Feat: hw2 done

HW2_111550013/HW2_111550013_code/problem1.cpp

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+// Problem 1: Gaussian elimination with partial pivoting
+#include <iostream>
+#include <iomanip>
+#include <cmath>
+using namespace std;
+
+const int N = 4;
+
+int main() {
+    double A[N][N+1] = {
+        {4, 2, -2, -1, 7},
+        {0, 4, 1, 2, 10},
+        {3, -2, 1, 2, 2},
+        {2, 0, 3, -5, 3}
+    };
+
+    // Forward elimination with partial pivoting
+    for (int k = 0; k < N - 1; k++) {
+        // Find pivot
+        int maxRow = k;
+        for (int i = k + 1; i < N; i++)
+            if (fabs(A[i][k]) > fabs(A[maxRow][k])) maxRow = i;
+
+        if (maxRow != k) {
+            cout << "Column " << (k+1) << ": swap row " << (k+1) << " with row " << (maxRow+1) << "\n";
+            for (int j = 0; j <= N; j++) swap(A[k][j], A[maxRow][j]);
+        }
+
+        // Eliminate
+        for (int i = k + 1; i < N; i++) {
+            double m = A[i][k] / A[k][k];
+            for (int j = k; j <= N; j++) A[i][j] -= m * A[k][j];
+        }
+    }
+
+    // Back substitution
+    double x[N];
+    for (int i = N - 1; i >= 0; i--) {
+        x[i] = A[i][N];
+        for (int j = i + 1; j < N; j++) x[i] -= A[i][j] * x[j];
+        x[i] /= A[i][i];
+    }
+
+    cout << "\nSolution:\n";
+    for (int i = 0; i < N; i++)
+        cout << "x" << (i+1) << " = " << fixed << setprecision(6) << x[i] << "\n";
+
+    return 0;
+}