#include <stdio.h>
#include <stdlib.h>
#include <malloc.h>
#include <math.h>
int GS(int,double **,double *,double);
double **TwoArrayAlloc(int ,int);
void TwoArrayFree(double **);

void main()
{
	int i,n;
	double ep,**a,*b;
	n=3;
	ep=1e-4;
	a=TwoArrayAlloc(n,n);
	b=(double *)calloc(n,sizeof(double));
	if(b==NULL)
	{
		printf("內存分配失敗\n");
		exit(1);
	}
	a[0][0]=3;a[0][1]=2;a[0][2]=1;
	a[1][0]=1;a[1][1]=5;a[1][2]=7;
	a[2][0]=5;a[2][1]=4;a[2][2]=3;
	b[0]=6;b[1]=12;b[2]=12;

	if(!GS(n,a,b,ep))
	{
		printf("不可以用高斯消元法求解\n");
		exit(0);
	}

	
  printf("該方程組的解為: \n");
	for(i=0;i<3;i++)
		printf("x%d = %.2f\n",i,b[i]);
	TwoArrayFree(a);
	free(b);
}
int GS(int n,double **a,double *b,double ep)
 {  
	int i,j,k,l;
	double t;
	for(k=1;k<=n;k++)
	{
		for(l=k;l<=n;l++)
			if(fabs(a[l-1][k-1])>ep)
				break;
			else if(l==n)
				return 0;
			if(l!=k)
			{
				for(j=k;j<=n;j++)
				{
					t=a[k-1][j-1];
					a[k-1][j-1]=a[l-1][j-1];
					a[l-1][j-1]=t;
				}
				t=b[k-1];
				b[k-1]=b[l-1];
				b[l-1]=t;
			}
			t=1/a[k-1][k-1];
			for(j=k+1;j<=n;j++)
				a[k-1][j-1]=t*a[k-1][j-1];
			b[k-1]*=t;
			for(i=k+1;i<=n;i++)
			{
				for(j=k+1;j<=n;j++)
					a[i-1][j-1]-=a[i-1][k-1]*a[k-1][j-1];
				b[i-1]-=a[i-1][k-1]*b[k-1];
			}

	}
	for(i=n-1;i>=1;i--)
		for(j=i+1;j<=n;j++)
			b[i-1]-=a[i-1][j-1]*b[j-1];
		return(1);
}
double **TwoArrayAlloc(int r,int c)
{
	double *x,**y;
	int n;
	x=(double *)calloc(r*c,sizeof(double));
	y=(double **)calloc(r,sizeof(double*));
	for(n=0;n<=r-1;++n)
		y[n]=&x[c*n];
	return(y);
}
void TwoArrayFree(double **x)
{
	free(x[0]);free(x);
}