c++高斯消元法求解线性方程组

#include<iostream>
#include<math.h>
#include<string.h>
using namespace std;
#define MaxNum 10
int unuse_result[MaxNum];
int GaussFun(int equ, int var, int result[],int array[MaxNum][MaxNum])
{
    int i, j, k, col, num1, num2;
    int max_r, ta, tb, gcdtemp, lcmtemp;
    int temp, unuse_x_num, unuse_index;
    col = 0;
    for (k = 0; k < equ && col < var; k++, col++)//循环处理增广矩阵的各行 
    {
        max_r = k;
        for (i = k + 1; i < equ; i++)
        {
            if (abs(array[i][col]) > abs(array[max_r][col]))
            {
                max_r = i;//保存绝对值最大的行 
            }
        }
        if (max_r != k)
        {
            for (j = k; j < var + 1; j++)
            {
                temp = array[k][j];
                array[k][j] = array[max_r][j];
                array[max_r][j] = temp;
            }
        }
        if (array[k][col] == 0)
        {
            k--;
            continue;
        }
        for (i = k + 1; i < equ; i++)
        {
            if (array[i][col] != 0)
            {
                num1 = abs(array[i][col]);
                num2 = abs(array[k][col]);
                while (num2 != 0)
                {
                    temp = num2;
                    num2 = num1 % num2;
                    num1 = temp;
                }
                gcdtemp = num1;//最大公约数 
                lcmtemp = (abs(array[i][col]) * abs(array[k][col])) / gcdtemp;
                ta = lcmtemp / abs(array[i][col]);
                tb = lcmtemp / abs(array[k][col]);
                if (array[i][col] * array[k][col] < 0)
                {
                    tb = -tb;
                }
                for (j = col; j < var + 1; j++)
                {
                    array[i][j] = array[i][j] * ta - array[k][j] * tb;
                }
            }
        }
    }
    for (i = k; i < equ; i++)
    {
        if (array[i][col] != 0)
        {
            return -1;
        }
    }
    if (k < var)
    {
        for (i = k - 1; i >= 0; i--)
        {
            unuse_x_num = 0;
            for (j = 0; j < var; j++)
            {
                if (array[i][j] != 0 && unuse_result[j])
                {
                    unuse_x_num++;
                    unuse_index = j;
                }
            }
            if (unuse_x_num > 1)
            {
                continue;
            }
            temp = array[i][var];
            for (j = 0; j < var; j++)
            {
                if (array[i][j] != 0 && j != unuse_index)
                {
                    temp -= array[i][j] * result[j];
                }
            }
            result[unuse_index] = temp / array[i][unuse_index];
            unuse_result[unuse_index] = 0;
        }
        return var - k;
    }
    for (i = var - 1; i >= 0; i--)
    {
        temp = array[i][var];
        for (j = i + 1; j < var; j++)
        {
            if (array[i][j] != 0)
            {
                temp -= array[i][j] * result[j];
            }
        }
        if (temp % array[i][i] != 0)
        {
            return -2;
        }
        result[i] = temp / array[i][i];
    }
    return 0;
}
int main()
{
    int i, type;
    int equnum, varnum;
    int array[MaxNum][MaxNum] = {
                            {3,5,-4,0},
                            {7,2,6,-4},
                            {4,-1,5,-5} };
    int result[MaxNum];
    equnum = 3;
    varnum = 3;
    type = GaussFun(equnum, varnum, result,array);//调用高斯函数
    if (type == -1)
    {
        cout << "该方程无解。" << endl;
    }
    else if (type == -2)
    {
        cout << "该方程又浮点数解没有整数解。" << endl;
    }
    else if (type > 0)
    {
        cout << "该方程有无穷多解！自由变量的数量为" << type << endl;
        for (i = 0; i < varnum; i++)
        {
            if (unuse_result[i])
            {
                cout << i + 1 << "是不确定的" << endl;
            }
            else
            {
                cout << i + 1 << result[i] << endl;
            }
        }
    }
    else
    {
        cout << "该方程的解为：" << endl;
        for (i = 0; i < varnum; i++)
        {
            cout << i + 1 << result[i] << endl;
        }
    }
    return 0;
}