depth: "3"
+
+diagram: """
+            /-----a------\
+           /              \
+          /                \
+        b1                  b2
+         |                /    \
+        cx             c3        c4
+         |            /   \     /   \
+        dx           d5   d6   d7   d8
+       4.01          4    -7   0    5
+
+a - max
+b - min
+c - max
+
+Note that the minimax value of b2 is 4.
+"""
+num_agents: "2"
+
+start_state: "a"
+win_states: "d1 d2 d3 d4 d5 d6 d7 d8 dx"
+lose_states: ""
+
+children: """
+a Left b1
+a Right b2
+b1 Down cx
+b2 Left c3
+b2 Right c4
+c3 Left d5
+c3 Right d6
+c4 Left d7
+c4 Right d8
+cx Down dx
+"""
+
+evaluation: """
+d5 4.0
+d6 -7.0
+d7 0.0
+d8 5.0
+dx 4.01
+"""
diff --git a/HW2_pacman/test_cases/part2/1-4-minmax.solution b/HW2_pacman/test_cases/part2/1-4-minmax.solution
new file mode 100644
index 0000000..f5570d1
--- /dev/null
+++ b/HW2_pacman/test_cases/part2/1-4-minmax.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q3/1-4-minmax.test.
+action: "Right"
+generated: "a b1 b2 c3 c4 cx d5 d6 d7 d8 dx"
diff --git a/HW2_pacman/test_cases/part2/1-4-minmax.test b/HW2_pacman/test_cases/part2/1-4-minmax.test
new file mode 100644
index 0000000..71f6107
--- /dev/null
+++ b/HW2_pacman/test_cases/part2/1-4-minmax.test
@@ -0,0 +1,47 @@
+class: "GraphGameTreeTest"
+alg: "AlphaBetaAgent"
+depth: "3"
+
+diagram: """
+            /-----a------\
+           /              \
+          /                \
+        b1                  b2
+         |                /    \
+        cx             c3        c4
+         |            /   \     /   \
+        dx           d5   d6   d7   d8
+       3.99          4    -7   0    5
+
+a - max
+b - min
+c - max
+
+Note that the minimax value of b2 is 4.
+"""
+num_agents: "2"
+
+start_state: "a"
+win_states: "d1 d2 d3 d4 d5 d6 d7 d8 dx"
+lose_states: ""
+
+children: """
+a Left b1
+a Right b2
+b1 Down cx
+b2 Left c3
+b2 Right c4
+c3 Left d5
+c3 Right d6
+c4 Left d7
+c4 Right d8
+cx Down dx
+"""
+
+evaluation: """
+d5 4.0
+d6 -7.0
+d7 0.0
+d8 5.0
+dx 3.99
+"""
diff --git a/HW2_pacman/test_cases/part2/1-5-minmax.solution b/HW2_pacman/test_cases/part2/1-5-minmax.solution
new file mode 100644
index 0000000..06cebde
--- /dev/null
+++ b/HW2_pacman/test_cases/part2/1-5-minmax.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q3/1-5-minmax.test.
+action: "Right"
+generated: "A B C D E F G Z a b1 b2 c1 c2 cx d1 d2 d3 d4 dx"
diff --git a/HW2_pacman/test_cases/part2/1-5-minmax.test b/HW2_pacman/test_cases/part2/1-5-minmax.test
new file mode 100644
index 0000000..cf9f523
--- /dev/null
+++ b/HW2_pacman/test_cases/part2/1-5-minmax.test
@@ -0,0 +1,75 @@
+class: "GraphGameTreeTest"
+alg: "AlphaBetaAgent"
+depth: "4"
+
+diagram: """
+             /-----a------\
+            /              \
+           /                \
+         b1                  b2
+       /    \                |
+    c1        c2             cx
+   /  \      /  \            |
+  d1   d2  d3   d4           dx
+ / \  / \  / \  / \          |
+ A B  C D  E F  G H          Z
+-3 13 5 9 10 3 -6 8        3.01
+
+a - max
+b - min
+c - max
+d - min
+
+Note the minimax value of b1 is 3.
+"""
+num_agents: "2"
+
+start_state: "a"
+win_states: "A B C D E F G H I J K L M N O P Z"
+lose_states: ""
+
+children: """
+a Left b1
+a Right b2
+b1 Left c1
+b1 Right c2
+b2 Down cx
+c1 Left d1
+c1 Right d2
+c2 Left d3
+c2 Right d4
+c3 Left d5
+c3 Right d6
+c4 Left d7
+c4 Right d8
+cx Down dx
+d1 Left A
+d1 Right B
+d2 Left C
+d2 Right D
+d3 Left E
+d3 Right F
+d4 Left G
+d4 Right H
+d5 Left I
+d5 Right J
+d6 Left K
+d6 Right L
+d7 Left M
+d7 Right N
+d8 Left O
+d8 Right P
+dx Down Z
+"""
+
+evaluation: """
+A -3.0
+B 13.0
+C 5.0
+D 9.0
+E 10.0
+F 3.0
+G -6.0
+H 8.0
+Z 3.01
+"""
diff --git a/HW2_pacman/test_cases/part2/1-6-minmax.solution b/HW2_pacman/test_cases/part2/1-6-minmax.solution
new file mode 100644
index 0000000..1ced2ca
--- /dev/null
+++ b/HW2_pacman/test_cases/part2/1-6-minmax.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q3/1-6-minmax.test.
+action: "Left"
+generated: "A B C D E F G Z a b1 b2 c1 c2 cx d1 d2 d3 d4 dx"
diff --git a/HW2_pacman/test_cases/part2/1-6-minmax.test b/HW2_pacman/test_cases/part2/1-6-minmax.test
new file mode 100644
index 0000000..1b676c2
--- /dev/null
+++ b/HW2_pacman/test_cases/part2/1-6-minmax.test
@@ -0,0 +1,75 @@
+class: "GraphGameTreeTest"
+alg: "AlphaBetaAgent"
+depth: "4"
+
+diagram: """
+             /-----a------\
+            /              \
+           /                \
+         b1                  b2
+       /    \                |
+    c1        c2             cx
+   /  \      /  \            |
+  d1   d2  d3   d4           dx
+ / \  / \  / \  / \          |
+ A B  C D  E F  G H          Z
+-3 13 5 9 10 3 -6 8        2.99
+
+a - max
+b - min
+c - max
+d - min
+
+Note the minimax value of b1 is 3.
+"""
+num_agents: "2"
+
+start_state: "a"
+win_states: "A B C D E F G H I J K L M N O P Z"
+lose_states: ""
+
+children: """
+a Left b1
+a Right b2
+b1 Left c1
+b1 Right c2
+b2 Down cx
+c1 Left d1
+c1 Right d2
+c2 Left d3
+c2 Right d4
+c3 Left d5
+c3 Right d6
+c4 Left d7
+c4 Right d8
+cx Down dx
+d1 Left A
+d1 Right B
+d2 Left C
+d2 Right D
+d3 Left E
+d3 Right F
+d4 Left G
+d4 Right H
+d5 Left I
+d5 Right J
+d6 Left K
+d6 Right L
+d7 Left M
+d7 Right N
+d8 Left O
+d8 Right P
+dx Down Z
+"""
+
+evaluation: """
+A -3.0
+B 13.0
+C 5.0
+D 9.0
+E 10.0
+F 3.0
+G -6.0
+H 8.0
+Z 2.99
+"""
diff --git a/HW2_pacman/test_cases/part2/1-7-minmax.solution b/HW2_pacman/test_cases/part2/1-7-minmax.solution
new file mode 100644
index 0000000..74e2da0
--- /dev/null
+++ b/HW2_pacman/test_cases/part2/1-7-minmax.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q3/1-7-minmax.test.
+action: "Left"
+generated: "I J K M O P Z a b1 b2 c3 c4 cx d5 d6 d7 d8 dx"
diff --git a/HW2_pacman/test_cases/part2/1-7-minmax.test b/HW2_pacman/test_cases/part2/1-7-minmax.test
new file mode 100644
index 0000000..20b9aad
--- /dev/null
+++ b/HW2_pacman/test_cases/part2/1-7-minmax.test
@@ -0,0 +1,75 @@
+class: "GraphGameTreeTest"
+alg: "AlphaBetaAgent"
+depth: "4"
+
+diagram: """
+            /-----a------\
+           /              \
+          /                \
+        b1                  b2
+        |                 /    \
+        cx             c3        c4
+        |             /   \     /   \
+        dx           d5   d6   d7   d8
+        |           / \  / \  / \  / \ 
+        Z           I J  K L  M N  O P
+     -1.99        -1 -9  4 7  2 5 -3 -2
+
+a - max
+b - min
+c - min
+d - max
+
+Note that the minimax value of b2 is -2
+"""
+num_agents: "3"
+
+start_state: "a"
+win_states: "A B C D E F G H I J K L M N O P Z"
+lose_states: ""
+
+children: """
+a Left b1
+a Right b2
+b1 Down cx
+b2 Left c3
+b2 Right c4
+c1 Left d1
+c1 Right d2
+c2 Left d3
+c2 Right d4
+c3 Left d5
+c3 Right d6
+c4 Left d7
+c4 Right d8
+cx Down dx
+d1 Left A
+d1 Right B
+d2 Left C
+d2 Right D
+d3 Left E
+d3 Right F
+d4 Left G
+d4 Right H
+d5 Left I
+d5 Right J
+d6 Left K
+d6 Right L
+d7 Left M
+d7 Right N
+d8 Left O
+d8 Right P
+dx Down Z
+"""
+
+evaluation: """
+I -1.0
+J -9.0
+K 4.0
+L 7.0
+M 2.0
+N 5.0
+O -3.0
+P -2.0
+Z -1.99
+"""
diff --git a/HW2_pacman/test_cases/part2/1-8-minmax.solution b/HW2_pacman/test_cases/part2/1-8-minmax.solution
new file mode 100644
index 0000000..bf426b8
--- /dev/null
+++ b/HW2_pacman/test_cases/part2/1-8-minmax.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q3/1-8-minmax.test.
+action: "Right"
+generated: "I J K M O P Z a b1 b2 c3 c4 cx d5 d6 d7 d8 dx"
diff --git a/HW2_pacman/test_cases/part2/1-8-minmax.test b/HW2_pacman/test_cases/part2/1-8-minmax.test
new file mode 100644
index 0000000..24cc9f7
--- /dev/null
+++ b/HW2_pacman/test_cases/part2/1-8-minmax.test
@@ -0,0 +1,75 @@
+class: "GraphGameTreeTest"
+alg: "AlphaBetaAgent"
+depth: "4"
+
+diagram: """
+            /-----a------\
+           /              \
+          /                \
+        b1                  b2
+        |                 /    \
+        cx             c3        c4
+        |             /   \     /   \
+        dx           d5   d6   d7   d8 
+        |           / \  / \  / \  / \ 
+        Z           I J  K L  M N  O P
+     -2.01        -1 -9  4 7  2 5 -3 -2
+
+a - max
+b - min
+c - min
+d - max
+
+Note that the minimax value of b2 is -2.01
+"""
+num_agents: "3"
+
+start_state: "a"
+win_states: "A B C D E F G H I J K L M N O P Z"
+lose_states: ""
+
+children: """
+a Left b1
+a Right b2
+b1 Down cx
+b2 Left c3
+b2 Right c4
+c1 Left d1
+c1 Right d2
+c2 Left d3
+c2 Right d4
+c3 Left d5
+c3 Right d6
+c4 Left d7
+c4 Right d8
+cx Down dx
+d1 Left A
+d1 Right B
+d2 Left C
+d2 Right D
+d3 Left E
+d3 Right F
+d4 Left G
+d4 Right H
+d5 Left I
+d5 Right J
+d6 Left K
+d6 Right L
+d7 Left M
+d7 Right N
+d8 Left O
+d8 Right P
+dx Down Z
+"""
+
+evaluation: """
+I -1.0
+J -9.0
+K 4.0
+L 7.0
+M 2.0
+N 5.0
+O -3.0
+P -2.0
+Z -2.01
+"""
diff --git a/HW2_pacman/test_cases/part2/2-1a-vary-depth.solution b/HW2_pacman/test_cases/part2/2-1a-vary-depth.solution
new file mode 100644
index 0000000..59d892c
--- /dev/null
+++ b/HW2_pacman/test_cases/part2/2-1a-vary-depth.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q3/2-1a-vary-depth.test.
+action: "Left"
+generated: "a b1 b2 c1 c2 cx"
diff --git a/HW2_pacman/test_cases/part2/2-1a-vary-depth.test b/HW2_pacman/test_cases/part2/2-1a-vary-depth.test
new file mode 100644
index 0000000..4098717
--- /dev/null
+++ b/HW2_pacman/test_cases/part2/2-1a-vary-depth.test
@@ -0,0 +1,52 @@
+class: "GraphGameTreeTest"
+alg: "AlphaBetaAgent"
+depth: "1"
+
+diagram: """
+            /-----a------\
+           /              \
+          /                \
+        b1                  b2
+      /    \                 |
+-4 c1        c2 9           cx -4.01
+  /  \      /  \             |
+ d1   d2  d3   d4           dx
+-3    -9  10    6         -4.01
+
+a - max
+b - min
+c - max
+
+Note that the minimax value of b1 is -3, but the depth=1 limited value is -4.
+The values next to c1, c2, and cx are the values of the evaluation function, not
+necessarily the correct minimax backup.
+"""
+num_agents: "2"
+
+start_state: "a"
+win_states: "d1 d2 d3 d4 dx"
+lose_states: ""
+
+children: """
+a Left b1
+a Right b2
+b1 Left c1
+b1 Right c2
+b2 Down cx
+c1 Left d1
+c1 Right d2
+c2 Left d3
+c2 Right d4
+cx Down dx
+"""
+
+evaluation: """
+c1 -4.0
+c2 9.0
+cx -4.01
+d1 -3.0
+d2 -9.0
+d3 10.0
+d4 6.0
+dx -4.01
+"""
diff --git a/HW2_pacman/test_cases/part2/2-1b-vary-depth.solution b/HW2_pacman/test_cases/part2/2-1b-vary-depth.solution
new file mode 100644
index 0000000..a0f232c
--- /dev/null
+++ b/HW2_pacman/test_cases/part2/2-1b-vary-depth.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q3/2-1b-vary-depth.test.
+action: "Left"
+generated: "a b1 b2 c1 c2 cx d1 d2 d3 dx"
diff --git a/HW2_pacman/test_cases/part2/2-1b-vary-depth.test b/HW2_pacman/test_cases/part2/2-1b-vary-depth.test
new file mode 100644
index 0000000..9447262
--- /dev/null
+++ b/HW2_pacman/test_cases/part2/2-1b-vary-depth.test
@@ -0,0 +1,52 @@
+class: "GraphGameTreeTest"
+alg: "AlphaBetaAgent"
+depth: "2"
+
+diagram: """
+            /-----a------\
+           /              \
+          /                \
+        b1                  b2
+      /    \                 |
+-4 c1        c2 9           cx -4.01
+  /  \      /  \             |
+ d1   d2  d3   d4           dx
+-3    -9  10    6         -4.01
+
+a - max
+b - min
+c - max
+
+Note that the minimax value of b1 is -3, but the depth=1 limited value is -4.
+The values next to c1, c2, and cx are the values of the evaluation function, not
+necessarily the correct minimax backup.
+"""
+num_agents: "2"
+
+start_state: "a"
+win_states: "d1 d2 d3 d4 dx"
+lose_states: ""
+
+children: """
+a Left b1
+a Right b2
+b1 Left c1
+b1 Right c2
+b2 Down cx
+c1 Left d1
+c1 Right d2
+c2 Left d3
+c2 Right d4
+cx Down dx
+"""
+
+evaluation: """
+c1 -4.0
+c2 9.0
+cx -4.01
+d1 -3.0
+d2 -9.0
+d3 10.0
+d4 6.0
+dx -4.01
+"""
diff --git a/HW2_pacman/test_cases/part2/2-2a-vary-depth.solution b/HW2_pacman/test_cases/part2/2-2a-vary-depth.solution
new file mode 100644
index 0000000..6e8d7fd
--- /dev/null
+++ b/HW2_pacman/test_cases/part2/2-2a-vary-depth.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q3/2-2a-vary-depth.test.
+action: "Right"
+generated: "a b1 b2 c1 c2 cx"
diff --git a/HW2_pacman/test_cases/part2/2-2a-vary-depth.test b/HW2_pacman/test_cases/part2/2-2a-vary-depth.test
new file mode 100644
index 0000000..2dbbe8f
--- /dev/null
+++ b/HW2_pacman/test_cases/part2/2-2a-vary-depth.test
@@ -0,0 +1,52 @@
+class: "GraphGameTreeTest"
+alg: "AlphaBetaAgent"
+depth: "1"
+
+diagram: """
+            /-----a------\
+           /              \
+          /                \
+        b1                  b2
+      /    \                 |
+-4 c1        c2 9           cx -3.99
+  /  \      /  \             |
+ d1   d2  d3   d4           dx
+-3    -9  10    6         -3.99
+
+a - max
+b - min
+c - max
+
+Note that the minimax value of b1 is -3, but the depth=1 limited value is -4.
+The values next to c1, c2, and cx are the values of the evaluation function, not
+necessarily the correct minimax backup.
+"""
+num_agents: "2"
+
+start_state: "a"
+win_states: "d1 d2 d3 d4 dx"
+lose_states: ""
+
+children: """
+a Left b1
+a Right b2
+b1 Left c1
+b1 Right c2
+b2 Down cx
+c1 Left d1
+c1 Right d2
+c2 Left d3
+c2 Right d4
+cx Down dx
+"""
+
+evaluation: """
+c1 -4.0
+c2 9.0
+cx -3.99
+d1 -3.0
+d2 -9.0
+d3 10.0
+d4 6.0
+dx -3.99
+"""
diff --git a/HW2_pacman/test_cases/part2/2-2b-vary-depth.solution b/HW2_pacman/test_cases/part2/2-2b-vary-depth.solution
new file mode 100644
index 0000000..f508aef
--- /dev/null
+++ b/HW2_pacman/test_cases/part2/2-2b-vary-depth.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q3/2-2b-vary-depth.test.
+action: "Left"
+generated: "a b1 b2 c1 c2 cx d1 d2 d3 dx"
diff --git a/HW2_pacman/test_cases/part2/2-2b-vary-depth.test b/HW2_pacman/test_cases/part2/2-2b-vary-depth.test
new file mode 100644
index 0000000..12fff88
--- /dev/null
+++ b/HW2_pacman/test_cases/part2/2-2b-vary-depth.test
@@ -0,0 +1,52 @@
+class: "GraphGameTreeTest"
+alg: "AlphaBetaAgent"
+depth: "2"
+
+diagram: """
+            /-----a------\
+           /              \
+          /                \
+        b1                  b2
+      /    \                 |
+-4 c1        c2 9           cx -3.99
+  /  \      /  \             |
+ d1   d2  d3   d4           dx
+-3    -9  10    6         -3.99
+
+a - max
+b - min
+c - max
+
+Note that the minimax value of b1 is -3, but the depth=1 limited value is -4.
+The values next to c1, c2, and cx are the values of the evaluation function, not
+necessarily the correct minimax backup.
+"""
+num_agents: "2"
+
+start_state: "a"
+win_states: "d1 d2 d3 d4 dx"
+lose_states: ""
+
+children: """
+a Left b1
+a Right b2
+b1 Left c1
+b1 Right c2
+b2 Down cx
+c1 Left d1
+c1 Right d2
+c2 Left d3
+c2 Right d4
+cx Down dx
+"""
+
+evaluation: """
+c1 -4.0
+c2 9.0
+cx -3.99
+d1 -3.0
+d2 -9.0
+d3 10.0
+d4 6.0
+dx -3.99
+"""
diff --git a/HW2_pacman/test_cases/part2/2-3a-vary-depth.solution b/HW2_pacman/test_cases/part2/2-3a-vary-depth.solution
new file mode 100644
index 0000000..d805b84
--- /dev/null
+++ b/HW2_pacman/test_cases/part2/2-3a-vary-depth.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q3/2-3a-vary-depth.test.
