// Problem 4: Jacobi and Gauss-Seidel methods
#include <iostream>
#include <iomanip>
#include <cmath>
#include <vector>
#include <algorithm>
using namespace std;

const double TOL = 1e-6;
const int MAX_ITER = 100;

int main() {
    // Rearranged system (weakly diagonally dominant):
    // 7x1 - 3x2 + 4x3 = 6
    // 2x1 + 5x2 + 3x3 = -5
    // -3x1 + 2x2 + 6x3 = 2

    double b[3] = {6, -5, 2};

    // Jacobi
    cout << "Jacobi Method:\n";
    vector<double> x = {0, 0, 0};
    for (int iter = 1; iter <= MAX_ITER; iter++) {
        vector<double> x_old = x;
        x[0] = (b[0] + 3*x_old[1] - 4*x_old[2]) / 7;
        x[1] = (b[1] - 2*x_old[0] - 3*x_old[2]) / 5;
        x[2] = (b[2] + 3*x_old[0] - 2*x_old[1]) / 6;

        double maxDiff = max({fabs(x[0]-x_old[0]), fabs(x[1]-x_old[1]), fabs(x[2]-x_old[2])});
        if (maxDiff < TOL) {
            cout << "Converged in " << iter << " iterations\n";
            break;
        }
    }
    for (int i = 0; i < 3; i++)
        cout << "x" << (i+1) << " = " << fixed << setprecision(6) << x[i] << "\n";

    // Gauss-Seidel
    cout << "\nGauss-Seidel Method:\n";
    x = {0, 0, 0};
    for (int iter = 1; iter <= MAX_ITER; iter++) {
        vector<double> x_old = x;
        x[0] = (b[0] + 3*x[1] - 4*x[2]) / 7;
        x[1] = (b[1] - 2*x[0] - 3*x[2]) / 5;
        x[2] = (b[2] + 3*x[0] - 2*x[1]) / 6;

        double maxDiff = max({fabs(x[0]-x_old[0]), fabs(x[1]-x_old[1]), fabs(x[2]-x_old[2])});
        if (maxDiff < TOL) {
            cout << "Converged in " << iter << " iterations\n";
            break;
        }
    }
    for (int i = 0; i < 3; i++)
        cout << "x" << (i+1) << " = " << fixed << setprecision(6) << x[i] << "\n";

    return 0;
}