列主元高斯消去法c++完整版

以下是列主元高斯消去法的C++完整版代码：

#include <iostream>
#include <cmath>

using namespace std;

const double EPSILON = 1e-10; // 定义一个极小值，用于判断浮点数是否为0

void gaussianElimination(double **A, double *B, int n) {
    // 高斯消去
    for (int k = 0; k < n - 1; k++) {
        // 选取主元
        int maxRow = k;
        double maxVal = fabs(A[k][k]);
        for (int i = k + 1; i < n; i++) {
            if (fabs(A[i][k]) > maxVal) {
                maxRow = i;
                maxVal = fabs(A[i][k]);
            }
        }
        
        // 交换行
        if (maxRow != k) {
            for (int j = k; j < n; j++) {
                swap(A[k][j], A[maxRow][j]);
            }
            swap(B[k], B[maxRow]);
        }
        
        // 消元
        for (int i = k + 1; i < n; i++) {
            double factor = A[i][k] / A[k][k];
            for (int j = k; j < n; j++) {
                A[i][j] -= factor * A[k][j];
            }
            B[i] -= factor * B[k];
        }
    }
    
    // 回代求解
    double *X = new double[n];
    for (int i = n - 1; i >= 0; i--) {
        X[i] = B[i];
        for (int j = i + 1; j < n; j++) {
            X[i] -= A[i][j] * X[j];
        }
        X[i] /= A[i][i];
    }
    
    // 输出结果
    cout << "The solution is: ";
    for (int i = 0; i < n; i++) {
        cout << X[i] << " ";
    }
    cout << endl;
    
    delete[] X;
}

int main() {
    int n;
    cout << "Enter the number of equations: ";
    cin >> n;
    
    double **A = new double*[n];
    double *B = new double[n];
    
    cout << "Enter the coefficients of the equations:" << endl;
    for (int i = 0; i < n; i++) {
        A[i] = new double[n];
        for (int j = 0; j < n; j++) {
            cin >> A[i][j];
        }
    }
    
    cout << "Enter the constants of the equations:" << endl;
    for (int i = 0; i < n; i++) {
        cin >> B[i];
    }
    
    gaussianElimination(A, B, n);
    
    for (int i = 0; i < n; i++) {
        delete[] A[i];
    }
    delete[] A;
    delete[] B;
    
    return 0;
}