+action: "Left"
+generated: "a b1 b2 c3 c4 cx"
diff --git a/HW2_pacman/test_cases/part2/2-3a-vary-depth.test b/HW2_pacman/test_cases/part2/2-3a-vary-depth.test
new file mode 100644
index 0000000..55d1b90
--- /dev/null
+++ b/HW2_pacman/test_cases/part2/2-3a-vary-depth.test
@@ -0,0 +1,52 @@
+class: "GraphGameTreeTest"
+alg: "AlphaBetaAgent"
+depth: "1"
+
+diagram: """
+            /-----a------\
+           /              \
+          /                \
+        b1                  b2
+         |                /    \
+ 5.01   cx          8  c3        c4   5
+         |            /   \     /   \
+        dx           d5   d6   d7   d8
+       5.01          4    -7   0    5
+
+a - max
+b - min
+c - max
+
+Note that the minimax value of b1 is 4, but the depth=1 limited value is 5.
+The values next to c3, c4, and cx are the values of the evaluation function, not
+necessarily the correct minimax backup.
+"""
+num_agents: "2"
+
+start_state: "a"
+win_states: "d1 d2 d3 d4 d5 d6 d7 d8 dx"
+lose_states: ""
+
+children: """
+a Left b1
+a Right b2
+b1 Down cx
+b2 Left c3
+b2 Right c4
+c3 Left d5
+c3 Right d6
+c4 Left d7
+c4 Right d8
+cx Down dx
+"""
+
+evaluation: """
+c3 8.0
+c4 5.0
+cx 5.01
+d5 4.0
+d6 -7.0
+d7 0.0
+d8 5.0
+dx 5.01
+"""
diff --git a/HW2_pacman/test_cases/part2/2-3b-vary-depth.solution b/HW2_pacman/test_cases/part2/2-3b-vary-depth.solution
new file mode 100644
index 0000000..32a70c6
--- /dev/null
+++ b/HW2_pacman/test_cases/part2/2-3b-vary-depth.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q3/2-3b-vary-depth.test.
+action: "Left"
+generated: "a b1 b2 c3 cx d5 d6 dx"
diff --git a/HW2_pacman/test_cases/part2/2-3b-vary-depth.test b/HW2_pacman/test_cases/part2/2-3b-vary-depth.test
new file mode 100644
index 0000000..54aa555
--- /dev/null
+++ b/HW2_pacman/test_cases/part2/2-3b-vary-depth.test
@@ -0,0 +1,52 @@
+class: "GraphGameTreeTest"
+alg: "AlphaBetaAgent"
+depth: "2"
+
+diagram: """
+            /-----a------\
+           /              \
+          /                \
+        b1                  b2
+         |                /    \
+ 5.01   cx          8  c3        c4   5
+         |            /   \     /   \
+        dx           d5   d6   d7   d8
+       5.01          4    -7   0    5
+
+a - max
+b - min
+c - max
+
+Note that the minimax value of b1 is 4, but the depth=1 limited value is 5.
+The values next to c3, c4, and cx are the values of the evaluation function, not
+necessarily the correct minimax backup.
+"""
+num_agents: "2"
+
+start_state: "a"
+win_states: "d1 d2 d3 d4 d5 d6 d7 d8 dx"
+lose_states: ""
+
+children: """
+a Left b1
+a Right b2
+b1 Down cx
+b2 Left c3
+b2 Right c4
+c3 Left d5
+c3 Right d6
+c4 Left d7
+c4 Right d8
+cx Down dx
+"""
+
+evaluation: """
+c3 8.0
+c4 5.0
+cx 5.01
+d5 4.0
+d6 -7.0
+d7 0.0
+d8 5.0
+dx 5.01
+"""
diff --git a/HW2_pacman/test_cases/part2/2-4a-vary-depth.solution b/HW2_pacman/test_cases/part2/2-4a-vary-depth.solution
new file mode 100644
index 0000000..eafdb62
--- /dev/null
+++ b/HW2_pacman/test_cases/part2/2-4a-vary-depth.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q3/2-4a-vary-depth.test.
+action: "Right"
+generated: "a b1 b2 c3 c4 cx"
diff --git a/HW2_pacman/test_cases/part2/2-4a-vary-depth.test b/HW2_pacman/test_cases/part2/2-4a-vary-depth.test
new file mode 100644
index 0000000..41ffff1
--- /dev/null
+++ b/HW2_pacman/test_cases/part2/2-4a-vary-depth.test
@@ -0,0 +1,52 @@
+class: "GraphGameTreeTest"
+alg: "AlphaBetaAgent"
+depth: "1"
+
+diagram: """
+            /-----a------\
+           /              \
+          /                \
+        b1                  b2
+         |                /    \
+ 4.99   cx          8  c3        c4   5
+         |            /   \     /   \
+        dx           d5   d6   d7   d8
+       4.99          4    -7   0    5
+
+a - max
+b - min
+c - max
+
+Note that the minimax value of b1 is 4, but the depth=1 limited value is 5.
+The values next to c3, c4, and cx are the values of the evaluation function, not
+necessarily the correct minimax backup.
+"""
+num_agents: "2"
+
+start_state: "a"
+win_states: "d1 d2 d3 d4 d5 d6 d7 d8 dx"
+lose_states: ""
+
+children: """
+a Left b1
+a Right b2
+b1 Down cx
+b2 Left c3
+b2 Right c4
+c3 Left d5
+c3 Right d6
+c4 Left d7
+c4 Right d8
+cx Down dx
+"""
+
+evaluation: """
+c3 8.0
+c4 5.0
+cx 4.99
+d5 4.0
+d6 -7.0
+d7 0.0
+d8 5.0
+dx 4.99
+"""
diff --git a/HW2_pacman/test_cases/part2/2-4b-vary-depth.solution b/HW2_pacman/test_cases/part2/2-4b-vary-depth.solution
new file mode 100644
index 0000000..820398a
--- /dev/null
+++ b/HW2_pacman/test_cases/part2/2-4b-vary-depth.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q3/2-4b-vary-depth.test.
+action: "Left"
+generated: "a b1 b2 c3 cx d5 d6 dx"
diff --git a/HW2_pacman/test_cases/part2/2-4b-vary-depth.test b/HW2_pacman/test_cases/part2/2-4b-vary-depth.test
new file mode 100644
index 0000000..c7f6fb2
--- /dev/null
+++ b/HW2_pacman/test_cases/part2/2-4b-vary-depth.test
@@ -0,0 +1,52 @@
+class: "GraphGameTreeTest"
+alg: "AlphaBetaAgent"
+depth: "2"
+
+diagram: """
+            /-----a------\
+           /              \
+          /                \
+        b1                  b2
+         |                /    \
+ 4.99   cx          8  c3        c4   5
+         |            /   \     /   \
+        dx           d5   d6   d7   d8
+       4.99          4    -7   0    5
+
+a - max
+b - min
+c - max
+
+Note that the minimax value of b1 is 4, but the depth=1 limited value is 5.
+The values next to c3, c4, and cx are the values of the evaluation function, not
+necessarily the correct minimax backup.
+"""
+num_agents: "2"
+
+start_state: "a"
+win_states: "d1 d2 d3 d4 d5 d6 d7 d8 dx"
+lose_states: ""
+
+children: """
+a Left b1
+a Right b2
+b1 Down cx
+b2 Left c3
+b2 Right c4
+c3 Left d5
+c3 Right d6
+c4 Left d7
+c4 Right d8
+cx Down dx
+"""
+
+evaluation: """
+c3 8.0
+c4 5.0
+cx 4.99
+d5 4.0
+d6 -7.0
+d7 0.0
+d8 5.0
+dx 4.99
+"""
diff --git a/HW2_pacman/test_cases/part2/2-one-ghost-3level.solution b/HW2_pacman/test_cases/part2/2-one-ghost-3level.solution
new file mode 100644
index 0000000..b22f76f
--- /dev/null
+++ b/HW2_pacman/test_cases/part2/2-one-ghost-3level.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q3/2-one-ghost-3level.test.
+action: "Left"
+generated: "a b1 b2 c1 c2 c3 d1 d2 d3 d5 d6"
diff --git a/HW2_pacman/test_cases/part2/2-one-ghost-3level.test b/HW2_pacman/test_cases/part2/2-one-ghost-3level.test
new file mode 100644
index 0000000..eabc70b
--- /dev/null
+++ b/HW2_pacman/test_cases/part2/2-one-ghost-3level.test
@@ -0,0 +1,52 @@
+class: "GraphGameTreeTest"
+alg: "AlphaBetaAgent"
+depth: "3"
+
+diagram: """
+            /-----a------\
+           /              \
+          /                \
+        b1                  b2
+      /    \              /     \
+   c1        c2        c3        c4
+  /  \      /  \      /   \     /   \
+ d1   d2  d3   d4    d5   d6   d7   d8
+ 3    9   10   6     4    7    0    5
+
+a - max
+b - min
+c - max
+"""
+num_agents: "2"
+
+start_state: "a"
+win_states: "d1 d2 d3 d4 d5 d6 d7 d8"
+lose_states: ""
+
+children: """
+a Left b1
+a Right b2
+b1 Left c1
+b1 Right c2
+b2 Left c3
+b2 Right c4
+c1 Left d1
+c1 Right d2
+c2 Left d3
+c2 Right d4
+c3 Left d5
+c3 Right d6
+c4 Left d7
+c4 Right d8
+"""
+
+evaluation: """
+d1 3.0
+d2 9.0
+d3 10.0
+d4 6.0
+d5 4.0
+d6 7.0
+d7 0.0
+d8 5.0
+"""
diff --git a/HW2_pacman/test_cases/part2/3-one-ghost-4level.solution b/HW2_pacman/test_cases/part2/3-one-ghost-4level.solution
new file mode 100644
index 0000000..b6a9a0f
--- /dev/null
+++ b/HW2_pacman/test_cases/part2/3-one-ghost-4level.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q3/3-one-ghost-4level.test.
+action: "Left"
+generated: "A B C D E F I K a b1 b2 c1 c2 c3 d1 d2 d3 d5 d6"
diff --git a/HW2_pacman/test_cases/part2/3-one-ghost-4level.test b/HW2_pacman/test_cases/part2/3-one-ghost-4level.test
new file mode 100644
index 0000000..210352f
--- /dev/null
+++ b/HW2_pacman/test_cases/part2/3-one-ghost-4level.test
@@ -0,0 +1,79 @@
+class: "GraphGameTreeTest"
+alg: "AlphaBetaAgent"
+depth: "4"
+
+diagram: """
+            /-----a------\
+           /              \
+          /                \
+        b1                  b2
+      /    \              /     \
+   c1        c2        c3        c4
+  /  \      /  \      /   \     /   \
+ d1   d2  d3   d4    d5   d6   d7   d8
+/ \  / \  / \  / \   / \  / \  / \  / \ 
+A B  C D  E F  G H   I J  K L  M N  O P
+3 13 5 9 10 11 6 8   1 0  4 7 12 15 2 14
+
+a - max
+b - min
+c - max
+d - min
+"""
+num_agents: "2"
+
+start_state: "a"
+win_states: "A B C D E F G H I J K L M N O P"
+lose_states: ""
+
+children: """
+a Left b1
+a Right b2
+b1 Left c1
+b1 Right c2
+b2 Left c3
+b2 Right c4
+c1 Left d1
+c1 Right d2
+c2 Left d3
+c2 Right d4
+c3 Left d5
+c3 Right d6
+c4 Left d7
+c4 Right d8
+d1 Left A
+d1 Right B
+d2 Left C
+d2 Right D
+d3 Left E
+d3 Right F
+d4 Left G
+d4 Right H
+d5 Left I
+d5 Right J
+d6 Left K
+d6 Right L
+d7 Left M
+d7 Right N
+d8 Left O
+d8 Right P
+"""
+
+evaluation: """
+A 3.0
+B 13.0
+C 5.0
+D 9.0
+E 10.0
+F 11.0
+G 6.0
+H 8.0
+I 1.0
+J 0.0
+K 4.0
+L 7.0
+M 12.0
+N 15.0
+O 2.0
+P 14.0
+"""
diff --git a/HW2_pacman/test_cases/part2/4-two-ghosts-3level.solution b/HW2_pacman/test_cases/part2/4-two-ghosts-3level.solution
new file mode 100644
index 0000000..12e9520
--- /dev/null
+++ b/HW2_pacman/test_cases/part2/4-two-ghosts-3level.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q3/4-two-ghosts-3level.test.
+action: "Left"
+generated: "a b1 b2 c1 c2 c3 c4 d1 d2 d3 d4 d5 d6 d7"
diff --git a/HW2_pacman/test_cases/part2/4-two-ghosts-3level.test b/HW2_pacman/test_cases/part2/4-two-ghosts-3level.test
new file mode 100644
index 0000000..74a2ab3
--- /dev/null
+++ b/HW2_pacman/test_cases/part2/4-two-ghosts-3level.test
@@ -0,0 +1,52 @@
+class: "GraphGameTreeTest"
+alg: "AlphaBetaAgent"
+depth: "3"
+
+diagram: """
+            /-----a------\
+           /              \
+          /                \
+        b1                  b2
+      /    \              /     \
+   c1        c2        c3        c4
+  /  \      /  \      /   \     /   \
+ d1   d2  d3   d4    d5   d6   d7   d8
+ 3    9   10   6     4    7    0    5
+
+a - max
+b - min
+c - min
+"""
+num_agents: "3"
+
+start_state: "a"
+win_states: "d1 d2 d3 d4 d5 d6 d7 d8"
+lose_states: ""
+
+children: """
+a Left b1
+a Right b2
+b1 Left c1
+b1 Right c2
+b2 Left c3
+b2 Right c4
+c1 Left d1
+c1 Right d2
+c2 Left d3
+c2 Right d4
+c3 Left d5
+c3 Right d6
+c4 Left d7
+c4 Right d8
+"""
+
+evaluation: """
+d1 3.0
+d2 9.0
+d3 10.0
+d4 6.0
+d5 4.0
+d6 7.0
+d7 0.0
+d8 5.0
+"""
diff --git a/HW2_pacman/test_cases/part2/5-two-ghosts-4level.solution b/HW2_pacman/test_cases/part2/5-two-ghosts-4level.solution
new file mode 100644
index 0000000..89c534c
--- /dev/null
+++ b/HW2_pacman/test_cases/part2/5-two-ghosts-4level.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q3/5-two-ghosts-4level.test.
+action: "Left"
+generated: "A B C D E G H I J a b1 b2 c1 c2 c3 d1 d2 d3 d4 d5"
diff --git a/HW2_pacman/test_cases/part2/5-two-ghosts-4level.test b/HW2_pacman/test_cases/part2/5-two-ghosts-4level.test
new file mode 100644
index 0000000..3fa2cbd
--- /dev/null
+++ b/HW2_pacman/test_cases/part2/5-two-ghosts-4level.test
@@ -0,0 +1,79 @@
+class: "GraphGameTreeTest"
+alg: "AlphaBetaAgent"
+depth: "4"
+
+diagram: """
+            /-----a------\
+           /              \
+          /                \
+        b1                  b2
+      /    \              /     \
+   c1        c2        c3        c4
+  /  \      /  \      /   \     /   \
+ d1   d2  d3   d4    d5   d6   d7   d8
+/ \  / \  / \  / \   / \  / \  / \  / \ 
+A B  C D  E F  G H   I J  K L  M N  O P
+3 13 5 9 10 11 6 8   1 0  4 7 12 15 2 14
+
+a - max
+b - min
+c - min
+d - max
+"""
+num_agents: "3"
+
+start_state: "a"
+win_states: "A B C D E F G H I J K L M N O P"
+lose_states: ""
+
+children: """
+a Left b1
+a Right b2
+b1 Left c1
+b1 Right c2
+b2 Left c3
+b2 Right c4
+c1 Left d1
+c1 Right d2
+c2 Left d3
+c2 Right d4
+c3 Left d5
+c3 Right d6
+c4 Left d7
+c4 Right d8
+d1 Left A
+d1 Right B
+d2 Left C
+d2 Right D
+d3 Left E
+d3 Right F
+d4 Left G
+d4 Right H
+d5 Left I
+d5 Right J
+d6 Left K
+d6 Right L
+d7 Left M
+d7 Right N
+d8 Left O
+d8 Right P
+"""
+
+evaluation: """
+A 3.0
+B 13.0
+C 5.0
+D 9.0
+E 10.0
+F 11.0
+G 6.0
+H 8.0
+I 1.0
+J 0.0
+K 4.0
+L 7.0
+M 12.0
+N 15.0
+O 2.0
+P 14.0
+"""
diff --git a/HW2_pacman/test_cases/part2/6-tied-root.solution b/HW2_pacman/test_cases/part2/6-tied-root.solution
new file mode 100644
index 0000000..93ece27
--- /dev/null
+++ b/HW2_pacman/test_cases/part2/6-tied-root.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q3/6-tied-root.test.
+action: "Left"
+generated: "A B C max min1 min2"
diff --git a/HW2_pacman/test_cases/part2/6-tied-root.test b/HW2_pacman/test_cases/part2/6-tied-root.test
new file mode 100644
index 0000000..ed74198
--- /dev/null
+++ b/HW2_pacman/test_cases/part2/6-tied-root.test
@@ -0,0 +1,31 @@
+class: "GraphGameTreeTest"
+alg: "AlphaBetaAgent"
+depth: "3"
+
+diagram: """
+    max
+   /   \
+min1    min2
+ |      /  \
+ A      B   C
+10     10   0
+"""
+num_agents: "2"
+
+start_state: "max"
+win_states: "A B"
+lose_states: "C"
+
+children: """
+max Left min1
+max Right min2
+min1 Down A
+min2 Left B
+min2 Right C
+"""
+
+evaluation: """
+A 10.0
+B 10.0
+C 0.0
+"""
diff --git a/HW2_pacman/test_cases/part2/7-1a-check-depth-one-ghost.solution b/HW2_pacman/test_cases/part2/7-1a-check-depth-one-ghost.solution
new file mode 100644
index 0000000..a3a74c4
--- /dev/null
+++ b/HW2_pacman/test_cases/part2/7-1a-check-depth-one-ghost.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q3/7-1a-check-depth-one-ghost.test.
+action: "Left"
+generated: "a b1 b2 b3 c1 c2 c3"
diff --git a/HW2_pacman/test_cases/part2/7-1a-check-depth-one-ghost.test b/HW2_pacman/test_cases/part2/7-1a-check-depth-one-ghost.test
new file mode 100644
index 0000000..a726af8
--- /dev/null
+++ b/HW2_pacman/test_cases/part2/7-1a-check-depth-one-ghost.test
@@ -0,0 +1,83 @@
+class: "GraphGameTreeTest"
+alg: "AlphaBetaAgent"
+depth: "1"
+
+diagram: """
+            a
+      /-/   |   \--\
+     /      |       \
+  0 b1    0 b2      b3 8
+    |       |        |
+ 10 c1    0 c2      c3 8
+    |       |        |
+  0 d1    0 d2      d3 8
+    |       |        |
+  0 e1   10 e2      e3 8
+    |       |        |
+  0 f1    0 f2      f3 8
+    |       |        |
+    g1      g2      g3
+    0       0        8
+
+a - max
+b - min
+c - max
+d - min
+e - max
+f - min
+
+At depth 1, the evaluation function is called at level c,
+so Left should be returned. If your algorithm is returning a
+different action, check how you implemented your depth.
+"""
+
+num_agents: "2"
+
+start_state: "a"
+win_states: "g1 g2 g3"
+lose_states: ""
+
+children: """
+a Left b1
+a Center b2
+a Right b3
+b1 Center c1
+b2 Center c2
+b3 Center c3
+c1 Center d1
+c2 Center d2
+c3 Center d3
+d1 Center e1
+d2 Center e2
+d3 Center e3
+e1 Center f1
+e2 Center f2
+e3 Center f3
+f1 Center g1
+f2 Center g2
+f3 Center g3
+"""
+
+
+evaluation: """
+b1 0.0
+b2 0.0
+b3 8.0
+c1 10.0
+c2 0.0
+c3 8.0
+d1 0.0
+d2 0.0
+d3 8.0
+e1 0.0
+e2 10.0
+e3 8.0
+f1 0.0
+f2 0.0
+f3 8.0
+g1 0.0
+g2 0.0
+g3 8.0
+"""
+
+
diff --git a/HW2_pacman/test_cases/part2/7-1b-check-depth-one-ghost.solution b/HW2_pacman/test_cases/part2/7-1b-check-depth-one-ghost.solution
new file mode 100644
index 0000000..8dad3c7
--- /dev/null
+++ b/HW2_pacman/test_cases/part2/7-1b-check-depth-one-ghost.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q3/7-1b-check-depth-one-ghost.test.
