在本程序中默认该现行规划问题有最优解

#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：