// 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;
}