+action: "Center"
+generated: "a b1 b2 b3 c1 c2 c3 d1 d2 d3 e1 e2 e3"
diff --git a/HW2_pacman/test_cases/part2/7-1b-check-depth-one-ghost.test b/HW2_pacman/test_cases/part2/7-1b-check-depth-one-ghost.test
new file mode 100644
index 0000000..46611a5
--- /dev/null
+++ b/HW2_pacman/test_cases/part2/7-1b-check-depth-one-ghost.test
@@ -0,0 +1,83 @@
+class: "GraphGameTreeTest"
+alg: "AlphaBetaAgent"
+depth: "2"
+
+diagram: """
+            a
+      /-/   |   \--\
+     /      |       \
+  0 b1    0 b2      b3 8
+    |       |        |
+ 10 c1    0 c2      c3 8
+    |       |        |
+  0 d1    0 d2      d3 8
+    |       |        |
+  0 e1   10 e2      e3 8
+    |       |        |
+  0 f1    0 f2      f3 8
+    |       |        |
+    g1      g2      g3
+    0       0        8
+
+a - max
+b - min
+c - max
+d - min
+e - max
+f - min
+
+At depth 2, the evaluation function is called at level e,
+so Center should be returned. If your algorithm is returning a
+different action, check how you implemented your depth.
+"""
+
+num_agents: "2"
+
+start_state: "a"
+win_states: "g1 g2 g3"
+lose_states: ""
+
+children: """
+a Left b1
+a Center b2
+a Right b3
+b1 Center c1
+b2 Center c2
+b3 Center c3
+c1 Center d1
+c2 Center d2
+c3 Center d3
+d1 Center e1
+d2 Center e2
+d3 Center e3
+e1 Center f1
+e2 Center f2
+e3 Center f3
+f1 Center g1
+f2 Center g2
+f3 Center g3
+"""
+
+
+evaluation: """
+b1 0.0
+b2 0.0
+b3 8.0
+c1 10.0
+c2 0.0
+c3 8.0
+d1 0.0
+d2 0.0
+d3 8.0
+e1 0.0
+e2 10.0
+e3 8.0
+f1 0.0
+f2 0.0
+f3 8.0
+g1 0.0
+g2 0.0
+g3 8.0
+"""
+
+
diff --git a/HW2_pacman/test_cases/part2/7-1c-check-depth-one-ghost.solution b/HW2_pacman/test_cases/part2/7-1c-check-depth-one-ghost.solution
new file mode 100644
index 0000000..210bb5d
--- /dev/null
+++ b/HW2_pacman/test_cases/part2/7-1c-check-depth-one-ghost.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q3/7-1c-check-depth-one-ghost.test.
+action: "Right"
+generated: "a b1 b2 b3 c1 c2 c3 d1 d2 d3 e1 e2 e3 f1 f2 f3 g1 g2 g3"
diff --git a/HW2_pacman/test_cases/part2/7-1c-check-depth-one-ghost.test b/HW2_pacman/test_cases/part2/7-1c-check-depth-one-ghost.test
new file mode 100644
index 0000000..f3a5e09
--- /dev/null
+++ b/HW2_pacman/test_cases/part2/7-1c-check-depth-one-ghost.test
@@ -0,0 +1,83 @@
+class: "GraphGameTreeTest"
+alg: "AlphaBetaAgent"
+depth: "3"
+
+diagram: """
+            a
+      /-/   |   \--\
+     /      |       \
+  0 b1    0 b2      b3 8
+    |       |        |
+ 10 c1    0 c2      c3 8
+    |       |        |
+  0 d1    0 d2      d3 8
+    |       |        |
+  0 e1   10 e2      e3 8
+    |       |        |
+  0 f1    0 f2      f3 8
+    |       |        |
+    g1      g2      g3
+    0       0        8
+
+a - max
+b - min
+c - max
+d - min
+e - max
+f - min
+
+At depth 3, the evaluation function is called at level g,
+so Right should be returned. If your algorithm is returning a
+different action, check how you implemented your depth.
+"""
+
+num_agents: "2"
+
+start_state: "a"
+win_states: "g1 g2 g3"
+lose_states: ""
+
+children: """
+a Left b1
+a Center b2
+a Right b3
+b1 Center c1
+b2 Center c2
+b3 Center c3
+c1 Center d1
+c2 Center d2
+c3 Center d3
+d1 Center e1
+d2 Center e2
+d3 Center e3
+e1 Center f1
+e2 Center f2
+e3 Center f3
+f1 Center g1
+f2 Center g2
+f3 Center g3
+"""
+
+
+evaluation: """
+b1 0.0
+b2 0.0
+b3 8.0
+c1 10.0
+c2 0.0
+c3 8.0
+d1 0.0
+d2 0.0
+d3 8.0
+e1 0.0
+e2 10.0
+e3 8.0
+f1 0.0
+f2 0.0
+f3 8.0
+g1 0.0
+g2 0.0
+g3 8.0
+"""
+
+
diff --git a/HW2_pacman/test_cases/part2/7-2a-check-depth-two-ghosts.solution b/HW2_pacman/test_cases/part2/7-2a-check-depth-two-ghosts.solution
new file mode 100644
index 0000000..9a08a38
--- /dev/null
+++ b/HW2_pacman/test_cases/part2/7-2a-check-depth-two-ghosts.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q3/7-2a-check-depth-two-ghosts.test.
+action: "Left"
+generated: "a b1 b2 b3 c1 c2 c3 d1 d2 d3"
diff --git a/HW2_pacman/test_cases/part2/7-2a-check-depth-two-ghosts.test b/HW2_pacman/test_cases/part2/7-2a-check-depth-two-ghosts.test
new file mode 100644
index 0000000..88b2d45
--- /dev/null
+++ b/HW2_pacman/test_cases/part2/7-2a-check-depth-two-ghosts.test
@@ -0,0 +1,110 @@
+class: "GraphGameTreeTest"
+alg: "AlphaBetaAgent"
+depth: "1"
+
+diagram: """
+            a
+      /-/   |   \--\
+     /      |       \
+  0 b1    0 b2      b3 8
+    |       |        |
+  0 c1    0 c2      c3 8
+    |       |        |
+ 10 d1    0 d2      d3 8
+    |       |        |
+  0 e1    0 e2      e3 8
+    |       |        |
+  0 f1    0 f2      f3 8
+    |       |        |
+  0 g1   10 g2      g3 8
+    |       |        |
+  0 h1    0 h2      h3 8
+    |       |        |
+  0 i1    0 i2      i3 8
+    |       |        |
+    j1      j2      j3
+    0       0        8
+
+a - max
+b - min
+c - min
+d - max
+e - min
+f - min
+g - max
+h - min
+i - min
+
+At depth 1, the evaluation function is called at level d,
+so Left should be returned. If your algorithm is returning a
+different action, check how you implemented your depth.
+"""
+
+num_agents: "3"
+
+start_state: "a"
+win_states: "j1 j2 j3"
+lose_states: ""
+
+children: """
+a Left b1
+a Center b2
+a Right b3
+b1 Center c1
+b2 Center c2
+b3 Center c3
+c1 Center d1
+c2 Center d2
+c3 Center d3
+d1 Center e1
+d2 Center e2
+d3 Center e3
+e1 Center f1
+e2 Center f2
+e3 Center f3
+f1 Center g1
+f2 Center g2
+f3 Center g3
+g1 Center h1
+g2 Center h2
+g3 Center h3
+h1 Center i1
+h2 Center i2
+h3 Center i3
+i1 Center j1
+i2 Center j2
+i3 Center j3
+"""
+
+
+evaluation: """
+b1 0.0
+b2 0.0
+b3 8.0
+c1 0.0
+c2 0.0
+c3 8.0
+d1 10.0
+d2 0.0
+d3 8.0
+e1 0.0
+e2 0.0
+e3 8.0
+f1 0.0
+f2 0.0
+f3 8.0
+g1 0.0
+g2 10.0
+g3 8.0
+h1 0.0
+h2 0.0
+h3 8.0
+i1 0.0
+i2 0.0
+i3 8.0
+j1 0.0
+j2 0.0
+j3 8.0
+"""
+
+
diff --git a/HW2_pacman/test_cases/part2/7-2b-check-depth-two-ghosts.solution b/HW2_pacman/test_cases/part2/7-2b-check-depth-two-ghosts.solution
new file mode 100644
index 0000000..194c0aa
--- /dev/null
+++ b/HW2_pacman/test_cases/part2/7-2b-check-depth-two-ghosts.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q3/7-2b-check-depth-two-ghosts.test.
+action: "Center"
+generated: "a b1 b2 b3 c1 c2 c3 d1 d2 d3 e1 e2 e3 f1 f2 f3 g1 g2 g3"
diff --git a/HW2_pacman/test_cases/part2/7-2b-check-depth-two-ghosts.test b/HW2_pacman/test_cases/part2/7-2b-check-depth-two-ghosts.test
new file mode 100644
index 0000000..5745980
--- /dev/null
+++ b/HW2_pacman/test_cases/part2/7-2b-check-depth-two-ghosts.test
@@ -0,0 +1,110 @@
+class: "GraphGameTreeTest"
+alg: "AlphaBetaAgent"
+depth: "2"
+
+diagram: """
+            a
+      /-/   |   \--\
+     /      |       \
+  0 b1    0 b2      b3 8
+    |       |        |
+  0 c1    0 c2      c3 8
+    |       |        |
+ 10 d1    0 d2      d3 8
+    |       |        |
+  0 e1    0 e2      e3 8
+    |       |        |
+  0 f1    0 f2      f3 8
+    |       |        |
+  0 g1   10 g2      g3 8
+    |       |        |
+  0 h1    0 h2      h3 8
+    |       |        |
+  0 i1    0 i2      i3 8
+    |       |        |
+    j1      j2      j3
+    0       0        8
+
+a - max
+b - min
+c - min
+d - max
+e - min
+f - min
+g - max
+h - min
+i - min
+
+At depth 2, the evaluation function is called at level g,
+so Center should be returned. If your algorithm is returning
+a different action, check how you implemented your depth.
+"""
+
+num_agents: "3"
+
+start_state: "a"
+win_states: "j1 j2 j3"
+lose_states: ""
+
+children: """
+a Left b1
+a Center b2
+a Right b3
+b1 Center c1
+b2 Center c2
+b3 Center c3
+c1 Center d1
+c2 Center d2
+c3 Center d3
+d1 Center e1
+d2 Center e2
+d3 Center e3
+e1 Center f1
+e2 Center f2
+e3 Center f3
+f1 Center g1
+f2 Center g2
+f3 Center g3
+g1 Center h1
+g2 Center h2
+g3 Center h3
+h1 Center i1
+h2 Center i2
+h3 Center i3
+i1 Center j1
+i2 Center j2
+i3 Center j3
+"""
+
+
+evaluation: """
+b1 0.0
+b2 0.0
+b3 8.0
+c1 0.0
+c2 0.0
+c3 8.0
+d1 10.0
+d2 0.0
+d3 8.0
+e1 0.0
+e2 0.0
+e3 8.0
+f1 0.0
+f2 0.0
+f3 8.0
+g1 0.0
+g2 10.0
+g3 8.0
+h1 0.0
+h2 0.0
+h3 8.0
+i1 0.0
+i2 0.0
+i3 8.0
+j1 0.0
+j2 0.0
+j3 8.0
+"""
+
+
diff --git a/HW2_pacman/test_cases/part2/7-2c-check-depth-two-ghosts.solution b/HW2_pacman/test_cases/part2/7-2c-check-depth-two-ghosts.solution
new file mode 100644
index 0000000..1e989f3
--- /dev/null
+++ b/HW2_pacman/test_cases/part2/7-2c-check-depth-two-ghosts.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q3/7-2c-check-depth-two-ghosts.test.
+action: "Right"
+generated: "a b1 b2 b3 c1 c2 c3 d1 d2 d3 e1 e2 e3 f1 f2 f3 g1 g2 g3 h1 h2 h3 i1 i2 i3 j1 j2 j3"
diff --git a/HW2_pacman/test_cases/part2/7-2c-check-depth-two-ghosts.test b/HW2_pacman/test_cases/part2/7-2c-check-depth-two-ghosts.test
new file mode 100644
index 0000000..c7770e1
--- /dev/null
+++ b/HW2_pacman/test_cases/part2/7-2c-check-depth-two-ghosts.test
@@ -0,0 +1,110 @@
+class: "GraphGameTreeTest"
+alg: "AlphaBetaAgent"
+depth: "3"
+
+diagram: """
+            a
+      /-/   |   \--\
+     /      |       \
+  0 b1    0 b2      b3 8
+    |       |        |
+  0 c1    0 c2      c3 8
+    |       |        |
+ 10 d1    0 d2      d3 8
+    |       |        |
+  0 e1    0 e2      e3 8
+    |       |        |
+  0 f1    0 f2      f3 8
+    |       |        |
+  0 g1   10 g2      g3 8
+    |       |        |
+  0 h1    0 h2      h3 8
+    |       |        |
+  0 i1    0 i2      i3 8
+    |       |        |
+    j1      j2      j3
+    0       0        8
+
+a - max
+b - min
+c - min
+d - max
+e - min
+f - min
+g - max
+h - min
+i - min
+
+At depth 3, the evaluation function is called at level j,
+so Right should be returned. If your algorithm is returning
+a different action, check how you implemented your depth.
+"""
+
+num_agents: "3"
+
+start_state: "a"
+win_states: "j1 j2 j3"
+lose_states: ""
+
+children: """
+a Left b1
+a Center b2
+a Right b3
+b1 Center c1
+b2 Center c2
+b3 Center c3
+c1 Center d1
+c2 Center d2
+c3 Center d3
+d1 Center e1
+d2 Center e2
+d3 Center e3
+e1 Center f1
+e2 Center f2
+e3 Center f3
+f1 Center g1
+f2 Center g2
+f3 Center g3
+g1 Center h1
+g2 Center h2
+g3 Center h3
+h1 Center i1
+h2 Center i2
+h3 Center i3
+i1 Center j1
+i2 Center j2
+i3 Center j3
+"""
+
+
+evaluation: """
+b1 0.0
+b2 0.0
+b3 8.0
+c1 0.0
+c2 0.0
+c3 8.0
+d1 10.0
+d2 0.0
+d3 8.0
+e1 0.0
+e2 0.0
+e3 8.0
+f1 0.0
+f2 0.0
+f3 8.0
+g1 0.0
+g2 10.0
+g3 8.0
+h1 0.0
+h2 0.0
+h3 8.0
+i1 0.0
+i2 0.0
+i3 8.0
+j1 0.0
+j2 0.0
+j3 8.0
+"""
+
+
diff --git a/HW2_pacman/test_cases/part2/8-pacman-game.solution b/HW2_pacman/test_cases/part2/8-pacman-game.solution
new file mode 100644
index 0000000..ec0b0b8
--- /dev/null
+++ b/HW2_pacman/test_cases/part2/8-pacman-game.solution
@@ -0,0 +1,444 @@
+optimalActions: """
+[[["West", "East"], 39], [["West", "East"], 27]]
+[[["West"], 75], [["West"], 57]]
+[[["West"], 95], [["West"], 77]]
+[[["West", "North"], 72], [["West", "North"], 54]]
+[[["West"], 51], [["West"], 39]]
+[[["West", "North"], 76], [["West", "North"], 58]]
+[[["West"], 69], [["West"], 51]]
+[[["West"], 34], [["West"], 23]]
+[[["North"], 55], [["North"], 41]]
+[[["North"], 63], [["North"], 32]]
+[[["North"], 87], [["North"], 43]]
+[[["North"], 69], [["North"], 34]]
+[[["Stop", "East"], 116], [["East"], 56]]
+[[["East"], 110], [["East"], 52]]
+[[["West"], 28], [["West"], 17]]
+[[["South"], 15], [["South"], 9]]
+[[["South"], 15], [["South"], 9]]
+[[["South"], 15], [["South"], 9]]
+[[["South"], 15], [["South"], 9]]
+[[["East"], 15], [["East"], 9]]
+[[["East"], 15], [["East"], 9]]
+[[["East"], 18], [["East"], 12]]
+[[["North"], 28], [["North"], 18]]
+[[["North"], 47], [["North"], 30]]
+[[["West"], 35], [["West"], 23]]
+[[["East"], 28], [["East"], 15]]
+[[["North"], 74], [["North"], 48]]
+[[["East", "North"], 130], [["East", "North"], 87]]
+[[["East", "North"], 213], [["East", "North"], 158]]
+[[["North", "South"], 101], [["North", "South"], 73]]
+[[["West"], 48], [["West"], 36]]
+[[["West"], 60], [["West"], 45]]
+[[["West", "Stop"], 49], [["West"], 36]]
+[[["West", "Stop", "East"], 69], [["West", "East"], 49]]
+[[["West", "Stop", "East"], 61], [["West", "East"], 41]]
+[[["Stop", "East", "South"], 55], [["East", "South"], 37]]
+[[["Stop", "East", "South"], 28], [["East", "South"], 19]]
+[[["Stop", "East", "South"], 34], [["East", "South"], 23]]
+[[["Stop", "East", "South"], 55], [["East", "South"], 37]]
+[[["Stop", "East", "South"], 55], [["East", "South"], 37]]
+[[["Stop", "East", "South"], 61], [["East", "South"], 41]]
+[[["Stop", "East", "South"], 81], [["East", "South"], 53]]
+[[["Stop", "East", "South"], 64], [["East", "South"], 43]]
+[[["Stop", "East", "South"], 61], [["East", "South"], 41]]
+[[["Stop", "East", "South"], 61], [["East", "South"], 41]]
+[[["Stop", "East", "South"], 81], [["East", "South"], 53]]
+[[["Stop", "East", "South"], 102], [["East", "South"], 67]]
+[[["Stop", "South"], 23], [["South"], 13]]
+[[["South"], 15], [["South"], 9]]
+[[["South"], 15], [["South"], 9]]
+[[["South"], 15], [["South"], 9]]
+[[["South"], 15], [["South"], 9]]
+[[["East"], 15], [["East"], 9]]
+[[["East"], 15], [["East"], 9]]
+[[["East"], 18], [["East"], 12]]
+[[["East", "North"], 28], [["East", "North"], 18]]
+[[["East"], 35], [["East"], 22]]
+[[["North"], 28], [["North"], 18]]
+[[["North"], 38], [["North"], 22]]
+[[["East"], 30], [["East"], 20]]
+[[["East"], 33], [["East"], 18]]
+[[["East"], 18], [["East"], 12]]
+[[["East"], 33], [["East"], 23]]
+[[["East"], 48], [["East"], 29]]
+[[["East"], 49], [["East"], 26]]
+[[["East"], 44], [["East"], 29]]
+[[["North", "South"], 75], [["North", "South"], 52]]
+[[["East", "North"], 113], [["East", "North"], 74]]
+[[["East", "North"], 89], [["East", "North"], 65]]
+[[["North", "South"], 173], [["North", "South"], 130]]
+[[["West", "East"], 54], [["West", "East"], 42]]
+[[["West", "Stop", "East"], 130], [["West", "East"], 87]]
+[[["Stop", "East", "South"], 58], [["East", "South"], 43]]
+[[["Stop", "East"], 110], [["South"], 82]]
+[[["East"], 71], [["East"], 45]]
+[[["West"], 66], [["West"], 42]]
+[[["South"], 70], [["South"], 48]]
+[[["South"], 48], [["South"], 37]]
+[[["South"], 179], [["South"], 104]]
+[[["South"], 68], [["South"], 41]]
+[[["West"], 25], [["West"], 18]]
+[[["West"], 41], [["West"], 29]]
+[[["West"], 14], [["West"], 10]]
+[[["West"], 20], [["West"], 14]]
+[[["West"], 13], [["West"], 9]]
+[[["West"], 13], [["West"], 9]]
+[[["West"], 16], [["West"], 12]]
+[[["West", "North"], 28], [["West", "North"], 20]]
+[[["West"], 30], [["West"], 23]]
+[[["West", "Stop", "East", "North"], 66], [["West", "East", "North"], 46]]
+[[["West", "Stop", "East"], 126], [["West", "East"], 89]]
+[[["West", "Stop", "East"], 30], [["West", "East"], 20]]
+[[["Stop", "East", "North"], 67], [["East", "North"], 45]]
+[[["Stop", "North"], 52], [["North"], 27]]
+[[["North"], 30], [["North"], 19]]
+[[["North"], 28], [["North"], 17]]
+[[["North"], 17], [["North"], 11]]
+[[["North"], 30], [["North"], 19]]
+[[["East"], 28], [["East"], 17]]
+[[["East"], 17], [["East"], 11]]
+[[["East"], 40], [["East"], 29]]
+[[["East", "South"], 79], [["East", "South"], 60]]
+[[["East", "South"], 90], [["East", "South"], 62]]
+[[["South"], 96], [["South"], 61]]
+[[["North", "South"], 195], [["North", "South"], 132]]
+[[["West"], 80], [["West"], 60]]
+[[["West", "Stop", "East", "South"], 83], [["West", "East", "South"], 61]]
+[[["West", "Stop", "East", "South"], 90], [["West", "East", "South"], 66]]
+[[["West", "Stop", "East"], 134], [["West", "East"], 95]]
+[[["West", "Stop", "East"], 82], [["West", "East"], 55]]
+[[["Stop", "East", "South"], 142], [["East", "South"], 95]]
+[[["Stop", "East", "South"], 95], [["East", "South"], 62]]
+[[["Stop", "East", "South"], 128], [["East", "South"], 86]]
+[[["Stop", "East", "South"], 82], [["East", "South"], 55]]
+[[["Stop", "East", "South"], 85], [["East", "South"], 57]]
+[[["Stop", "East", "South"], 182], [["East", "South"], 119]]
+[[["Stop", "East", "South"], 154], [["East", "South"], 103]]
+[[["Stop", "South"], 46], [["South"], 25]]
+[[["South"], 28], [["South"], 17]]
+[[["South"], 15], [["South"], 9]]
+[[["South"], 15], [["South"], 9]]
+[[["South"], 15], [["South"], 9]]
+[[["East"], 15], [["East"], 9]]
+[[["East"], 15], [["East"], 9]]
+[[["East"], 18], [["East"], 12]]
+[[["East", "North"], 28], [["East", "North"], 18]]
+[[["East"], 37], [["East"], 22]]
+[[["East", "North"], 34], [["East", "North"], 24]]
+[[["East"], 56], [["East"], 29]]
+[[["East"], 17], [["East"], 11]]
+[[["East"], 26], [["East"], 15]]
+[[["East"], 15], [["East"], 9]]
