/* http://www.mrwadlo.com */

#include <stdio.h>
#include <conio.h>

int m_size[3];

double fact( double num );

int main()
{
	int xp, yp, zp;
	double x,y,z;

	clrscr();

	printf("\nWelcome to the cubic calculator. This program can determine the number of\n");
	printf("possible combinations of path leading from one third-dimension location to\n");
	printf("another. The start point is assumed to be at the origin (0,0,0). The end point\n");
	printf("is located at a specified location with integer axis values. Each move is one\n");
	printf("unit in the direction of either X, Y, or Z (diagonal moves prohibited).\n\n");

	printf("Enter X Axis Vertex Count (unit length): ");
	scanf("%d", &xp );
	printf("Enter Y Axis Vertex Count (unit length): ");
	scanf("%d", &yp );
	printf("Enter Z Axis Vertex Count (unit length): ");
	scanf("%d", &zp );

	if ( xp+yp+zp > 173 )
	{
		printf("\nError may result when x+y+z > 173. Press any key to continue.\n");
		getch();
	}

	x = (double)xp;
	y = (double)yp;
	z = (double)zp;

	printf("\nPlotting paths from (0,0,0) to (%G,%G,%G)...\n",x,y,z);
	
	printf("\nSolution: %.18G\n", fact( x + y + z - 3 ) / ( fact( x - 1) * fact( y - 1) * fact( z - 1) ));

	getch();
	return 0;
}

double fact( double num )
{
	double val = num - 1;

	while ( val > 1 )
	{
		num *= val;
		val--;
	}

	if ( num == 0 )
		return 1;

	return num;
}