// Name:	Andrew Lebon
// Date:	06 December, 2019
// Prog:	prog09.c
// Desc:    This program uses Cramer's Rule to find the solution of three linear equations in three variables.
//			The program does this by calling a function named det3, which recieves the starting address for
//			the 3x3 array and returns the determinant of that array.
#include<stdio.h>
#include<stdlib.h>
#include<math.h>

// A is a 3*3 matrix
int det3(int **A)
{
	int det = A[0][0]*( A[1][1]*A[2][2] - A[1][2]*A[2][1] ) - A[0][1]*( A[1][0]*A[2][2] - A[1][2]*A[2][0] ) + A[0][2]*( A[1][0]*A[2][1] - A[1][1]*A[2][0] );
	return (det);
}

void copyAbtoB(int **A, int*b, int **bs, int n)
{
	int i,j;
	for(i=0;i<3;i++)
	{
		for(j=0;j<3;j++)
		{
			bs[i][j] = A[i][j];
		}
	}

	for(i=0;i<3;i++)
	{
		bs[i][n] = b[i];
	}
}


int main()
{
	int i,j,k;
	int **A = (int**)malloc(sizeof(int*)*3);
	int *b = (int*)malloc(sizeof(int)*3);
	for(i=0;i<3;i++)
	{
		A[i] = (int*)calloc(3,sizeof(int));
	}

	for(i=0;i<3;i++)
	{
		printf("Enter equation %d: ",i+1);
		for(j=0;j<4;j++)
		{
		if(j<3)
		{
			scanf("%d",&A[i][j]);
		}
		else
		{
			scanf("%d",&b[i]);
		}
		}
	}

	int det = det3(A);
	if(det == 0)
	{
		printf("System does not have a unique solution because determinant is 0\n");
	}
	else
	{
		int **bs = (int**)malloc(sizeof(int*)*3);
		for(i=0;i<3;i++)
		{
			bs[i] = (int*)calloc(3,sizeof(int));
		}

		int *detB = (int*)calloc(3,sizeof(int));

		for(i=0;i<3;i++)
		{
			copyAbtoB(A,b,bs,i);
			detB[i] = det3(bs);
		}

		float x = (detB[0]*1.0)/(det*1.0);
		float y = (detB[1]*1.0)/(det*1.0);
		float z = (detB[2]*1.0)/(det*1.0);

		printf("System has unique solution ( %f, %f, %f)\n",x,y,z);

	}

	return(0);
}