c++实现单纯形法现行规划问题的求解

在本程序中默认该现行规划问题有最优解

针对此问题：

#include<iostream>
using namespace std;

int check(float *sigema, int m) {
    for (int i = 1; i <= m ; i++) {
        if (sigema[i] > 0) {
            return 0;
        }
    }
    return 1;
}

//此程序已经化为标准型的线性规划问题中,且默认有最优解
int main(int argc, char* argv[])
{
    //数据输入部分
    int m, n;
    cout << "请输入变量个数：";
    cin >> m;
    cout << "请输入不等式个数:";
    cin >> n;
    float **matrix = new float*[n + 1];      //系数矩阵
    for (int i = 1; i <= n; i++) {
        matrix[i] = new float[m + 2];
    }
    float *cj = new float[m + 1];
    float *cB = new float[n + 1];   //基变量系数
    int *XB = new int[n + 1];   //用来标注基变量x的下标
    float *b = new float[n + 1];
    float *sigema = new float[n + 1];
    float *sita = new float[n + 1];
    //初始化
    for (int i = 0; i <= m; i++) {
        cj[i] = 0;
    }
    for (int i = 0; i <= n; i++) {
        cB[i] = 0;
        XB[i] = 0;
        b[i] = 0;
        sigema[i] = 0;
        sita[i] = 0;
    }
    cout << "请输入目标函数系数(用空格间开)：" << endl;
    for (int i = 1; i <= m; i++) {
        cin >> cj[i];
    }
    cout << "请输入各不等式的系数和常量(用空格间开)：" << endl;
    for (int i = 1; i <= n; i++) {
        cout << "不等式" << i << ": ";
        for (int j = 1; j <= m + 1; j++) {
            cin >> matrix[i][j];
        }
    }
    cout << "请输入目标函数中基变量下标：" << endl;
    for (int i = 1; i <= n; i++) {
        cin >> XB[i];
        cB[i] = cj[XB[i]];
        //常量
        b[i] = matrix[i][m + 1];
    }

    //计算检验数
    for (int i = 1; i <= m; i++) {
        sigema[i] = cj[i];
        for (int j = 1; j <= n; j++) {
            sigema[i] -= cB[j] * matrix[j][i];
        }
    }

    while (check(sigema, m) == 0) {
        //寻找入基变量
    float maxn = sigema[1];
    int sigema_xindex = 0;
    float sigema_xcoefficient = 0;
    for (int i = 1; i <= m; i++) {
        if (maxn <= sigema[i]) {
            maxn = sigema[i];
            sigema_xindex = i;
            sigema_xcoefficient = cj[i];
        }
    }
    //计算sita
    for (int i = 1; i <= n; i++) {
        if (matrix[i][sigema_xindex] > 0) {
            sita[i] = b[i] / matrix[i][sigema_xindex];
        }
        else {
            sita[i] = 9999; //表示sita值为负数
        }
    }
    //寻找出基变量
    float minn = sita[1];
    int sita_xindex = 0;
    for (int i = 1; i <= n; i++) {
        if (minn >= sita[i] && sita[i] > 0) {
            minn = sita[i];
            sita_xindex = i;
        }
    }
    //入基出基变换,先入基再出基
    //入基操作
    for (int i = 1; i <= n; i++) {
        if (i == sita_xindex) {
            XB[i] = sigema_xindex;
            cB[i] = sigema_xcoefficient;
            break;
        }
    }
    //出基计算  
    //化1
    //cout << endl << "此处为化1的结果------" << endl;
    float mul1 = matrix[sita_xindex][sigema_xindex];
    for (int i = 1; i <= m; i++) {
        matrix[sita_xindex][i] /= mul1;
    }
    b[sita_xindex] /= mul1;
    //化0
    //cout << endl << "此处为化0的结果------" << endl;
    for (int i = 1; i <= n; i++) {
        if (i == sita_xindex) {
            continue;
        }
        float mul2 = matrix[i][sigema_xindex] / matrix[sita_xindex][sigema_xindex];
        for (int j = 1; j <= m; j++) {
            matrix[i][j] -= (matrix[sita_xindex][j] * mul2);
        }
        b[i] -= (b[sita_xindex] * mul2);
    }
    for (int i = 1; i <= n; i++) {
        if (i == sita_xindex) {
            continue;
        }
    }
    for (int i = 1; i <= m; i++) {
        sigema[i] = cj[i];
        for (int j = 1; j <= n; j++) {
            sigema[i] -= cB[j] * matrix[j][i];
        }
    }
    }
    float MaxZ = 0;
    float *result = new float[m + 1];
    for (int i = 0; i <= m; i++) {
        result[i] = 0;
    }
    for (int i = 1; i <= n; i++) {
        result[XB[i]] = b[i];
    }
    cout << "最优解为：X = (";
    for (int i = 1; i < m; i++) {
        cout << result[i] << ",";
    }
    cout << result[m] << ")" << endl;
    for (int i = 1; i <= m; i++) {
        MaxZ += result[i] * cj[i];
    }
    cout << "最优值为：MzxZ = " << MaxZ;
    return 0;
}

程序运行结果：