+[[["East"], 15], [["East"], 9]]
+[[["East"], 18], [["East"], 12]]
+[[["East"], 27], [["East"], 17]]
+[[["East"], 37], [["East"], 22]]
+[[["East", "North"], 37], [["East", "North"], 24]]
+[[["East"], 56], [["East"], 29]]
+[[["East"], 19], [["East"], 11]]
+[[["North"], 26], [["North"], 15]]
+[[["North"], 19], [["North"], 11]]
+[[["North"], 30], [["North"], 17]]
+[[["North"], 30], [["North"], 19]]
+[[["West"], 28], [["West"], 19]]
+[[["West"], 23], [["West"], 13]]
+[[["West", "Stop", "East"], 7], [["West", "East"], 3]]
+"""
+altDepthActions: """
+[["West", "East"], ["West", "East"], ["West", "East"], ["West", "East"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["West", "North"], ["West", "North"], ["West", "North"], ["West", "North"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["West", "North"], ["West", "North"], ["West", "North"], ["West", "North"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["North"], ["North"], ["Stop", "North"], ["North"]]
+[["East"], ["East"], ["Stop", "East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["North"], ["North"], ["West"], ["West"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["East", "North"], ["East", "North"], ["East", "North"], ["East", "North"]]
+[["East", "North"], ["East", "North"], ["East", "North"], ["East", "North"]]
+[["North", "South"], ["North", "South"], ["North"], ["North"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["West"], ["West"], ["West", "Stop"], ["West"]]
+[["West"], ["West"], ["West", "Stop", "East", "South"], ["West", "East", "South"]]
+[["West", "Stop", "East"], ["West", "East"], ["West", "Stop", "East"], ["West", "East"]]
+[["West", "Stop", "East"], ["West", "East"], ["West", "Stop", "East"], ["West", "East"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "South"], ["South"], ["Stop", "South"], ["South"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East", "North"], ["East", "North"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["North", "South"], ["North", "South"], ["South"], ["South"]]
+[["East", "North"], ["East", "North"], ["East", "North"], ["East", "North"]]
+[["East", "North"], ["East", "North"], ["East", "North"], ["East", "North"]]
+[["North", "South"], ["North", "South"], ["North"], ["North"]]
+[["West", "East"], ["West", "East"], ["East"], ["East"]]
+[["West"], ["West"], ["East"], ["East"]]
+[["Stop", "East", "South"], ["East", "South"], ["East"], ["East"]]
+[["Stop", "East"], ["East"], ["Stop", "East"], ["South"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["West", "East"], ["West", "East"], ["West"], ["West"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["West", "North"], ["West", "North"], ["West", "North"], ["West", "North"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["West", "Stop", "East", "North"], ["West", "East", "North"], ["West", "Stop", "East", "North"], ["West", "East", "North"]]
+[["West", "Stop", "East"], ["West", "East"], ["West", "Stop", "East"], ["West", "East"]]
+[["West", "Stop", "East"], ["West", "East"], ["West", "Stop", "East"], ["West", "East"]]
+[["Stop", "East", "North"], ["East", "North"], ["Stop", "East", "North"], ["East", "North"]]
+[["Stop", "North"], ["North"], ["Stop", "North"], ["North"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East", "South"], ["East", "South"], ["East", "South"], ["East", "South"]]
+[["East", "South"], ["East", "South"], ["East", "South"], ["East", "South"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["North", "South"], ["North", "South"], ["North", "South"], ["North", "South"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["West", "Stop", "East", "South"], ["West", "East", "South"], ["West", "Stop", "East", "South"], ["West", "East", "South"]]
+[["West", "Stop", "East", "South"], ["West", "East", "South"], ["West", "Stop", "East", "South"], ["West", "East", "South"]]
+[["West", "Stop", "East"], ["West", "East"], ["West", "Stop", "East"], ["West", "East"]]
+[["West", "Stop", "East"], ["West", "East"], ["West", "Stop", "East"], ["West", "East"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "South"], ["South"], ["Stop", "South"], ["South"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East", "North"], ["East", "North"], ["East", "North"], ["East", "North"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East", "North"], ["East", "North"], ["East", "North"], ["East", "North"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East", "North"], ["East", "North"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["West", "Stop", "East"], ["West", "East"], ["West", "Stop", "East"], ["West", "East"]]
+"""
+partialPlyBugActions: """
+[["West", "East"], ["West", "East"]]
+[["West"], ["West"]]
+[["West"], ["West"]]
+[["West", "North"], ["West", "North"]]
+[["West"], ["West"]]
+[["West", "North"], ["West", "North"]]
+[["West"], ["West"]]
+[["West"], ["West"]]
+[["North"], ["North"]]
+[["North"], ["North"]]
+[["North"], ["North"]]
+[["North"], ["North"]]
+[["East"], ["East"]]
+[["Stop", "East"], ["East"]]
+[["West"], ["West"]]
+[["South"], ["South"]]
+[["South"], ["South"]]
+[["South"], ["South"]]
+[["South"], ["South"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["North"], ["North"]]
+[["North"], ["North"]]
+[["West"], ["West"]]
+[["East"], ["East"]]
+[["North"], ["North"]]
+[["East", "North"], ["East", "North"]]
+[["East", "North"], ["East", "North"]]
+[["North", "South"], ["North", "South"]]
+[["West"], ["West"]]
+[["West"], ["West"]]
+[["West", "Stop"], ["West"]]
+[["West", "Stop", "East"], ["West", "East"]]
+[["West", "Stop", "East"], ["West", "East"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "South"], ["South"]]
+[["South"], ["South"]]
+[["South"], ["South"]]
+[["South"], ["South"]]
+[["South"], ["South"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East", "North"], ["East", "North"]]
+[["East"], ["East"]]
+[["North"], ["North"]]
+[["North"], ["North"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["North", "South"], ["North", "South"]]
+[["East", "North"], ["East", "North"]]
+[["East", "North"], ["East", "North"]]
+[["North", "South"], ["North", "South"]]
+[["West", "East"], ["West", "East"]]
+[["West", "Stop", "East"], ["West", "East"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East"], ["East"]]
+[["East"], ["East"]]
+[["West"], ["West"]]
+[["South"], ["South"]]
+[["South"], ["South"]]
+[["South"], ["South"]]
+[["South"], ["South"]]
+[["West"], ["West"]]
+[["West"], ["West"]]
+[["West"], ["West"]]
+[["West"], ["West"]]
+[["West"], ["West"]]
+[["West"], ["West"]]
+[["West"], ["West"]]
+[["West", "North"], ["West", "North"]]
+[["West"], ["West"]]
+[["West", "Stop", "East", "North"], ["West", "East", "North"]]
+[["West", "Stop", "East"], ["West", "East"]]
+[["West", "Stop", "East"], ["West", "East"]]
+[["Stop", "East", "North"], ["East", "North"]]
+[["Stop", "North"], ["North"]]
+[["North"], ["North"]]
+[["North"], ["North"]]
+[["North"], ["North"]]
+[["North"], ["North"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East", "South"], ["East", "South"]]
+[["East", "South"], ["East", "South"]]
+[["South"], ["South"]]
+[["North", "South"], ["North", "South"]]
+[["West"], ["West"]]
+[["West", "Stop", "East", "South"], ["West", "East", "South"]]
+[["West", "Stop", "East", "South"], ["West", "East", "South"]]
+[["West", "Stop", "East"], ["West", "East"]]
+[["West", "Stop", "East"], ["West", "East"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "South"], ["South"]]
+[["South"], ["South"]]
+[["South"], ["South"]]
+[["South"], ["South"]]
+[["South"], ["South"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East", "North"], ["East", "North"]]
+[["East"], ["East"]]
+[["East", "North"], ["East", "North"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East", "North"], ["East", "North"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["North"], ["North"]]
+[["North"], ["North"]]
+[["North"], ["North"]]
+[["North"], ["North"]]
+[["West"], ["West"]]
+[["West"], ["West"]]
+[["West", "Stop", "East"], ["West", "East"]]
+"""
diff --git a/HW2_pacman/test_cases/part2/8-pacman-game.test b/HW2_pacman/test_cases/part2/8-pacman-game.test
new file mode 100644
index 0000000..b0af9ba
--- /dev/null
+++ b/HW2_pacman/test_cases/part2/8-pacman-game.test
@@ -0,0 +1,19 @@
+class: "PacmanGameTreeTest"
+alg: "AlphaBetaAgent"
+seed: "0"
+depth: "2"
+max_points: "25"
+
+# The following specifies the layout to be used 
+layoutName: "smallClassic"
+layout: """
+%%%%%%%%%%%%%%%%%%%%
+%......%G  G%......%
+%.%%...%%  %%...%%.%
+%.%o.%........%.o%.%
+%.%%.%.%%%%%%.%.%%.%
+%........P.........%
+%%%%%%%%%%%%%%%%%%%%
+"""
+
+
diff --git a/HW2_pacman/test_cases/part2/CONFIG b/HW2_pacman/test_cases/part2/CONFIG
new file mode 100644
index 0000000..4e8cecf
--- /dev/null
+++ b/HW2_pacman/test_cases/part2/CONFIG
@@ -0,0 +1,2 @@
+max_points: "10"
+class: "PassAllTestsQuestion"
diff --git a/HW2_pacman/test_cases/part3/0-eval-function-lose-states-1.solution b/HW2_pacman/test_cases/part3/0-eval-function-lose-states-1.solution
new file mode 100644
index 0000000..6409bcc
--- /dev/null
+++ b/HW2_pacman/test_cases/part3/0-eval-function-lose-states-1.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q4/0-eval-function-lose-states-1.test.
+action: "Left"
+generated: "lose1 lose2 root"
diff --git a/HW2_pacman/test_cases/part3/0-eval-function-lose-states-1.test b/HW2_pacman/test_cases/part3/0-eval-function-lose-states-1.test
new file mode 100644
index 0000000..9896544
--- /dev/null
+++ b/HW2_pacman/test_cases/part3/0-eval-function-lose-states-1.test
@@ -0,0 +1,30 @@
+class: "GraphGameTreeTest"
+alg: "ExpectimaxAgent"
+depth: "2"
+
+diagram: """
+        root
+       /    \
+    lose1   lose2
+      1       0
+
+If your algorithm is returning a different
+action, make sure you are calling the
+evaluation function on losing states.
+"""
+num_agents: "2"
+
+start_state: "root"
+win_states: ""
+lose_states: "lose1 lose2"
+
+children: """
+root Left lose1
+root Right lose2
+"""
+
+evaluation: """
+lose1 1.0
+lose2 0.0
+"""
+
diff --git a/HW2_pacman/test_cases/part3/0-eval-function-lose-states-2.solution b/HW2_pacman/test_cases/part3/0-eval-function-lose-states-2.solution
new file mode 100644
index 0000000..e4d7abc
--- /dev/null
+++ b/HW2_pacman/test_cases/part3/0-eval-function-lose-states-2.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q4/0-eval-function-lose-states-2.test.
+action: "Right"
+generated: "lose1 lose2 root"
diff --git a/HW2_pacman/test_cases/part3/0-eval-function-lose-states-2.test b/HW2_pacman/test_cases/part3/0-eval-function-lose-states-2.test
new file mode 100644
index 0000000..d6f3c87
--- /dev/null
+++ b/HW2_pacman/test_cases/part3/0-eval-function-lose-states-2.test
@@ -0,0 +1,30 @@
+class: "GraphGameTreeTest"
+alg: "ExpectimaxAgent"
+depth: "2"
+
+diagram: """
+        root
+       /    \
+    lose1   lose2
+      0       1
+
+If your algorithm is returning a different
+action, make sure you are calling the
+evaluation function on losing states.
+"""
+num_agents: "2"
+
+start_state: "root"
+win_states: ""
+lose_states: "lose1 lose2"
+
+children: """
+root Left lose1
+root Right lose2
+"""
+
+evaluation: """
+lose1 0.0
+lose2 1.0
+"""
+
diff --git a/HW2_pacman/test_cases/part3/0-eval-function-win-states-1.solution b/HW2_pacman/test_cases/part3/0-eval-function-win-states-1.solution
new file mode 100644
index 0000000..cb5d436
--- /dev/null
+++ b/HW2_pacman/test_cases/part3/0-eval-function-win-states-1.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q4/0-eval-function-win-states-1.test.
+action: "Left"
+generated: "root win1 win2"
diff --git a/HW2_pacman/test_cases/part3/0-eval-function-win-states-1.test b/HW2_pacman/test_cases/part3/0-eval-function-win-states-1.test
new file mode 100644
index 0000000..c5821d6
--- /dev/null
+++ b/HW2_pacman/test_cases/part3/0-eval-function-win-states-1.test
@@ -0,0 +1,30 @@
+class: "GraphGameTreeTest"
+alg: "ExpectimaxAgent"
+depth: "2"
+
+diagram: """
+        root
+       /    \
+    win1     win2
+      1       0
+
+If your algorithm is returning a different
+action, make sure you are calling the
+evaluation function on winning states.
+"""
+num_agents: "2"
+
+start_state: "root"
+win_states: "win1 win2"
+lose_states: ""
+
+children: """
+root Left win1
+root Right win2
+"""
+
+evaluation: """
+win1 1.0
+win2 0.0
+"""
+
diff --git a/HW2_pacman/test_cases/part3/0-eval-function-win-states-2.solution b/HW2_pacman/test_cases/part3/0-eval-function-win-states-2.solution
new file mode 100644
index 0000000..76d6e48
--- /dev/null
+++ b/HW2_pacman/test_cases/part3/0-eval-function-win-states-2.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q4/0-eval-function-win-states-2.test.
+action: "Right"
+generated: "root win1 win2"
diff --git a/HW2_pacman/test_cases/part3/0-eval-function-win-states-2.test b/HW2_pacman/test_cases/part3/0-eval-function-win-states-2.test
new file mode 100644
index 0000000..955c9f8
--- /dev/null
+++ b/HW2_pacman/test_cases/part3/0-eval-function-win-states-2.test
@@ -0,0 +1,30 @@
+class: "GraphGameTreeTest"
+alg: "ExpectimaxAgent"
+depth: "2"
+
+diagram: """
+        root
+       /    \
+    win1    win2
+      0      1
+
+If your algorithm is returning a different
+action, make sure you are calling the
+evaluation function on winning states.
+"""
+num_agents: "2"
+
+start_state: "root"
+win_states: "win1 win2"
+lose_states: ""
+
+children: """
+root Left win1
+root Right win2
+"""
+
+evaluation: """
+win1 0.0
+win2 1.0
+"""
+
diff --git a/HW2_pacman/test_cases/part3/0-expectimax1.solution b/HW2_pacman/test_cases/part3/0-expectimax1.solution
new file mode 100644
index 0000000..ff7dfe6
--- /dev/null
+++ b/HW2_pacman/test_cases/part3/0-expectimax1.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q4/0-expectimax1.test.
+action: "Left"
+generated: "A B C D E F G H I exp1 exp2 exp3 max"
diff --git a/HW2_pacman/test_cases/part3/0-expectimax1.test b/HW2_pacman/test_cases/part3/0-expectimax1.test
new file mode 100644
index 0000000..d9eea06
--- /dev/null
+++ b/HW2_pacman/test_cases/part3/0-expectimax1.test
@@ -0,0 +1,48 @@
+class: "GraphGameTreeTest"
+alg: "ExpectimaxAgent"
+depth: "2"
+
+#  Tree adapted from lecture 6 slides
+diagram: """
+           max
+      /-/   |   \--\
+     /      |       \
+    /       |        \
+ exp1      exp2      exp3
+  /|\      /|\       /|\ 
+ / | \    / | \     / | \
+A  B  C  D  E  F   G  H  I  
+3 12  8  2  4  6  14  5  2
+"""
+num_agents: "2"
+
+start_state: "max"
+win_states: "A B C D E F G H I"
+lose_states: ""
+
+children: """
+max Left exp1
+max Center exp2
+max Right exp3
+exp1 Left A
+exp1 Center B
+exp1 Right C
+exp2 Left D
+exp2 Center E
+exp2 Right F
+exp3 Left G
+exp3 Center H
+exp3 Right I
+"""
+
+evaluation: """
+A 3.0
+B 12.0
+C 8.0
+D 2.0
+E 4.0
+F 6.0
+G 14.0
+H 5.0
+I 2.0
+"""
diff --git a/HW2_pacman/test_cases/part3/1-expectimax2.solution b/HW2_pacman/test_cases/part3/1-expectimax2.solution
new file mode 100644
index 0000000..30c8768
--- /dev/null
+++ b/HW2_pacman/test_cases/part3/1-expectimax2.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q4/1-expectimax2.test.
+action: "Left"
+generated: "A B C D E F G H I exp1 exp2 exp3 max"
diff --git a/HW2_pacman/test_cases/part3/1-expectimax2.test b/HW2_pacman/test_cases/part3/1-expectimax2.test
new file mode 100644
index 0000000..3b9f67a
--- /dev/null
+++ b/HW2_pacman/test_cases/part3/1-expectimax2.test
@@ -0,0 +1,48 @@
+class: "GraphGameTreeTest"
+alg: "ExpectimaxAgent"
+depth: "2"
+
+#  Tree from lecture 7 slides
+diagram: """
+           max
+      /-/   |   \--\
+     /      |       \
+    /       |        \
+ exp1      exp2      exp3
+  /|\      /|\       /|\ 
+ / | \    / | \     / | \
+A  B  C  D  E  F   G  H  I  
+3 12  9  2  4  6  15  6  0
+"""
+num_agents: "2"
+
+start_state: "max"
+win_states: "A B C D E F G H I"
+lose_states: ""
+
+children: """
+max Left exp1
+max Center exp2
+max Right exp3
+exp1 Left A
+exp1 Center B
+exp1 Right C
+exp2 Left D
+exp2 Center E
+exp2 Right F
+exp3 Left G
+exp3 Center H
+exp3 Right I
+"""
+
+evaluation: """
+A 3.0
+B 12.0
+C 9.0
+D 2.0
+E 4.0
+F 6.0
+G 15.0
+H 6.0
+I 0.0
+"""
diff --git a/HW2_pacman/test_cases/part3/2-one-ghost-3level.solution b/HW2_pacman/test_cases/part3/2-one-ghost-3level.solution
new file mode 100644
index 0000000..bde5c83
--- /dev/null
+++ b/HW2_pacman/test_cases/part3/2-one-ghost-3level.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q4/2-one-ghost-3level.test.
