gauss

#include <cmath>
#include <algorithm>

int gauss(int n, double *A, double *b, double *x) {
    for (int k = 0; k < n; k++) {
        int max_row = k;
        for (int i = k + 1; i < n; i++) {
            if (std::fabs(A[i * n + k]) > std::fabs(A[max_row * n + k])) {
                max_row = i;
            }
        }

        if (max_row != k) {
            for (int j = k; j < n; j++) {
                std::swap(A[k * n + j], A[max_row * n + j]);
            }
            std::swap(b[k], b[max_row]);
        }

        if (std::fabs(A[k * n + k]) < 1e-15) {
            return 1;
        }

        for (int i = k + 1; i < n; i++) {
            double factor = A[i * n + k] / A[k * n + k];
            for (int j = k; j < n; ++j) {
                A[i * n + j] -= factor * A[k * n + j];
            }
            b[i] -= factor * b[k];
        }
    }

    for (int i = n - 1; i >= 0; i--) {
        x[i] = b[i];
        for (int j = i + 1; j < n; j++) {
            x[i] -= A[i * n + j] * x[j];
        }
        x[i] /= A[i * n + i];
    }

    return 0;
}