//GUASS.CPP--高斯消去法解線性方程組
#include<iostream>
#include<cmath>
using namespace std;
const int ROW=5;
void print_err();
void print_x(float x[]);
void main()	
{
    float a[ROW][ROW]={                     //系數矩陣
	{1.0,1.0/2.0,1.0/3.0,1.0/4.0,1.0/5.0},
	{1.0/2.0,1.0/3.0,1.0/4.0,1.0/5.0,1.0/6.0},
	{1.0/3.0,1.0/4.0,1.0/5.0,1.0/6.0,1.0/7.0},
	{1.0/4.0,1.0/5.0,1.0/6.0,1.0/7.0,1.0/8.0},
	{1.0/5.0,1.0/6.0,1.0/7.0,1.0/8.0,1.0/9.0}};
	float b[ROW]={137.0/60.0,87.0/60.0,459.0/420.0,
		          743.0/840.0,1879.0/2520.0};   //右端向量
    int i,j,k;
	float t;
   	for(k=0;k<ROW-1;k++)
	{
		if(fabs(a[k][k])<1e-5)     //如果a矩陣對角線的元素為零，輸出錯誤信息
		{
			print_err();
			return;
		}
		for(i=k+1;i<ROW;i++)       //消元過程
		{
			for(j=k+1;j<ROW;j++)
				a[i][j]=a[i][j]-a[i][k]*a[k][j]/a[k][k];
			b[i]=b[i]-a[i][k]*b[k]/a[k][k];
		}
	}
	b[ROW-1]=b[ROW-1]/a[ROW-1][ROW-1];    //消元結束，回代開始
	for(i=ROW-2;i>=0;i--)
	{	
		t=0;
	    for(j=i+1;j<ROW;j++)
		    t+=b[j]*a[i][j];
	    b[i]=(b[i]-t)/a[i][i];
	}
    print_x(b);
}

//print_x()輸出線性方程組Hx=b的解
void print_x(float x[])
{
	int i;
	cout<<"此線性方程組的解為:"<<endl;
	for(i=0;i<ROW;i++)
	{
		cout.precision(6);
		cout<<x[i]<<endl;
	}
}

//print_err()輸出錯誤信息
void print_err()
{
	cout<<"Failure!The work can't continue. "<<endl;
}