+action: "Left"
+generated: "a b1 b2 c1 c2 c3 c4 d1 d2 d3 d4 d5 d6 d7 d8"
diff --git a/HW2_pacman/test_cases/part3/2-one-ghost-3level.test b/HW2_pacman/test_cases/part3/2-one-ghost-3level.test
new file mode 100644
index 0000000..a9c6123
--- /dev/null
+++ b/HW2_pacman/test_cases/part3/2-one-ghost-3level.test
@@ -0,0 +1,52 @@
+class: "GraphGameTreeTest"
+alg: "ExpectimaxAgent"
+depth: "3"
+
+diagram: """
+            /-----a------\
+           /              \
+          /                \
+        b1                  b2
+      /    \              /     \
+   c1        c2        c3        c4
+  /  \      /  \      /   \     /   \
+ d1   d2  d3   d4    d5   d6   d7   d8
+ 3    9   10   6     4    7    0    5
+
+a - max
+b - exp
+c - max
+"""
+num_agents: "2"
+
+start_state: "a"
+win_states: "d1 d2 d3 d4 d5 d6 d7 d8"
+lose_states: ""
+
+children: """
+a Left b1
+a Right b2
+b1 Left c1
+b1 Right c2
+b2 Left c3
+b2 Right c4
+c1 Left d1
+c1 Right d2
+c2 Left d3
+c2 Right d4
+c3 Left d5
+c3 Right d6
+c4 Left d7
+c4 Right d8
+"""
+
+evaluation: """
+d1 3.0
+d2 9.0
+d3 10.0
+d4 6.0
+d5 4.0
+d6 7.0
+d7 0.0
+d8 5.0
+"""
diff --git a/HW2_pacman/test_cases/part3/3-one-ghost-4level.solution b/HW2_pacman/test_cases/part3/3-one-ghost-4level.solution
new file mode 100644
index 0000000..4ba2b47
--- /dev/null
+++ b/HW2_pacman/test_cases/part3/3-one-ghost-4level.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q4/3-one-ghost-4level.test.
+action: "Right"
+generated: "A B C D E F G H I J K L M N O P a b1 b2 c1 c2 c3 c4 d1 d2 d3 d4 d5 d6 d7 d8"
diff --git a/HW2_pacman/test_cases/part3/3-one-ghost-4level.test b/HW2_pacman/test_cases/part3/3-one-ghost-4level.test
new file mode 100644
index 0000000..c74d459
--- /dev/null
+++ b/HW2_pacman/test_cases/part3/3-one-ghost-4level.test
@@ -0,0 +1,79 @@
+class: "GraphGameTreeTest"
+alg: "ExpectimaxAgent"
+depth: "4"
+
+diagram: """
+            /-----a------\
+           /              \
+          /                \
+        b1                  b2
+      /    \              /     \
+   c1        c2        c3        c4
+  /  \      /  \      /   \     /   \
+ d1   d2  d3   d4    d5   d6   d7   d8
+/ \  / \  / \  / \   / \  / \  / \  / \ 
+A B  C D  E F  G H   I J  K L  M N  O P
+3 13 5 9 10 11 6 8   1 0  4 7 12 15 2 14
+
+a - max
+b - exp
+c - max
+d - exp
+"""
+num_agents: "2"
+
+start_state: "a"
+win_states: "A B C D E F G H I J K L M N O P"
+lose_states: ""
+
+children: """
+a Left b1
+a Right b2
+b1 Left c1
+b1 Right c2
+b2 Left c3
+b2 Right c4
+c1 Left d1
+c1 Right d2
+c2 Left d3
+c2 Right d4
+c3 Left d5
+c3 Right d6
+c4 Left d7
+c4 Right d8
+d1 Left A
+d1 Right B
+d2 Left C
+d2 Right D
+d3 Left E
+d3 Right F
+d4 Left G
+d4 Right H
+d5 Left I
+d5 Right J
+d6 Left K
+d6 Right L
+d7 Left M
+d7 Right N
+d8 Left O
+d8 Right P
+"""
+
+evaluation: """
+A 3.0
+B 13.0
+C 5.0
+D 9.0
+E 10.0
+F 11.0
+G 6.0
+H 8.0
+I 1.0
+J 0.0
+K 4.0
+L 7.0
+M 12.0
+N 15.0
+O 2.0
+P 14.0
+"""
diff --git a/HW2_pacman/test_cases/part3/4-two-ghosts-3level.solution b/HW2_pacman/test_cases/part3/4-two-ghosts-3level.solution
new file mode 100644
index 0000000..6dbd664
--- /dev/null
+++ b/HW2_pacman/test_cases/part3/4-two-ghosts-3level.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q4/4-two-ghosts-3level.test.
+action: "Left"
+generated: "a b1 b2 c1 c2 c3 c4 d1 d2 d3 d4 d5 d6 d7 d8"
diff --git a/HW2_pacman/test_cases/part3/4-two-ghosts-3level.test b/HW2_pacman/test_cases/part3/4-two-ghosts-3level.test
new file mode 100644
index 0000000..85918c7
--- /dev/null
+++ b/HW2_pacman/test_cases/part3/4-two-ghosts-3level.test
@@ -0,0 +1,52 @@
+class: "GraphGameTreeTest"
+alg: "ExpectimaxAgent"
+depth: "3"
+
+diagram: """
+            /-----a------\
+           /              \
+          /                \
+        b1                  b2
+      /    \              /     \
+   c1        c2        c3        c4
+  /  \      /  \      /   \     /   \
+ d1   d2  d3   d4    d5   d6   d7   d8
+ 3    9   10   6     4    7    0    5
+
+a - max
+b - exp
+c - exp
+"""
+num_agents: "3"
+
+start_state: "a"
+win_states: "d1 d2 d3 d4 d5 d6 d7 d8"
+lose_states: ""
+
+children: """
+a Left b1
+a Right b2
+b1 Left c1
+b1 Right c2
+b2 Left c3
+b2 Right c4
+c1 Left d1
+c1 Right d2
+c2 Left d3
+c2 Right d4
+c3 Left d5
+c3 Right d6
+c4 Left d7
+c4 Right d8
+"""
+
+evaluation: """
+d1 3.0
+d2 9.0
+d3 10.0
+d4 6.0
+d5 4.0
+d6 7.0
+d7 0.0
+d8 5.0
+"""
diff --git a/HW2_pacman/test_cases/part3/5-two-ghosts-4level.solution b/HW2_pacman/test_cases/part3/5-two-ghosts-4level.solution
new file mode 100644
index 0000000..caccbea
--- /dev/null
+++ b/HW2_pacman/test_cases/part3/5-two-ghosts-4level.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q4/5-two-ghosts-4level.test.
+action: "Left"
+generated: "A B C D E F G H I J K L M N O P a b1 b2 c1 c2 c3 c4 d1 d2 d3 d4 d5 d6 d7 d8"
diff --git a/HW2_pacman/test_cases/part3/5-two-ghosts-4level.test b/HW2_pacman/test_cases/part3/5-two-ghosts-4level.test
new file mode 100644
index 0000000..8fda1bd
--- /dev/null
+++ b/HW2_pacman/test_cases/part3/5-two-ghosts-4level.test
@@ -0,0 +1,79 @@
+class: "GraphGameTreeTest"
+alg: "ExpectimaxAgent"
+depth: "4"
+
+diagram: """
+            /-----a------\
+           /              \
+          /                \
+        b1                  b2
+      /    \              /     \
+   c1        c2        c3        c4
+  /  \      /  \      /   \     /   \
+ d1   d2  d3   d4    d5   d6   d7   d8
+/ \  / \  / \  / \   / \  / \  / \  / \ 
+A B  C D  E F  G H   I J  K L  M N  O P
+3 13 5 9 10 11 6 8   1 0  4 7 12 15 2 14
+
+a - max
+b - exp
+c - exp
+d - max
+"""
+num_agents: "3"
+
+start_state: "a"
+win_states: "A B C D E F G H I J K L M N O P"
+lose_states: ""
+
+children: """
+a Left b1
+a Right b2
+b1 Left c1
+b1 Right c2
+b2 Left c3
+b2 Right c4
+c1 Left d1
+c1 Right d2
+c2 Left d3
+c2 Right d4
+c3 Left d5
+c3 Right d6
+c4 Left d7
+c4 Right d8
+d1 Left A
+d1 Right B
+d2 Left C
+d2 Right D
+d3 Left E
+d3 Right F
+d4 Left G
+d4 Right H
+d5 Left I
+d5 Right J
+d6 Left K
+d6 Right L
+d7 Left M
+d7 Right N
+d8 Left O
+d8 Right P
+"""
+
+evaluation: """
+A 3.0
+B 13.0
+C 5.0
+D 9.0
+E 10.0
+F 11.0
+G 6.0
+H 8.0
+I 1.0
+J 0.0
+K 4.0
+L 7.0
+M 12.0
+N 15.0
+O 2.0
+P 14.0
+"""
diff --git a/HW2_pacman/test_cases/part3/6-1a-check-depth-one-ghost.solution b/HW2_pacman/test_cases/part3/6-1a-check-depth-one-ghost.solution
new file mode 100644
index 0000000..22aebdc
--- /dev/null
+++ b/HW2_pacman/test_cases/part3/6-1a-check-depth-one-ghost.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q4/6-1a-check-depth-one-ghost.test.
+action: "Left"
+generated: "a b1 b2 b3 c1 c2 c3"
diff --git a/HW2_pacman/test_cases/part3/6-1a-check-depth-one-ghost.test b/HW2_pacman/test_cases/part3/6-1a-check-depth-one-ghost.test
new file mode 100644
index 0000000..e5dd267
--- /dev/null
+++ b/HW2_pacman/test_cases/part3/6-1a-check-depth-one-ghost.test
@@ -0,0 +1,83 @@
+class: "GraphGameTreeTest"
+alg: "ExpectimaxAgent"
+depth: "1"
+
+diagram: """
+            a
+      /-/   |   \--\
+     /      |       \
+  0 b1    0 b2      b3 8
+    |       |        |
+ 10 c1    0 c2      c3 8
+    |       |        |
+  0 d1    0 d2      d3 8
+    |       |        |
+  0 e1   10 e2      e3 8
+    |       |        |
+  0 f1    0 f2      f3 8
+    |       |        |
+    g1      g2      g3
+    0       0        8
+
+a - max
+b - min
+c - max
+d - min
+e - max
+f - min
+
+At depth 1, the evaluation function is called at level c,
+so Left should be returned. If your algorithm is returning a
+different action, check how you implemented your depth.
+"""
+
+num_agents: "2"
+
+start_state: "a"
+win_states: "g1 g2 g3"
+lose_states: ""
+
+children: """
+a Left b1
+a Center b2
+a Right b3
+b1 Center c1
+b2 Center c2
+b3 Center c3
+c1 Center d1
+c2 Center d2
+c3 Center d3
+d1 Center e1
+d2 Center e2
+d3 Center e3
+e1 Center f1
+e2 Center f2
+e3 Center f3
+f1 Center g1
+f2 Center g2
+f3 Center g3
+"""
+
+
+evaluation: """
+b1 0.0
+b2 0.0
+b3 8.0
+c1 10.0
+c2 0.0
+c3 8.0
+d1 0.0
+d2 0.0
+d3 8.0
+e1 0.0
+e2 10.0
+e3 8.0
+f1 0.0
+f2 0.0
+f3 8.0
+g1 0.0
+g2 0.0
+g3 8.0
+"""
+
+
diff --git a/HW2_pacman/test_cases/part3/6-1b-check-depth-one-ghost.solution b/HW2_pacman/test_cases/part3/6-1b-check-depth-one-ghost.solution
new file mode 100644
index 0000000..e34e3d3
--- /dev/null
+++ b/HW2_pacman/test_cases/part3/6-1b-check-depth-one-ghost.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q4/6-1b-check-depth-one-ghost.test.
+action: "Center"
+generated: "a b1 b2 b3 c1 c2 c3 d1 d2 d3 e1 e2 e3"
diff --git a/HW2_pacman/test_cases/part3/6-1b-check-depth-one-ghost.test b/HW2_pacman/test_cases/part3/6-1b-check-depth-one-ghost.test
new file mode 100644
index 0000000..527d543
--- /dev/null
+++ b/HW2_pacman/test_cases/part3/6-1b-check-depth-one-ghost.test
@@ -0,0 +1,83 @@
+class: "GraphGameTreeTest"
+alg: "ExpectimaxAgent"
+depth: "2"
+
+diagram: """
+            a
+      /-/   |   \--\
+     /      |       \
+  0 b1    0 b2      b3 8
+    |       |        |
+ 10 c1    0 c2      c3 8
+    |       |        |
+  0 d1    0 d2      d3 8
+    |       |        |
+  0 e1   10 e2      e3 8
+    |       |        |
+  0 f1    0 f2      f3 8
+    |       |        |
+    g1      g2      g3
+    0       0        8
+
+a - max
+b - min
+c - max
+d - min
+e - max
+f - min
+
+At depth 2, the evaluation function is called at level e,
+so Center should be returned. If your algorithm is returning a
+different action, check how you implemented your depth.
+"""
+
+num_agents: "2"
+
+start_state: "a"
+win_states: "g1 g2 g3"
+lose_states: ""
+
+children: """
+a Left b1
+a Center b2
+a Right b3
+b1 Center c1
+b2 Center c2
+b3 Center c3
+c1 Center d1
+c2 Center d2
+c3 Center d3
+d1 Center e1
+d2 Center e2
+d3 Center e3
+e1 Center f1
+e2 Center f2
+e3 Center f3
+f1 Center g1
+f2 Center g2
+f3 Center g3
+"""
+
+
+evaluation: """
+b1 0.0
+b2 0.0
+b3 8.0
+c1 10.0
+c2 0.0
+c3 8.0
+d1 0.0
+d2 0.0
+d3 8.0
+e1 0.0
+e2 10.0
+e3 8.0
+f1 0.0
+f2 0.0
+f3 8.0
+g1 0.0
+g2 0.0
+g3 8.0
+"""
+
+
diff --git a/HW2_pacman/test_cases/part3/6-1c-check-depth-one-ghost.solution b/HW2_pacman/test_cases/part3/6-1c-check-depth-one-ghost.solution
new file mode 100644
index 0000000..cd33b5a
--- /dev/null
+++ b/HW2_pacman/test_cases/part3/6-1c-check-depth-one-ghost.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q4/6-1c-check-depth-one-ghost.test.
+action: "Right"
+generated: "a b1 b2 b3 c1 c2 c3 d1 d2 d3 e1 e2 e3 f1 f2 f3 g1 g2 g3"
diff --git a/HW2_pacman/test_cases/part3/6-1c-check-depth-one-ghost.test b/HW2_pacman/test_cases/part3/6-1c-check-depth-one-ghost.test
new file mode 100644
index 0000000..cfd9df0
--- /dev/null
+++ b/HW2_pacman/test_cases/part3/6-1c-check-depth-one-ghost.test
@@ -0,0 +1,83 @@
+class: "GraphGameTreeTest"
+alg: "ExpectimaxAgent"
+depth: "3"
+
+diagram: """
+            a
+      /-/   |   \--\
+     /      |       \
+  0 b1    0 b2      b3 8
+    |       |        |
+ 10 c1    0 c2      c3 8
+    |       |        |
+  0 d1    0 d2      d3 8
+    |       |        |
+  0 e1   10 e2      e3 8
+    |       |        |
+  0 f1    0 f2      f3 8
+    |       |        |
+    g1      g2      g3
+    0       0        8
+
+a - max
+b - min
+c - max
+d - min
+e - max
+f - min
+
+At depth 3, the evaluation function is called at level g,
+so Right should be returned. If your algorithm is returning a
+different action, check how you implemented your depth.
+"""
+
+num_agents: "2"
+
+start_state: "a"
+win_states: "g1 g2 g3"
+lose_states: ""
+
+children: """
+a Left b1
+a Center b2
+a Right b3
+b1 Center c1
+b2 Center c2
+b3 Center c3
+c1 Center d1
+c2 Center d2
+c3 Center d3
+d1 Center e1
+d2 Center e2
+d3 Center e3
+e1 Center f1
+e2 Center f2
+e3 Center f3
+f1 Center g1
+f2 Center g2
+f3 Center g3
+"""
+
+
+evaluation: """
+b1 0.0
+b2 0.0
+b3 8.0
+c1 10.0
+c2 0.0
+c3 8.0
+d1 0.0
+d2 0.0
+d3 8.0
+e1 0.0
+e2 10.0
+e3 8.0
+f1 0.0
+f2 0.0
+f3 8.0
+g1 0.0
+g2 0.0
+g3 8.0
+"""
+
+
diff --git a/HW2_pacman/test_cases/part3/6-2a-check-depth-two-ghosts.solution b/HW2_pacman/test_cases/part3/6-2a-check-depth-two-ghosts.solution
new file mode 100644
index 0000000..0e9c9e9
--- /dev/null
+++ b/HW2_pacman/test_cases/part3/6-2a-check-depth-two-ghosts.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q4/6-2a-check-depth-two-ghosts.test.
+action: "Left"
+generated: "a b1 b2 b3 c1 c2 c3 d1 d2 d3"
diff --git a/HW2_pacman/test_cases/part3/6-2a-check-depth-two-ghosts.test b/HW2_pacman/test_cases/part3/6-2a-check-depth-two-ghosts.test
new file mode 100644
index 0000000..c9cfa54
--- /dev/null
+++ b/HW2_pacman/test_cases/part3/6-2a-check-depth-two-ghosts.test
@@ -0,0 +1,110 @@
+class: "GraphGameTreeTest"
+alg: "ExpectimaxAgent"
+depth: "1"
+
+diagram: """
+            a
+      /-/   |   \--\
+     /      |       \
+  0 b1    0 b2      b3 8
+    |       |        |
+  0 c1    0 c2      c3 8
+    |       |        |
+ 10 d1    0 d2      d3 8
+    |       |        |
+  0 e1    0 e2      e3 8
+    |       |        |
+  0 f1    0 f2      f3 8
+    |       |        |
+  0 g1   10 g2      g3 8
+    |       |        |
+  0 h1    0 h2      h3 8
+    |       |        |
+  0 i1    0 i2      i3 8
+    |       |        |
+    j1      j2      j3
+    0       0        8
+
+a - max
+b - min
+c - min
+d - max
+e - min
+f - min
+g - max
+h - min
+i - min
+
+At depth 1, the evaluation function is called at level d,
+so Left should be returned. If your algorithm is returning a
+different action, check how you implemented your depth.
+"""
+
+num_agents: "3"
+
+start_state: "a"
+win_states: "j1 j2 j3"
+lose_states: ""
+
+children: """
+a Left b1
+a Center b2
+a Right b3
+b1 Center c1
+b2 Center c2
+b3 Center c3
+c1 Center d1
+c2 Center d2
+c3 Center d3
+d1 Center e1
+d2 Center e2
+d3 Center e3
+e1 Center f1
+e2 Center f2
+e3 Center f3
+f1 Center g1
+f2 Center g2
+f3 Center g3
+g1 Center h1
+g2 Center h2
+g3 Center h3
+h1 Center i1
+h2 Center i2
+h3 Center i3
+i1 Center j1
+i2 Center j2
+i3 Center j3
+"""
+
+
+evaluation: """
+b1 0.0
+b2 0.0
+b3 8.0
+c1 0.0
+c2 0.0
+c3 8.0
+d1 10.0
+d2 0.0
+d3 8.0
+e1 0.0
+e2 0.0
+e3 8.0
+f1 0.0
+f2 0.0
+f3 8.0
+g1 0.0
+g2 10.0
+g3 8.0
+h1 0.0
+h2 0.0
+h3 8.0
+i1 0.0
+i2 0.0
+i3 8.0
+j1 0.0
+j2 0.0
+j3 8.0
+"""
+
+
diff --git a/HW2_pacman/test_cases/part3/6-2b-check-depth-two-ghosts.solution b/HW2_pacman/test_cases/part3/6-2b-check-depth-two-ghosts.solution
new file mode 100644
index 0000000..3fcde21
--- /dev/null
+++ b/HW2_pacman/test_cases/part3/6-2b-check-depth-two-ghosts.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q4/6-2b-check-depth-two-ghosts.test.
