#include <iostream>

#include <fstream>

#include <cmath>

using namespace std;

double GaussElimination2UTM(double* matrix, int dimension){

????double sign=1;

????double temp;

????for(int cnt1=0; cnt1<dimension; cnt1++){

????????//在此引入置換操作，如果主元很?。ㄐ∮?.001）那么進(jìn)行行交換，此操作在行列式中引入了負(fù)號，消元函數(shù)返回行列式由于置換操作需要加入的符號

????????for(int cnt2=cnt1+1; cnt2<dimension; cnt2++){

????????????if(abs(matrix[cnt1*dimension+cnt1])>1e-3) break;

????????????for(int cnt3=0; cnt3<dimension; cnt3++){

????????????????temp=matrix[cnt1*dimension+cnt3];

????????????????matrix[cnt1*dimension+cnt3]=matrix[cnt2*dimension+cnt3];

????????????????matrix[cnt2*dimension+cnt3]=temp;

????????????}

????????????sign*=-1;

????????}

????????for(int cnt2=cnt1+1; cnt2<dimension; cnt2++){

????????????for(int cnt3=dimension-1; cnt3>=cnt1; cnt3--){

????????????????matrix[cnt2*dimension+cnt3] += -1*matrix[cnt1*dimension+cnt3]*matrix[cnt2*dimension+cnt1]/matrix[cnt1*dimension+cnt1];

std::cout<<matrix[cnt2*dimension+cnt3]<<"="<<matrix[cnt1*dimension+cnt3]<<"*"<<matrix[cnt2*dimension+cnt1]<<"/"<<matrix[cnt1*dimension+cnt1]<<std::endl;

????????????}

????????}

????}

????return sign;

}

double Determinant(double* matrix, int dimension){

????double determinant=1;

????determinant=GaussElimination2UTM(matrix, dimension);

std::cout<<"------------------------"<<std::endl;

????for(int cnt=0; cnt<dimension; cnt++){

????????determinant *= matrix[cnt*dimension+cnt];

for(int jfd=0;jfd<dimension;jfd++){

std::cout<<","<<matrix[cnt*dimension+jfd];

}

std::cout<< std::endl;

????}

????return determinant;

}

int main(){

????int dimension = 6;

????double matrix[100]={

2,3,4,5,6,7,

10,9,13,14,15,16,

21,11,2,12,1,3,

4,5,7,9,3,2,

31,21,31,5,11,16,

4,2,8,9,4,8

};

????cout << Determinant(matrix, dimension) << '\n';

????return 0;

}