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

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

double fact( double num );

int main()
{
	int sides_p;
        double sides[26];
	int axis;
	int i;
        double numer=0, denom=1;

	clrscr();

	printf("\nWelcome to the hypercubic calculator. This program can determine the number of\n");
	printf("possible combinations of path leading from one location to another. The start\n");
	printf("and end point are located at a location with integer axis values. The start\n");
	printf("point is assumed to be at the origin. Each move is in the direction of one of\n");
	printf("the axis (diagonal moves prohibited).\n\n");

        do {
		printf("Enter total number of Axis (3 is a normal cube; 26 maximum): ");
		scanf("%d",&axis);
	} while ( axis > 26 || axis < 1 );

	if ( axis != 1 )
	{
		printf("\nError may result when sum of Axis Vertices > 173.\n\n");

		for ( i=0 ; i<axis ; i++ )
		{
			printf("Enter %c-Axis Vertex Count (unit length): ", i+65);
			scanf("%d", &sides_p );
			sides[i] = (double)sides_p;
		}

		for ( i=0 ; i<axis ; i++ )
		{
			numer += sides[i];
			denom *= fact(sides[i] - 1);
		}
        

		numer = fact(numer - axis);
	}
	else
	{
		numer = 1;
		denom = 1;
	}

	printf("\nAnswer: %G", numer/denom);

	getch();
	return 0;
}

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

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

	if ( num == 0 )
		return 1;

	return num;
}