高斯消元法 -math

 

 

#include <bits/stdc++.h>
#define dbg(x) std::cerr << #x << "=" << x << "\n"
using i64 = long long;

const int N = 105;
std::vector<double> f[N];

void output(int n) {
    for (int i = 1; i <= n; i++) {
        for (int j = 1; j <= n + 1; j++) {
            std::cerr << f[i][j] << " \n"[j == n + 1];
        }
    }
    std::cerr << "\n";
}
signed main() {
    std::ios::sync_with_stdio(false);
    std::cin.tie(nullptr);
    std::cout << std::fixed << std::setprecision(2);
    std::cerr << std::fixed << std::setprecision(2);
    int n;
    std::cin >> n;
    for (int i = 1; i <= n; i++) {
        f[i].resize(n + 2);
        for (int j = 1; j <= n + 1; j++) {
            std::cin >> f[i][j];
        }
    }
    //运用矩阵的左上到右下的对角线性质算答案
    for (int i = 1; i <= n; i++) {//第i行第i列的数拿去减掉其他行的数
        if (f[i][i] == 0) {
            int flag = 1;
            for (int j = i; j <= n; j++) {
                if (f[j][i] == 0) continue;
                std::swap(f[i], f[j]);
                //output(n);
                flag = 0;
                break;
            }
            if (flag) {
                std::cout << "No Solution\n";
                return 0;
            }
        }
        for (int j = 1; j <= n; j++) {
            if (j == i) continue;//不是自己这行
            if (f[j][i] == 0) continue;//如果自己是0就不用减了，加快速度 

            double coef = f[j][i] / f[i][i];
            for (int k = 1; k <= n + 1; k++) {
                f[j][k] -= f[i][k] * coef;
            }
            //output(n);
        }
    }

    for (int i = 1; i <= n; i++) {
        if (f[i][i] == 0) {
            std::cout << "No Solution\n";
            return 0;
        }
    }
    for (int i = 1; i <= n; i++) {
        if (f[i][n + 1] == 0) std::cout << 0.00 << "\n";
        else std::cout << 1.0 * f[i][n + 1] / f[i][i] << "\n";
    }
    return 0;
}