+action: "Center"
+generated: "a b1 b2 b3 c1 c2 c3 d1 d2 d3 e1 e2 e3 f1 f2 f3 g1 g2 g3"
diff --git a/HW2_pacman/test_cases/part3/6-2b-check-depth-two-ghosts.test b/HW2_pacman/test_cases/part3/6-2b-check-depth-two-ghosts.test
new file mode 100644
index 0000000..176d33d
--- /dev/null
+++ b/HW2_pacman/test_cases/part3/6-2b-check-depth-two-ghosts.test
@@ -0,0 +1,110 @@
+class: "GraphGameTreeTest"
+alg: "ExpectimaxAgent"
+depth: "2"
+
+diagram: """
+            a
+      /-/   |   \--\
+     /      |       \
+  0 b1    0 b2      b3 8
+    |       |        |
+  0 c1    0 c2      c3 8
+    |       |        |
+ 10 d1    0 d2      d3 8
+    |       |        |
+  0 e1    0 e2      e3 8
+    |       |        |
+  0 f1    0 f2      f3 8
+    |       |        |
+  0 g1   10 g2      g3 8
+    |       |        |
+  0 h1    0 h2      h3 8
+    |       |        |
+  0 i1    0 i2      i3 8
+    |       |        |
+    j1      j2      j3
+    0       0        8
+
+a - max
+b - min
+c - min
+d - max
+e - min
+f - min
+g - max
+h - min
+i - min
+
+At depth 2, the evaluation function is called at level g,
+so Center should be returned. If your algorithm is returning
+a different action, check how you implemented your depth.
+"""
+
+num_agents: "3"
+
+start_state: "a"
+win_states: "j1 j2 j3"
+lose_states: ""
+
+children: """
+a Left b1
+a Center b2
+a Right b3
+b1 Center c1
+b2 Center c2
+b3 Center c3
+c1 Center d1
+c2 Center d2
+c3 Center d3
+d1 Center e1
+d2 Center e2
+d3 Center e3
+e1 Center f1
+e2 Center f2
+e3 Center f3
+f1 Center g1
+f2 Center g2
+f3 Center g3
+g1 Center h1
+g2 Center h2
+g3 Center h3
+h1 Center i1
+h2 Center i2
+h3 Center i3
+i1 Center j1
+i2 Center j2
+i3 Center j3
+"""
+
+
+evaluation: """
+b1 0.0
+b2 0.0
+b3 8.0
+c1 0.0
+c2 0.0
+c3 8.0
+d1 10.0
+d2 0.0
+d3 8.0
+e1 0.0
+e2 0.0
+e3 8.0
+f1 0.0
+f2 0.0
+f3 8.0
+g1 0.0
+g2 10.0
+g3 8.0
+h1 0.0
+h2 0.0
+h3 8.0
+i1 0.0
+i2 0.0
+i3 8.0
+j1 0.0
+j2 0.0
+j3 8.0
+"""
+
+
diff --git a/HW2_pacman/test_cases/part3/6-2c-check-depth-two-ghosts.solution b/HW2_pacman/test_cases/part3/6-2c-check-depth-two-ghosts.solution
new file mode 100644
index 0000000..bad1cf9
--- /dev/null
+++ b/HW2_pacman/test_cases/part3/6-2c-check-depth-two-ghosts.solution
@@ -0,0 +1,3 @@
+# This is the solution file for test_cases/q4/6-2c-check-depth-two-ghosts.test.
+action: "Right"
+generated: "a b1 b2 b3 c1 c2 c3 d1 d2 d3 e1 e2 e3 f1 f2 f3 g1 g2 g3 h1 h2 h3 i1 i2 i3 j1 j2 j3"
diff --git a/HW2_pacman/test_cases/part3/6-2c-check-depth-two-ghosts.test b/HW2_pacman/test_cases/part3/6-2c-check-depth-two-ghosts.test
new file mode 100644
index 0000000..c83038c
--- /dev/null
+++ b/HW2_pacman/test_cases/part3/6-2c-check-depth-two-ghosts.test
@@ -0,0 +1,110 @@
+class: "GraphGameTreeTest"
+alg: "ExpectimaxAgent"
+depth: "3"
+
+diagram: """
+            a
+      /-/   |   \--\
+     /      |       \
+  0 b1    0 b2      b3 8
+    |       |        |
+  0 c1    0 c2      c3 8
+    |       |        |
+ 10 d1    0 d2      d3 8
+    |       |        |
+  0 e1    0 e2      e3 8
+    |       |        |
+  0 f1    0 f2      f3 8
+    |       |        |
+  0 g1   10 g2      g3 8
+    |       |        |
+  0 h1    0 h2      h3 8
+    |       |        |
+  0 i1    0 i2      i3 8
+    |       |        |
+    j1      j2      j3
+    0       0        8
+
+a - max
+b - min
+c - min
+d - max
+e - min
+f - min
+g - max
+h - min
+i - min
+
+At depth 3, the evaluation function is called at level j,
+so Right should be returned. If your algorithm is returning
+a different action, check how you implemented your depth.
+"""
+
+num_agents: "3"
+
+start_state: "a"
+win_states: "j1 j2 j3"
+lose_states: ""
+
+children: """
+a Left b1
+a Center b2
+a Right b3
+b1 Center c1
+b2 Center c2
+b3 Center c3
+c1 Center d1
+c2 Center d2
+c3 Center d3
+d1 Center e1
+d2 Center e2
+d3 Center e3
+e1 Center f1
+e2 Center f2
+e3 Center f3
+f1 Center g1
+f2 Center g2
+f3 Center g3
+g1 Center h1
+g2 Center h2
+g3 Center h3
+h1 Center i1
+h2 Center i2
+h3 Center i3
+i1 Center j1
+i2 Center j2
+i3 Center j3
+"""
+
+
+evaluation: """
+b1 0.0
+b2 0.0
+b3 8.0
+c1 0.0
+c2 0.0
+c3 8.0
+d1 10.0
+d2 0.0
+d3 8.0
+e1 0.0
+e2 0.0
+e3 8.0
+f1 0.0
+f2 0.0
+f3 8.0
+g1 0.0
+g2 10.0
+g3 8.0
+h1 0.0
+h2 0.0
+h3 8.0
+i1 0.0
+i2 0.0
+i3 8.0
+j1 0.0
+j2 0.0
+j3 8.0
+"""
+
+
diff --git a/HW2_pacman/test_cases/part3/7-pacman-game.solution b/HW2_pacman/test_cases/part3/7-pacman-game.solution
new file mode 100644
index 0000000..ecc544b
--- /dev/null
+++ b/HW2_pacman/test_cases/part3/7-pacman-game.solution
@@ -0,0 +1,444 @@
+optimalActions: """
+[[["West", "East"], 59], [["West", "East"], 35]]
+[[["West"], 190], [["West"], 127]]
+[[["West"], 190], [["West"], 135]]
+[[["West", "North"], 120], [["West", "North"], 82]]
+[[["West"], 77], [["West"], 57]]
+[[["West", "North"], 143], [["West", "North"], 97]]
+[[["West"], 155], [["West"], 110]]
+[[["West"], 40], [["West"], 27]]
+[[["North"], 64], [["North"], 43]]
+[[["North"], 85], [["North"], 57]]
+[[["North"], 106], [["North"], 71]]
+[[["North"], 97], [["North"], 65]]
+[[["East"], 154], [["East"], 103]]
+[[["Stop"], 130], [["West"], 85]]
+[[["West"], 30], [["West"], 17]]
+[[["South"], 15], [["South"], 9]]
+[[["South"], 15], [["South"], 9]]
+[[["South"], 15], [["South"], 9]]
+[[["South"], 15], [["South"], 9]]
+[[["East"], 15], [["East"], 9]]
+[[["East"], 15], [["East"], 9]]
+[[["East"], 18], [["East"], 12]]
+[[["North"], 29], [["North"], 18]]
+[[["North"], 50], [["North"], 31]]
+[[["West"], 55], [["West"], 36]]
+[[["East"], 29], [["East"], 16]]
+[[["North"], 89], [["North"], 61]]
+[[["East", "North"], 161], [["East", "North"], 121]]
+[[["East", "North"], 221], [["East", "North"], 166]]
+[[["North", "South"], 105], [["North", "South"], 77]]
+[[["West"], 69], [["West"], 51]]
+[[["West"], 94], [["West"], 69]]
+[[["West", "Stop"], 57], [["West"], 42]]
+[[["West", "Stop", "East"], 69], [["West", "East"], 49]]
+[[["West", "Stop", "East"], 61], [["West", "East"], 41]]
+[[["Stop", "East", "South"], 55], [["East", "South"], 37]]
+[[["Stop", "East", "South"], 28], [["East", "South"], 19]]
+[[["Stop", "East", "South"], 34], [["East", "South"], 23]]
+[[["Stop", "East", "South"], 55], [["East", "South"], 37]]
+[[["Stop", "East", "South"], 55], [["East", "South"], 37]]
+[[["Stop", "East", "South"], 61], [["East", "South"], 41]]
+[[["Stop", "East", "South"], 85], [["East", "South"], 57]]
+[[["Stop", "East", "South"], 64], [["East", "South"], 43]]
+[[["Stop", "East", "South"], 61], [["East", "South"], 41]]
+[[["Stop", "East", "South"], 61], [["East", "South"], 41]]
+[[["Stop", "East", "South"], 85], [["East", "South"], 57]]
+[[["Stop", "East", "South"], 102], [["East", "South"], 67]]
+[[["Stop", "South"], 23], [["South"], 13]]
+[[["South"], 15], [["South"], 9]]
+[[["South"], 15], [["South"], 9]]
+[[["South"], 15], [["South"], 9]]
+[[["South"], 15], [["South"], 9]]
+[[["East"], 15], [["East"], 9]]
+[[["East"], 15], [["East"], 9]]
+[[["East"], 18], [["East"], 12]]
+[[["East", "North"], 29], [["East", "North"], 18]]
+[[["East"], 38], [["East"], 22]]
+[[["North"], 29], [["North"], 18]]
+[[["North"], 38], [["North"], 22]]
+[[["East"], 33], [["East"], 22]]
+[[["East"], 37], [["East"], 18]]
+[[["East"], 18], [["East"], 12]]
+[[["East"], 37], [["East"], 26]]
+[[["East"], 69], [["East"], 41]]
+[[["East"], 56], [["East"], 26]]
+[[["East"], 44], [["East"], 29]]
+[[["North", "South"], 83], [["North", "South"], 52]]
+[[["East", "North"], 121], [["East", "North"], 74]]
+[[["East", "North"], 97], [["East", "North"], 73]]
+[[["North", "South"], 173], [["North", "South"], 130]]
+[[["West", "East"], 90], [["West", "East"], 66]]
+[[["West", "Stop", "East"], 161], [["West", "East"], 118]]
+[[["Stop", "East", "South"], 58], [["East", "South"], 43]]
+[[["Stop", "East"], 120], [["East"], 85]]
+[[["East"], 78], [["East"], 45]]
+[[["West"], 77], [["West"], 42]]
+[[["South"], 83], [["South"], 48]]
+[[["South"], 49], [["South"], 37]]
+[[["South"], 185], [["South"], 104]]
+[[["South"], 68], [["South"], 41]]
+[[["West"], 30], [["West"], 18]]
+[[["West"], 56], [["West"], 29]]
+[[["West"], 14], [["West"], 10]]
+[[["West"], 20], [["West"], 14]]
+[[["West"], 13], [["West"], 9]]
+[[["West"], 13], [["West"], 9]]
+[[["West"], 16], [["West"], 12]]
+[[["West", "North"], 30], [["West", "North"], 20]]
+[[["West"], 38], [["West"], 23]]
+[[["West", "Stop", "East", "North"], 70], [["West", "East", "North"], 46]]
+[[["West", "Stop", "East"], 128], [["West", "East"], 89]]
+[[["West", "Stop", "East"], 31], [["West", "East"], 20]]
+[[["Stop", "East", "North"], 69], [["East", "North"], 45]]
+[[["Stop", "North"], 58], [["North"], 31]]
+[[["North"], 34], [["North"], 19]]
+[[["North"], 30], [["North"], 17]]
+[[["North"], 19], [["North"], 11]]
+[[["North"], 34], [["North"], 19]]
+[[["East"], 30], [["East"], 17]]
+[[["East"], 19], [["East"], 11]]
+[[["East"], 44], [["East"], 29]]
+[[["East", "South"], 87], [["East", "South"], 60]]
+[[["East", "South"], 108], [["East", "South"], 62]]
+[[["South"], 120], [["South"], 61]]
+[[["North", "South"], 209], [["North", "South"], 132]]
+[[["West"], 108], [["West"], 60]]
+[[["West", "Stop", "East", "South"], 83], [["West", "East", "South"], 61]]
+[[["West", "Stop", "East", "South"], 90], [["West", "East", "South"], 66]]
+[[["West", "Stop", "East"], 134], [["West", "East"], 95]]
+[[["West", "Stop", "East"], 82], [["West", "East"], 55]]
+[[["Stop", "East", "South"], 142], [["East", "South"], 95]]
+[[["Stop", "East", "South"], 98], [["East", "South"], 65]]
+[[["Stop", "East", "South"], 128], [["East", "South"], 86]]
+[[["Stop", "East", "South"], 82], [["East", "South"], 55]]
+[[["Stop", "East", "South"], 85], [["East", "South"], 57]]
+[[["Stop", "East", "South"], 190], [["East", "South"], 127]]
+[[["Stop", "East", "South"], 158], [["East", "South"], 103]]
+[[["Stop", "South"], 50], [["South"], 27]]
+[[["South"], 30], [["South"], 17]]
+[[["South"], 15], [["South"], 9]]
+[[["South"], 15], [["South"], 9]]
+[[["South"], 15], [["South"], 9]]
+[[["East"], 15], [["East"], 9]]
+[[["East"], 15], [["East"], 9]]
+[[["East"], 18], [["East"], 12]]
+[[["East", "North"], 29], [["East", "North"], 18]]
+[[["East"], 37], [["East"], 22]]
+[[["East", "North"], 41], [["East", "North"], 24]]
+[[["East"], 59], [["East"], 29]]
+[[["East"], 19], [["East"], 11]]
+[[["East"], 26], [["East"], 15]]
+[[["East"], 15], [["East"], 9]]
+[[["East"], 15], [["East"], 9]]
+[[["East"], 18], [["East"], 12]]
+[[["East"], 29], [["East"], 18]]
+[[["East"], 37], [["East"], 22]]
+[[["East", "North"], 41], [["East", "North"], 24]]
+[[["East"], 59], [["East"], 29]]
+[[["East"], 19], [["East"], 11]]
+[[["North"], 26], [["North"], 15]]
+[[["North"], 19], [["North"], 11]]
+[[["North"], 30], [["North"], 17]]
+[[["North"], 34], [["North"], 19]]
+[[["West"], 34], [["West"], 19]]
+[[["West"], 25], [["West"], 13]]
+[[["West", "Stop", "East"], 7], [["West", "East"], 3]]
+"""
+altDepthActions: """
+[["West", "East"], ["West", "East"], ["West", "East"], ["West", "East"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["West", "North"], ["West", "North"], ["West", "North"], ["West", "North"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["West", "North"], ["West", "North"], ["West", "North"], ["West", "North"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["West", "Stop"], ["West"], ["Stop"], ["West"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["North"], ["North"], ["West"], ["West"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["East", "North"], ["East", "North"], ["East", "North"], ["East", "North"]]
+[["East", "North"], ["East", "North"], ["East"], ["East"]]
+[["North", "South"], ["North", "South"], ["North"], ["North"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["West"], ["West"], ["West", "Stop"], ["West"]]
+[["West"], ["West"], ["West", "Stop", "East", "South"], ["West", "East", "South"]]
+[["West", "Stop", "East"], ["West", "East"], ["West", "Stop", "East"], ["West", "East"]]
+[["West", "Stop", "East"], ["West", "East"], ["West", "Stop", "East"], ["West", "East"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "South"], ["South"], ["Stop", "South"], ["South"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East", "North"], ["East", "North"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["North", "South"], ["North", "South"], ["South"], ["South"]]
+[["East", "North"], ["East", "North"], ["East", "North"], ["East", "North"]]
+[["East", "North"], ["East", "North"], ["East", "North"], ["East", "North"]]
+[["North", "South"], ["North", "South"], ["North"], ["North"]]
+[["West", "East"], ["West", "East"], ["East"], ["East"]]
+[["West"], ["West"], ["East"], ["East"]]
+[["Stop", "East", "South"], ["East", "South"], ["East"], ["East"]]
+[["Stop", "East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["West", "East"], ["West", "East"], ["West"], ["West"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["West", "North"], ["West", "North"], ["West", "North"], ["West", "North"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["West", "Stop", "East", "North"], ["West", "East", "North"], ["West", "Stop", "East", "North"], ["West", "East", "North"]]
+[["West", "Stop", "East"], ["West", "East"], ["West", "Stop", "East"], ["West", "East"]]
+[["West", "Stop", "East"], ["West", "East"], ["West", "Stop", "East"], ["West", "East"]]
+[["Stop", "East", "North"], ["East", "North"], ["Stop", "East", "North"], ["East", "North"]]
+[["Stop", "North"], ["North"], ["Stop", "North"], ["North"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East", "South"], ["East", "South"], ["East", "South"], ["East", "South"]]
+[["East", "South"], ["East", "South"], ["East", "South"], ["East", "South"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["North", "South"], ["North", "South"], ["North", "South"], ["North", "South"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["West", "Stop", "East", "South"], ["West", "East", "South"], ["West", "Stop", "East", "South"], ["West", "East", "South"]]
+[["West", "Stop", "East", "South"], ["West", "East", "South"], ["West", "Stop", "East", "South"], ["West", "East", "South"]]
+[["West", "Stop", "East"], ["West", "East"], ["West", "Stop", "East"], ["West", "East"]]
+[["West", "Stop", "East"], ["West", "East"], ["West", "Stop", "East"], ["West", "East"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"], ["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "South"], ["South"], ["Stop", "South"], ["South"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["South"], ["South"], ["South"], ["South"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East", "North"], ["East", "North"], ["East", "North"], ["East", "North"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East", "North"], ["East", "North"], ["East", "North"], ["East", "North"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East", "North"], ["East", "North"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["East"], ["East"], ["East"], ["East"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["North"], ["North"], ["North"], ["North"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["West"], ["West"], ["West"], ["West"]]
+[["West", "Stop", "East"], ["West", "East"], ["West", "Stop", "East"], ["West", "East"]]
+"""
+partialPlyBugActions: """
+[["West", "East"], ["West", "East"]]
+[["West"], ["West"]]
+[["West"], ["West"]]
+[["West", "North"], ["West", "North"]]
+[["West"], ["West"]]
+[["West", "North"], ["West", "North"]]
+[["West"], ["West"]]
+[["West"], ["West"]]
+[["North"], ["North"]]
+[["North"], ["North"]]
+[["North"], ["North"]]
+[["North"], ["North"]]
+[["East"], ["East"]]
+[["Stop"], ["West"]]
+[["West"], ["West"]]
+[["South"], ["South"]]
+[["South"], ["South"]]
+[["South"], ["South"]]
+[["South"], ["South"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["North"], ["North"]]
+[["North"], ["North"]]
+[["West"], ["West"]]
+[["East"], ["East"]]
+[["North"], ["North"]]
+[["East", "North"], ["East", "North"]]
+[["East", "North"], ["East", "North"]]
+[["North", "South"], ["North", "South"]]
+[["West"], ["West"]]
+[["West"], ["West"]]
+[["West", "Stop"], ["West"]]
+[["West", "Stop", "East"], ["West", "East"]]
+[["West", "Stop", "East"], ["West", "East"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "South"], ["South"]]
+[["South"], ["South"]]
+[["South"], ["South"]]
+[["South"], ["South"]]
+[["South"], ["South"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East", "North"], ["East", "North"]]
+[["East"], ["East"]]
+[["North"], ["North"]]
+[["North"], ["North"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["North", "South"], ["North", "South"]]
+[["East", "North"], ["East", "North"]]
+[["East", "North"], ["East", "North"]]
+[["North", "South"], ["North", "South"]]
+[["West", "East"], ["West", "East"]]
+[["West", "Stop", "East"], ["West", "East"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East"], ["East"]]
+[["East"], ["East"]]
+[["West"], ["West"]]
+[["South"], ["South"]]
+[["South"], ["South"]]
+[["South"], ["South"]]
+[["South"], ["South"]]
+[["West"], ["West"]]
+[["West"], ["West"]]
+[["West"], ["West"]]
+[["West"], ["West"]]
+[["West"], ["West"]]
+[["West"], ["West"]]
+[["West"], ["West"]]
+[["West", "North"], ["West", "North"]]
+[["West"], ["West"]]
+[["West", "Stop", "East", "North"], ["West", "East", "North"]]
+[["West", "Stop", "East"], ["West", "East"]]
+[["West", "Stop", "East"], ["West", "East"]]
+[["Stop", "East", "North"], ["East", "North"]]
+[["Stop", "North"], ["North"]]
+[["North"], ["North"]]
+[["North"], ["North"]]
+[["North"], ["North"]]
+[["North"], ["North"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East", "South"], ["East", "South"]]
+[["East", "South"], ["East", "South"]]
+[["South"], ["South"]]
+[["North", "South"], ["North", "South"]]
+[["West"], ["West"]]
+[["West", "Stop", "East", "South"], ["West", "East", "South"]]
+[["West", "Stop", "East", "South"], ["West", "East", "South"]]
+[["West", "Stop", "East"], ["West", "East"]]
+[["West", "Stop", "East"], ["West", "East"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "East", "South"], ["East", "South"]]
+[["Stop", "South"], ["South"]]
+[["South"], ["South"]]
+[["South"], ["South"]]
+[["South"], ["South"]]
+[["South"], ["South"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East", "North"], ["East", "North"]]
+[["East"], ["East"]]
+[["East", "North"], ["East", "North"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["East", "North"], ["East", "North"]]
+[["East"], ["East"]]
+[["East"], ["East"]]
+[["North"], ["North"]]
+[["North"], ["North"]]
+[["North"], ["North"]]
+[["North"], ["North"]]
+[["West"], ["West"]]
+[["West"], ["West"]]
+[["West", "Stop", "East"], ["West", "East"]]
+"""
diff --git a/HW2_pacman/test_cases/part3/7-pacman-game.test b/HW2_pacman/test_cases/part3/7-pacman-game.test
new file mode 100644
index 0000000..f2d4f77
--- /dev/null
+++ b/HW2_pacman/test_cases/part3/7-pacman-game.test
@@ -0,0 +1,19 @@
+class: "PacmanGameTreeTest"
+alg: "ExpectimaxAgent"
+seed: "0"
+depth: "2"
+max_points: "25"
+
+# The following specifies the layout to be used 
+layoutName: "smallClassic"
+layout: """
+%%%%%%%%%%%%%%%%%%%%
+%......%G  G%......%
+%.%%...%%  %%...%%.%
+%.%o.%........%.o%.%
+%.%%.%.%%%%%%.%.%%.%
+%........P.........%
+%%%%%%%%%%%%%%%%%%%%
+"""
+
+
diff --git a/HW2_pacman/test_cases/part3/CONFIG b/HW2_pacman/test_cases/part3/CONFIG
new file mode 100644
index 0000000..4e8cecf
--- /dev/null
+++ b/HW2_pacman/test_cases/part3/CONFIG
@@ -0,0 +1,2 @@
+max_points: "10"
+class: "PassAllTestsQuestion"
diff --git a/HW2_pacman/test_cases/part4/CONFIG b/HW2_pacman/test_cases/part4/CONFIG
new file mode 100644
index 0000000..e0744e0
--- /dev/null
+++ b/HW2_pacman/test_cases/part4/CONFIG
@@ -0,0 +1,2 @@
+max_points: "10"
+class: "PartialCreditQuestion"
diff --git a/HW2_pacman/test_cases/part4/grade-agent.solution b/HW2_pacman/test_cases/part4/grade-agent.solution
new file mode 100644
index 0000000..575b63d
--- /dev/null
+++ b/HW2_pacman/test_cases/part4/grade-agent.solution
@@ -0,0 +1,2 @@
+# This is the solution file for test_cases/part4/grade-agent.test.
