【模板】高斯消元法(Gaussian Elimination) 题解

思路分析

按题目要求使用对应数据结构与算法模拟/递推求解，注意数据范围边界与时间复杂度。

参考代码

#include <cmath>
#include <iomanip>
#include <iostream>
#include <vector>
using namespace std;

const double EPS = 1e-8;

int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    int n;
    if (!(cin >> n)) return 0;
    vector<vector<double>> a(n, vector<double>(n + 1));
    for (int i = 0; i < n; ++i) {
        for (int j = 0; j <= n; ++j) cin >> a[i][j];
    }
    for (int col = 0; col < n; ++col) {
        int piv = col;
        for (int i = col + 1; i < n; ++i) {
            if (fabs(a[i][col]) > fabs(a[piv][col])) piv = i;
        }
        if (fabs(a[piv][col]) < EPS) {
            cout << "No Solution\n";
            return 0;
        }
        swap(a[col], a[piv]);
        for (int i = 0; i < n; ++i) {
            if (i == col) continue;
            double factor = a[i][col] / a[col][col];
            for (int j = col; j <= n; ++j) {
                a[i][j] -= factor * a[col][j];
            }
        }
    }
    cout << fixed << setprecision(2);
    for (int i = 0; i < n; ++i) {
        double val = a[i][n] / a[i][i];
        if (fabs(val) < 0.005) val = 0.0;
        cout << val << "\n";
    }
    return 0;
}