python/TangDou/AcWing/Gauss/P3389.cpp

#include <bits/stdc++.h>

using namespace std;
const int N = 110;

const double eps = 1e-8;
double a[N][N];
int n;
int gauss() {
    int c, r;
    for (c = 0, r = 0; c < n; c++) {
        int t = r;
        for (int i = r; i < n; i++)
            if (abs(a[i][c]) > abs(a[t][c])) t = i;

        if (abs(a[t][c]) < eps) continue;

        if (r != t) swap(a[t], a[r]);

        for (int i = n; i >= c; i--) a[r][i] /= a[r][c];

        for (int i = r + 1; i < n; i++)
            for (int j = n; j >= c; j--)
                a[i][j] -= a[r][j] * a[i][c];
        r++;
    }

    if (r < n) {
        for (int i = r; i < n; i++)
            if (abs(a[i][n]) > eps)
                return 2;
        return 1;
    }

    for (int i = n - 2; i >= 0; i--)
        for (int j = i + 1; j < n; j++)
            a[i][n] -= a[i][j] * a[j][n];

    return 0;
}

int main() {
    cin >> n;

    for (int i = 0; i < n; i++)
        for (int j = 0; j <= n; j++)
            cin >> a[i][j];

    int t = gauss();
    //经验教训：
    // 1、一定要复制题目中输出的字符串，我就是因为"No Solution" -> "No solution"挂了第一个点
    // 2、Luogu的模板题中，没有强制区分无解和无穷多组解。
    if (t == 2 || t == 1)
        puts("No Solution");
    // else if (t == 1)
    //   puts("Infinite group solutions");
    else {
        for (int i = 0; i < n; i++) {
            if (abs(a[i][n]) < eps) a[i][n] = 0;
            printf("%.2lf\n", a[i][n]);
        }
    }
    return 0;
}