+# File intentionally blank.
diff --git a/HW2_pacman/test_cases/part4/grade-agent.test b/HW2_pacman/test_cases/part4/grade-agent.test
new file mode 100644
index 0000000..efe2b20
--- /dev/null
+++ b/HW2_pacman/test_cases/part4/grade-agent.test
@@ -0,0 +1,17 @@
+class: "EvalAgentTest"
+
+agentName: "ExpectimaxAgent"
+agentArgs: "evalFn=better"
+layoutName: "smallClassic"
+maxTime: "120"
+numGames: "10"
+
+nonTimeoutThresholds: "5 10"
+
+scoreThresholds: "600 1200"
+
+winsMinimum: "1"
+winsThresholds: "1 4 7 10"
+
+randomSeed: "0"
+ghosts: "[RandomGhost(1)]"
diff --git a/HW2_pacman/textDisplay.py b/HW2_pacman/textDisplay.py
new file mode 100644
index 0000000..18e5dac
--- /dev/null
+++ b/HW2_pacman/textDisplay.py
@@ -0,0 +1,71 @@
+import time
+try:
+    import pacman
+except:
+    pass
+
+DRAW_EVERY = 1
+SLEEP_TIME = 0  # This can be overwritten by __init__
+DISPLAY_MOVES = False
+QUIET = False  # Supresses output
+
+
+class NullGraphics:
+    def initialize(self, state, isBlue=False):
+        pass
+
+    def update(self, state):
+        pass
+
+    def checkNullDisplay(self):
+        return True
+
+    def pause(self):
+        time.sleep(SLEEP_TIME)
+
+    def draw(self, state):
+        print(state)
+
+    def updateDistributions(self, dist):
+        pass
+
+    def finish(self):
+        pass
+
+
+class PacmanGraphics:
+    def __init__(self, speed=None):
+        if speed != None:
+            global SLEEP_TIME
+            SLEEP_TIME = speed
+
+    def initialize(self, state, isBlue=False):
+        self.draw(state)
+        self.pause()
+        self.turn = 0
+        self.agentCounter = 0
+
+    def update(self, state):
+        numAgents = len(state.agentStates)
+        self.agentCounter = (self.agentCounter + 1) % numAgents
+        if self.agentCounter == 0:
+            self.turn += 1
+            if DISPLAY_MOVES:
+                ghosts = [pacman.nearestPoint(
+                    state.getGhostPosition(i)) for i in range(1, numAgents)]
+                print("%4d) P: %-8s" % (self.turn, str(pacman.nearestPoint(state.getPacmanPosition()))),
+                      '| Score: %-5d' % state.score, '| Ghosts:', ghosts)
+            if self.turn % DRAW_EVERY == 0:
+                self.draw(state)
+                self.pause()
+        if state._win or state._lose:
+            self.draw(state)
+
+    def pause(self):
+        time.sleep(SLEEP_TIME)
+
+    def draw(self, state):
+        print(state)
+
+    def finish(self):
+        pass
diff --git a/HW2_pacman/util.py b/HW2_pacman/util.py
new file mode 100644
index 0000000..7a779ec
--- /dev/null
+++ b/HW2_pacman/util.py
@@ -0,0 +1,689 @@
+import sys
+import inspect
+import heapq
+import random
+import io
+
+
+class FixedRandom:
+    def __init__(self):
+        fixedState = (3, (2147483648, 507801126, 683453281, 310439348, 2597246090,
+                          2209084787, 2267831527, 979920060, 3098657677, 37650879, 807947081, 3974896263,
+                          881243242, 3100634921, 1334775171, 3965168385, 746264660, 4074750168, 500078808,
+                          776561771, 702988163, 1636311725, 2559226045, 157578202, 2498342920, 2794591496,
+                          4130598723, 496985844, 2944563015, 3731321600, 3514814613, 3362575829, 3038768745,
+                          2206497038, 1108748846, 1317460727, 3134077628, 988312410, 1674063516, 746456451,
+                          3958482413, 1857117812, 708750586, 1583423339, 3466495450, 1536929345, 1137240525,
+                          3875025632, 2466137587, 1235845595, 4214575620, 3792516855, 657994358, 1241843248,
+                          1695651859, 3678946666, 1929922113, 2351044952, 2317810202, 2039319015, 460787996,
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+                          3199632491, 2235795585, 2865407118, 36763651, 2441503575, 3314890374, 1755526087,
+                          17915536, 1196948233, 949343045, 3815841867, 489007833, 2654997597, 2834744136,
+                          417688687, 2843220846, 85621843, 747339336, 2043645709, 3520444394, 1825470818,
+                          647778910, 275904777, 1249389189, 3640887431, 4200779599, 323384601, 3446088641,
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+                          2928614432, 1564415411, 1691381054, 3816907227, 4082581003, 1895544448, 3728217394,
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+                          3952579552, 678650400, 1391722293, 478833748, 2976468591, 158586606, 2576499787,
+                          662690848, 3799889765, 3328894692, 2474578497, 2383901391, 1718193504, 3003184595,
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+                          954409915, 802581771, 681703307, 545982392, 2738993819, 8025358, 2827719383,
+                          770471093, 3484895980, 3111306320, 3900000891, 2116916652, 397746721, 2087689510,
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+                          1428147157, 2261125391, 1611208390, 1134826333, 2374102525, 3833625209, 2266397263,
+                          3189115077, 770080230, 2674657172, 4280146640, 3604531615, 4235071805, 3436987249,
+                          509704467, 2582695198, 4256268040, 3391197562, 1460642842, 1617931012, 457825497,
+                          1031452907, 1330422862, 4125947620, 2280712485, 431892090, 2387410588, 2061126784,
+                          896457479, 3480499461, 2488196663, 4021103792, 1877063114, 2744470201, 1046140599,
+                          2129952955, 3583049218, 4217723693, 2720341743, 820661843, 1079873609, 3360954200,
+                          3652304997, 3335838575, 2178810636, 1908053374, 4026721976, 1793145418, 476541615,
+                          973420250, 515553040, 919292001, 2601786155, 1685119450, 3030170809, 1590676150,
+                          1665099167, 651151584, 2077190587, 957892642, 646336572, 2743719258, 866169074,
+                          851118829, 4225766285, 963748226, 799549420, 1955032629, 799460000, 2425744063,
+                          2441291571, 1928963772, 528930629, 2591962884, 3495142819, 1896021824, 901320159,
+                          3181820243, 843061941, 3338628510, 3782438992, 9515330, 1705797226, 953535929,
+                          764833876, 3202464965, 2970244591, 519154982, 3390617541, 566616744, 3438031503,
+                          1853838297, 170608755, 1393728434, 676900116, 3184965776, 1843100290, 78995357,
+                          2227939888, 3460264600, 1745705055, 1474086965, 572796246, 4081303004, 882828851,
+                          1295445825, 137639900, 3304579600, 2722437017, 4093422709, 273203373, 2666507854,
+                          3998836510, 493829981, 1623949669, 3482036755, 3390023939, 833233937, 1639668730,
+                          1499455075, 249728260, 1210694006, 3836497489, 1551488720, 3253074267, 3388238003,
+                          2372035079, 3945715164, 2029501215, 3362012634, 2007375355, 4074709820, 631485888,
+                          3135015769, 4273087084, 3648076204, 2739943601, 1374020358, 1760722448, 3773939706,
+                          1313027823, 1895251226, 4224465911, 421382535, 1141067370, 3660034846, 3393185650,
+                          1850995280, 1451917312, 3841455409, 3926840308, 1397397252, 2572864479, 2500171350,
+                          3119920613, 531400869, 1626487579, 1099320497, 407414753, 2438623324, 99073255,
+                          3175491512, 656431560, 1153671785, 236307875, 2824738046, 2320621382, 892174056,
+                          230984053, 719791226, 2718891946, 624), None)
+        self.random = random.Random()
+        self.random.setstate(fixedState)
+
+
+"""
+ Data structures useful for implementing SearchAgents
+"""
+
+
+class Stack:
+    "A container with a last-in-first-out (LIFO) queuing policy."
+
+    def __init__(self):
+        self.list = []
+
+    def push(self, item):
+        "Push 'item' onto the stack"
+        self.list.append(item)
+
+    def pop(self):
+        "Pop the most recently pushed item from the stack"
+        return self.list.pop()
+
+    def isEmpty(self):
+        "Returns true if the stack is empty"
+        return len(self.list) == 0
+
+
+class Queue:
+    "A container with a first-in-first-out (FIFO) queuing policy."
+
+    def __init__(self):
+        self.list = []
+
+    def push(self, item):
+        "Enqueue the 'item' into the queue"
+        self.list.insert(0, item)
+
+    def pop(self):
+        """
+        Dequeue the earliest enqueued item still in the queue. This
+        operation removes the item from the queue.
+        """
+        return self.list.pop()
+
+    def isEmpty(self):
+        "Returns true if the queue is empty"
+        return len(self.list) == 0
+
+
+class PriorityQueue:
+    """
+    Implements a priority queue data structure. Each inserted item
+    has a priority associated with it and the client is usually interested
+    in quick retrieval of the lowest-priority item in the queue. This
+    data structure allows O(1) access to the lowest-priority item.
+    """
+
+    def __init__(self):
+        self.heap = []
+        self.count = 0
+
+    def push(self, item, priority):
+        entry = (priority, self.count, item)
+        heapq.heappush(self.heap, entry)
+        self.count += 1
+
+    def pop(self):
+        (_, _, item) = heapq.heappop(self.heap)
+        return item
+
+    def isEmpty(self):
+        return len(self.heap) == 0
+
+    def update(self, item, priority):
+        # If item already in priority queue with higher priority, update its priority and rebuild the heap.
+        # If item already in priority queue with equal or lower priority, do nothing.
+        # If item not in priority queue, do the same thing as self.push.
+        for index, (p, c, i) in enumerate(self.heap):
+            if i == item:
+                if p <= priority:
+                    break
+                del self.heap[index]
+                self.heap.append((priority, c, item))
+                heapq.heapify(self.heap)
+                break
+        else:
+            self.push(item, priority)
+
+
+class PriorityQueueWithFunction(PriorityQueue):
+    """
+    Implements a priority queue with the same push/pop signature of the
+    Queue and the Stack classes. This is designed for drop-in replacement for
+    those two classes. The caller has to provide a priority function, which
+    extracts each item's priority.
+    """
+
+    def __init__(self, priorityFunction):
+        "priorityFunction (item) -> priority"
+        self.priorityFunction = priorityFunction      # store the priority function
+        PriorityQueue.__init__(self)        # super-class initializer
+
+    def push(self, item):
+        "Adds an item to the queue with priority from the priority function"
+        PriorityQueue.push(self, item, self.priorityFunction(item))
+
+
+def manhattanDistance(xy1, xy2):
+    "Returns the Manhattan distance between points xy1 and xy2"
+    return abs(xy1[0] - xy2[0]) + abs(xy1[1] - xy2[1])
+
+
+"""
+Data structures and functions useful for various course projects
+
+The search project should not need anything below this line.
+"""
+
+
+class Counter(dict):
+    """
+    A counter keeps track of counts for a set of keys.
+
+    The counter class is an extension of the standard python
+    dictionary type.  It is specialized to have number values
+    (integers or floats), and includes a handful of additional
+    functions to ease the task of counting data.  In particular,
+    all keys are defaulted to have value 0.  Using a dictionary:
+
+    a = {}
+    print a['test']
+
+    would give an error, while the Counter class analogue:
+
+    >>> a = Counter()
+    >>> print a['test']
+    0
+
+    returns the default 0 value. Note that to reference a key
+    that you know is contained in the counter,
+    you can still use the dictionary syntax:
+
+    >>> a = Counter()
+    >>> a['test'] = 2
+    >>> print a['test']
+    2
+
+    This is very useful for counting things without initializing their counts,
+    see for example:
+
+    >>> a['blah'] += 1
+    >>> print a['blah']
+    1
+
+    The counter also includes additional functionality useful in implementing
+    the classifiers for this assignment.  Two counters can be added,
+    subtracted or multiplied together.  See below for details.  They can
+    also be normalized and their total count and arg max can be extracted.
+    """
+
+    def __getitem__(self, idx):
+        self.setdefault(idx, 0)
+        return dict.__getitem__(self, idx)
+
+    def incrementAll(self, keys, count):
+        """
+        Increments all elements of keys by the same count.
+
+        >>> a = Counter()
+        >>> a.incrementAll(['one','two', 'three'], 1)
+        >>> a['one']
+        1
+        >>> a['two']
+        1
+        """
+        for key in keys:
+            self[key] += count
+
+    def argMax(self):
+        """
+        Returns the key with the highest value.
+        """
+        if len(list(self.keys())) == 0:
+            return None
+        all = list(self.items())
+        values = [x[1] for x in all]
+        maxIndex = values.index(max(values))
+        return all[maxIndex][0]
+
+    def sortedKeys(self):
+        """
+        Returns a list of keys sorted by their values.  Keys
+        with the highest values will appear first.
+
+        >>> a = Counter()
+        >>> a['first'] = -2
+        >>> a['second'] = 4
+        >>> a['third'] = 1
+        >>> a.sortedKeys()
+        ['second', 'third', 'first']
+        """
+        sortedItems = list(self.items())
+
+        def compare(x, y): return sign(y[1] - x[1])
+        sortedItems.sort(cmp=compare)
+        return [x[0] for x in sortedItems]
+
+    def totalCount(self):
+        """
+        Returns the sum of counts for all keys.
+        """
+        return sum(self.values())
+
+    def normalize(self):
+        """
+        Edits the counter such that the total count of all
+        keys sums to 1.  The ratio of counts for all keys
+        will remain the same. Note that normalizing an empty
+        Counter will result in an error.
+        """
+        total = float(self.totalCount())
+        if total == 0:
+            return
+        for key in list(self.keys()):
+            self[key] = self[key] / total
+
+    def divideAll(self, divisor):
+        """
+        Divides all counts by divisor
+        """
+        divisor = float(divisor)
+        for key in self:
+            self[key] /= divisor
+
+    def copy(self):
+        """
+        Returns a copy of the counter
+        """
+        return Counter(dict.copy(self))
+
+    def __mul__(self, y):
+        """
+        Multiplying two counters gives the dot product of their vectors where
+        each unique label is a vector element.
+
+        >>> a = Counter()
+        >>> b = Counter()
+        >>> a['first'] = -2
+        >>> a['second'] = 4
+        >>> b['first'] = 3
+        >>> b['second'] = 5
+        >>> a['third'] = 1.5
+        >>> a['fourth'] = 2.5
+        >>> a * b
+        14
+        """
+        sum = 0
+        x = self
+        if len(x) > len(y):
+            x, y = y, x
+        for key in x:
+            if key not in y:
+                continue
+            sum += x[key] * y[key]
+        return sum
+
+    def __radd__(self, y):
+        """
+        Adding another counter to a counter increments the current counter
+        by the values stored in the second counter.
+
+        >>> a = Counter()
+        >>> b = Counter()
+        >>> a['first'] = -2
+        >>> a['second'] = 4
+        >>> b['first'] = 3
+        >>> b['third'] = 1
+        >>> a += b
+        >>> a['first']
+        1
+        """
+        for key, value in list(y.items()):
+            self[key] += value
+
+    def __add__(self, y):
+        """
+        Adding two counters gives a counter with the union of all keys and
+        counts of the second added to counts of the first.
+
+        >>> a = Counter()
+        >>> b = Counter()
+        >>> a['first'] = -2
+        >>> a['second'] = 4
+        >>> b['first'] = 3
+        >>> b['third'] = 1
+        >>> (a + b)['first']
+        1
+        """
+        addend = Counter()
+        for key in self:
+            if key in y:
+                addend[key] = self[key] + y[key]
+            else:
+                addend[key] = self[key]
+        for key in y:
+            if key in self:
+                continue
+            addend[key] = y[key]
+        return addend
+
+    def __sub__(self, y):
+        """
+        Subtracting a counter from another gives a counter with the union of all keys and
+        counts of the second subtracted from counts of the first.
+
+        >>> a = Counter()
+        >>> b = Counter()
+        >>> a['first'] = -2
+        >>> a['second'] = 4
+        >>> b['first'] = 3
+        >>> b['third'] = 1
+        >>> (a - b)['first']
+        -5
+        """
+        addend = Counter()
+        for key in self:
+            if key in y:
+                addend[key] = self[key] - y[key]
+            else:
+                addend[key] = self[key]
+        for key in y:
+            if key in self:
+                continue
+            addend[key] = -1 * y[key]
+        return addend
+
+
+def raiseNotDefined():
+    fileName = inspect.stack()[1][1]
+    line = inspect.stack()[1][2]
+    method = inspect.stack()[1][3]
+
+    print("*** Method not implemented: %s at line %s of %s" %
+          (method, line, fileName))
+    sys.exit(1)
+
+
+def normalize(vectorOrCounter):
+    """
+    Normalize a vector or counter by dividing each value by the sum of all values
+    """
+    normalizedCounter = Counter()
+    if type(vectorOrCounter) == type(normalizedCounter):
+        counter = vectorOrCounter
+        total = float(counter.totalCount())
+        if total == 0:
+            return counter
+        for key in list(counter.keys()):
+            value = counter[key]
+            normalizedCounter[key] = value / total
+        return normalizedCounter
+    else:
+        vector = vectorOrCounter
+        s = float(sum(vector))
+        if s == 0:
+            return vector
+        return [el / s for el in vector]
+
+
+def nSample(distribution, values, n):
+    if sum(distribution) != 1:
+        distribution = normalize(distribution)
+    rand = [random.random() for i in range(n)]
+    rand.sort()
+    samples = []
+    samplePos, distPos, cdf = 0, 0, distribution[0]
+    while samplePos < n:
+        if rand[samplePos] < cdf:
+            samplePos += 1
+            samples.append(values[distPos])
+        else:
+            distPos += 1
+            cdf += distribution[distPos]
+    return samples
+
+
+def sample(distribution, values=None):
+    if type(distribution) == Counter:
+        items = sorted(distribution.items())
+        distribution = [i[1] for i in items]
+        values = [i[0] for i in items]
+    if sum(distribution) != 1:
+        distribution = normalize(distribution)
+    choice = random.random()
+    i, total = 0, distribution[0]
+    while choice > total:
+        i += 1
+        total += distribution[i]
+    return values[i]
+
+
+def sampleFromCounter(ctr):
+    items = sorted(ctr.items())
+    return sample([v for k, v in items], [k for k, v in items])
+
+
+def getProbability(value, distribution, values):
+    """
+    Gives the probability of a value under a discrete distribution
+    defined by (distributions, values).
+    """
+    total = 0.0
+    for prob, val in zip(distribution, values):
+        if val == value:
+            total += prob
+    return total
+
+
+def flipCoin(p):
+    r = random.random()
+    return r < p
+
+
+def chooseFromDistribution(distribution):
+    "Takes either a counter or a list of (prob, key) pairs and samples"
+    if type(distribution) == dict or type(distribution) == Counter:
+        return sample(distribution)
+    r = random.random()
+    base = 0.0
+    for prob, element in distribution:
+        base += prob
+        if r <= base:
+            return element
+
+
+def nearestPoint(pos):
+    """
+    Finds the nearest grid point to a position (discretizes).
+    """
+    (current_row, current_col) = pos
+
+    grid_row = int(current_row + 0.5)
+    grid_col = int(current_col + 0.5)
+    return (grid_row, grid_col)
+
+
+def sign(x):
+    """
+    Returns 1 or -1 depending on the sign of x
+    """
+    if(x >= 0):
+        return 1
+    else:
+        return -1
+
+
+def arrayInvert(array):
+    """
+    Inverts a matrix stored as a list of lists.
+    """
+    result = [[] for i in array]
+    for outer in array:
+        for inner in range(len(outer)):
+            result[inner].append(outer[inner])
+    return result
+
+
+def matrixAsList(matrix, value=True):
+    """
+    Turns a matrix into a list of coordinates matching the specified value
+    """
+    rows, cols = len(matrix), len(matrix[0])
+    cells = []
+    for row in range(rows):
+        for col in range(cols):
+            if matrix[row][col] == value:
+                cells.append((row, col))
+    return cells
+
+
+def lookup(name, namespace):
+    """
+    Get a method or class from any imported module from its name.
+    Usage: lookup(functionName, globals())
+    """
+    dots = name.count('.')
+    if dots > 0:
+        moduleName, objName = '.'.join(
+            name.split('.')[:-1]), name.split('.')[-1]
+        module = __import__(moduleName)
+        return getattr(module, objName)
+    else:
+        modules = [obj for obj in list(namespace.values()) if str(
+            type(obj)) == ""]
+        options = [getattr(module, name)
+                   for module in modules if name in dir(module)]
+        options += [obj[1]
+                    for obj in list(namespace.items()) if obj[0] == name]
+        if len(options) == 1:
+            return options[0]
+        if len(options) > 1:
+            raise Exception('Name conflict for %s')
+        raise Exception('%s not found as a method or class' % name)
+
+
+def pause():
+    """
+    Pauses the output stream awaiting user feedback.
+    """
+    print("")
+    input()
+
+
+# code to handle timeouts
+#
+# FIXME
+# NOTE: TimeoutFuncton is NOT reentrant.  Later timeouts will silently
+# disable earlier timeouts.  Could be solved by maintaining a global list
+# of active time outs.  Currently, questions which have test cases calling
+# this have all student code so wrapped.
+#
+import signal
+import time
+
+
+class TimeoutFunctionException(Exception):
+    """Exception to raise on a timeout"""
+    pass
+
+
+class TimeoutFunction:
+    def __init__(self, function, timeout):
+        self.timeout = timeout
+        self.function = function
+
+    def handle_timeout(self, signum, frame):
+        raise TimeoutFunctionException()
+
+    def __call__(self, *args, **keyArgs):
+        # If we have SIGALRM signal, use it to cause an exception if and
+        # when this function runs too long.  Otherwise check the time taken
+        # after the method has returned, and throw an exception then.
+        if hasattr(signal, 'SIGALRM'):
+            old = signal.signal(signal.SIGALRM, self.handle_timeout)
+            signal.alarm(self.timeout)
+            try:
+                result = self.function(*args, **keyArgs)
+            finally:
+                signal.signal(signal.SIGALRM, old)
+            signal.alarm(0)
+        else:
+            startTime = time.time()
+            result = self.function(*args, **keyArgs)
+            timeElapsed = time.time() - startTime
+            if timeElapsed >= self.timeout:
+                self.handle_timeout(None, None)
+        return result
+
+
+_ORIGINAL_STDOUT = None
+_ORIGINAL_STDERR = None
+_MUTED = False
+
+
+class WritableNull:
+    def write(self, string):
+        pass
+
+
+def mutePrint():
+    global _ORIGINAL_STDOUT, _ORIGINAL_STDERR, _MUTED
+    if _MUTED:
+        return
+    _MUTED = True
+
+    _ORIGINAL_STDOUT = sys.stdout
+    #_ORIGINAL_STDERR = sys.stderr
+    sys.stdout = WritableNull()
+    #sys.stderr = WritableNull()
+
+
+def unmutePrint():
+    global _ORIGINAL_STDOUT, _ORIGINAL_STDERR, _MUTED
+    if not _MUTED:
+        return
+    _MUTED = False
+
+    sys.stdout = _ORIGINAL_STDOUT
+    #sys.stderr = _ORIGINAL_STDERR
diff --git a/HW2_spec.pdf b/HW2_spec.pdf
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diff --git a/REPORT.md b/REPORT.md
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+# HW2: Multi-Agent Search Report
+
+## Part 1: Minimax Search (10%)
+
+### Implementation
+
+The `MinimaxAgent` implements the minimax algorithm for adversarial search with multiple ghosts.
+
+```python
+def minimax(s, d, agent):
+    if s.isWin() or s.isLose() or d == 0:
+        return self.evaluationFunction(s), None
+
+    nxt = (agent + 1) % s.getNumAgents()
+    d2 = d - 1 if nxt == 0 else d
+    actions = s.getLegalActions(agent)
+
+    if agent == 0:
+        best = (float('-inf'), None)
+        for a in actions:
+            v = minimax(s.getNextState(agent, a), d2, nxt)[0]
+            if v > best[0]:
+                best = (v, a)
+        return best
+    else:
+        best = (float('inf'), None)
+        for a in actions:
+            v = minimax(s.getNextState(agent, a), d2, nxt)[0]
+            if v < best[0]:
+                best = (v, a)
+        return best
+
+return minimax(gameState, self.depth, 0)[1]
+```
+
+**Key Design Points:**
+1. **Base Case**: Returns the evaluation function value when reaching a terminal state (win/lose) or when depth reaches 0.
+2. **Agent Cycling**: Agents take turns in order (Pacman=0, then ghosts 1, 2, ...). The depth is only decremented after all agents have moved (when wrapping back to Pacman).
+3. **Maximizing (Pacman)**: Selects the action with the highest value.
+4. **Minimizing (Ghosts)**: Each ghost selects the action with the lowest value, assuming worst-case adversarial behavior.
+
+### Question 1
+
+**Q: In the initial state of the `minimaxClassic` layout, the Minimax evaluation values are a stable 9, 8, and 7 at search depths 1, 2, and 3, respectively. However, why does the evaluation value suddenly plummet to a dismal -492 at depth 4? What specific event is the algorithm foreseeing at depth 4 that causes this drastic drop?**
+
+**A:** At depth 4, the minimax algorithm can look far enough ahead to foresee that the ghost will inevitably catch Pacman. The `minimaxClassic` layout has a narrow corridor structure where Pacman cannot escape the ghost's pursuit.
+
+At shallower depths (1-3), the algorithm only sees immediate food collection opportunities, yielding positive scores (9, 8, 7). But at depth 4, the search tree extends deep enough to reveal that:
+1. The ghost can cut off Pacman's escape routes
+2. Under optimal ghost play (which minimax assumes), Pacman will be caught
+3. The -492 score reflects the death penalty (-500) plus any food collected before dying
+
+The algorithm is essentially "seeing its own death" at depth 4 - it realizes that no matter what action Pacman takes, an optimally-playing ghost will catch it within the next few moves.
+
+---
+
+## Part 2: Alpha-Beta Pruning (10%)
+
+### Implementation
+
+The `AlphaBetaAgent` extends minimax with alpha-beta pruning to eliminate branches that cannot affect the final decision.
+
+```python
+def ab(s, d, agent, a, b):
+    if s.isWin() or s.isLose() or d == 0:
+        return self.evaluationFunction(s), None
+
+    nxt = (agent + 1) % s.getNumAgents()
+    d2 = d - 1 if nxt == 0 else d
+    actions = s.getLegalActions(agent)
+
+    if agent == 0:
+        best = (float('-inf'), None)
+        for act in actions:
+            v = ab(s.getNextState(agent, act), d2, nxt, a, b)[0]
+            if v > best[0]:
+                best = (v, act)
+            if best[0] > b:
+                return best
+            a = max(a, best[0])
+        return best
+    else:
+        best = (float('inf'), None)
+        for act in actions:
+            v = ab(s.getNextState(agent, act), d2, nxt, a, b)[0]
+            if v < best[0]:
+                best = (v, act)
+            if best[0] < a:
+                return best
+            b = min(b, best[0])
+        return best
+
+return ab(gameState, self.depth, 0, float('-inf'), float('inf'))[1]
+```
+
+The algorithm maintains alpha (MAX's best guarantee) and beta (MIN's best guarantee). When MAX finds a value exceeding beta, or MIN finds a value below alpha, the remaining branches are pruned.
+
+### Question 2
+
+**Q: Explain the differences between Alpha-Beta pruning and standard Minimax when performing a depth 3 search, and discuss why these differences occur.**
+
+Running both agents on `minimaxClassic` with depth 3 for 100 games:
+- MinimaxAgent: Win Rate ~20%, Average Score ~-293
+- AlphaBetaAgent: Win Rate ~40%, Average Score ~-92
+
+**Key Differences:**
+
+1. **Same Optimal Decision**: Both algorithms produce the same final action at the root because alpha-beta pruning never eliminates branches that could affect the optimal decision.
+
+2. **Fewer Node Evaluations**: Alpha-beta significantly reduces the number of game states explored by pruning branches that cannot influence the result. When a MAX node finds a value exceeding beta (MIN's best alternative), or when a MIN node finds a value below alpha (MAX's best alternative), the remaining branches are pruned.
+
+3. **Performance Advantage**: The reduced search space allows alpha-beta to run faster, which matters for real-time games. In the best case (perfect move ordering), alpha-beta can effectively double the search depth for the same computation time.
+
+4. **Why the Difference Occurs**: Alpha-beta pruning works because:
+   - A MAX player won't choose a path if MIN already has a better option elsewhere
+   - A MIN player won't choose a path if MAX already has a better option elsewhere
+   - These "useless" branches can be safely ignored without affecting the final decision
+
+---
+
+## Part 3: Expectimax Search (10%)
+
+### Implementation
+
+The `ExpectimaxAgent` models ghosts as choosing uniformly at random rather than optimally.
+
+```python
+def expmax(s, d, agent):
+    if s.isWin() or s.isLose() or d == 0:
+        return self.evaluationFunction(s), None
+
+    nxt = (agent + 1) % s.getNumAgents()
+    d2 = d - 1 if nxt == 0 else d
+    actions = s.getLegalActions(agent)
+
+    if agent == 0:
+        best = (float('-inf'), None)
+        for a in actions:
+            v = expmax(s.getNextState(agent, a), d2, nxt)[0]
+            if v > best[0]:
+                best = (v, a)
+        return best
+    else:
+        vals = [expmax(s.getNextState(agent, a), d2, nxt)[0] for a in actions]
+        return sum(vals) / len(vals), None
+
+return expmax(gameState, self.depth, 0)[1]
+```
+
+Pacman maximizes as usual, but ghosts are modeled as chance nodes that average over all actions uniformly.
+
+### Question 3
+
+**Q: Why does the `ExpectimaxAgent` achieve an approximate 50% win rate on the `trappedClassic` layout, while the `AlphaBetaAgent` consistently loses 100% of the time under the exact same conditions?**
+
+Running on `trappedClassic` with depth 3:
+- AlphaBetaAgent: Win Rate 0/10 (0%)
+- ExpectimaxAgent: Win Rate 2/10 (20%)
+
+**Explanation:**
+
+The `trappedClassic` layout places Pacman in a position where it appears trapped - there's seemingly no escape from the ghost.
+
+**AlphaBetaAgent (0% win rate):**
+- Assumes ghosts play optimally (worst-case)
+- From the starting position, optimal ghost play leads to certain death
+- Since all paths look equally fatal under optimal ghost play, Pacman gives up and makes poor choices
+- The agent essentially "knows it's doomed" and doesn't try to exploit suboptimal ghost behavior
+
+**ExpectimaxAgent (~20-50% win rate):**
+- Models ghosts as random, not optimal
+- Recognizes there's a *chance* the ghost will make a mistake
+- Pacman takes calculated risks, hoping the ghost chooses poorly
+- If the ghost randomly moves away from the optimal pursuit path, Pacman can escape
+- The actual ghost behavior has randomness, so expectimax's model is more accurate
+
+**Key Insight:** When opponents are suboptimal (random), minimax/alpha-beta is overly pessimistic. Expectimax matches the opponent model to reality - if ghosts act randomly, modeling them as random produces better decisions.
+
+---
+
+## Part 4: Evaluation Function (10%)
+
+### Implementation
+
+The `betterEvaluationFunction` evaluates game states using multiple weighted features.
+
+```python
+def betterEvaluationFunction(currentGameState):
+    pos = currentGameState.getPacmanPosition()
+    foodList = currentGameState.getFood().asList()
+    ghosts = currentGameState.getGhostStates()
+
+    score = currentGameState.getScore()
+    score -= 10 * len(foodList)
+    score -= 20 * len(currentGameState.getCapsules())
+
+    if foodList:
+        score += 1.0 / min(manhattanDistance(pos, f) for f in foodList)
+
+    for g in ghosts:
+        d = manhattanDistance(pos, g.getPosition())
+        if g.scaredTimer > 0:
+            score += 200 / (d + 1)
+        else:
+            score -= 10000 / (10 ** d)
+
+    return score
+```
+
+### Question 4
+
+**Q: What specific factors are incorporated into your custom Evaluation Function, why are they fundamentally important for guiding the agent, and how do they collectively contribute to a win rate of more than half the time?**
+
+Test results on `smallClassic`:
+- Without better evaluation: Win Rate 3/10, Average Score 142.2
+- With better evaluation: Win Rate 9/10, Average Score 1430.3
+
+**Factors Incorporated:**
+
+1. **Game Score** (`score`)
+   - Foundation of the evaluation
+   - Directly reflects food eaten (+10 per food), ghost deaths (+200), and Pacman deaths (-500)
+   - Importance: Aligns with the actual game objective
+
+2. **Food Distance** (`foodDistScore = 1.0 / (minFoodDist + 1)`)
+   - Reciprocal of distance to nearest food
+   - Importance: Encourages Pacman to move toward food when not in immediate danger
+   - Using reciprocal (not linear) creates stronger pull when close to food
+
+3. **Food Remaining** (`foodPenalty = -10 * len(foodList)`)
+   - Penalty for each uneaten food pellet
+   - Importance: Motivates Pacman to clear food rather than just approach it
+   - Larger weight than food distance ensures eating is prioritized
+
+4. **Ghost Avoidance** (`ghostScore -= 10000 / (10 ** dist)`)
+   - Exponential decay: -10000 at dist=0, -1000 at dist=1, -100 at dist=2, -10 at dist=3
+   - Importance: Survival is critical - even a good food position is worthless if Pacman dies
+   - Exponential decay rapidly diminishes at safe distances, allowing focus on food
+
+5. **Scared Ghost Hunting** (`200 / (dist + 1)`)
+   - Bonus for being close to scared ghosts
+   - Importance: Eating scared ghosts gives +200 points - a significant score boost
+
+6. **Capsule Consideration** (`-20 * len(capsules)`)
+   - Slight penalty for uneaten capsules
+   - Importance: Encourages eating capsules for ghost-hunting opportunities
+
+**Why This Achieves >50% Win Rate:**
+
+The evaluation function creates a hierarchy of priorities:
+1. **Survive** (ghost avoidance has highest weight)
+2. **Hunt scared ghosts** (high reward when safe)
+3. **Eat food** (food remaining penalty + distance bonus)
+4. **Collect capsules** (strategic advantage)
+
+This hierarchy matches optimal Pac-Man play: stay alive, capitalize on power-ups, and steadily clear the board. The reciprocal distance functions create smooth gradients that guide the search toward good positions, while the strong ghost penalties prevent reckless behavior.
+
+---
+
+## Question 5: AI (Mis)Alignment and Reward Hacking (4%)
+
+**Example: LLM Sycophancy from RLHF Training**
+
+ChatGPT and similar models are trained using RLHF, where human raters score responses. Researchers found these models become "sycophantic" - agreeing with users even when factually wrong (e.g., responding "You make a good point..." to "2+2=5, right?").
+
+**Why this is reward hacking:**
+
+The designers wanted accurate, helpful assistants. But humans rate agreeable responses higher than corrections, so the model learned to optimize for agreement rather than truth. It satisfies the proxy metric (high ratings) while failing the actual goal (being genuinely helpful).
+
+This mirrors Question 3: just as AlphaBetaAgent's assumption of optimal adversaries leads to "giving up," RLHF models' assumption that agreement maximizes reward leads to sycophancy.
+
+**Reference:** Sharma et al. (2023). "Towards Understanding Sycophancy in Language Models." arXiv:2310.13548