/*
 *	tn.c
 *	Copyright (c) 1999 by Scott M. Harrison.  All rights reserved.
 */

/*
 *	This program determines the chances to roll a specific
 *	number of successes with a specific target number on a
 *	specific number of dice.
 */

#include <stdio.h>
#include <stdlib.h>
#include <math.h>

/*
 *	This routine determines the percentage chance
 *	to roll the provided target number on one die
 *	using the rule of six.
 */
double targetNumberPercentage(int tn)

	{
	double retval;
	int divValue = (tn - 1) / 6;
	int modValue = (tn - 1) % 6;

	retval = (double)(6 - modValue) / pow(6.0, (double)(divValue + 1));
	return retval;
	}

/*
 *	This routine determines the factorial of the
 *	provided number.
 */
double factorial(int number)

	{
	double retval = 1.0;
	int i;

	for (i = 2; i <= number; i++)
		retval *= (double) i;
	return retval;
	}

/*
 *	This routine determines the number of possible
 *	combinations of a set in a group.
 */
double combination(int set, int group)

	{
	return (factorial(group) / (factorial(set) * factorial(group - set)));
	}

void main(int argc, char *argv[])

	{
	int retval = 0;

	if (argc != 4) {
		fprintf(stderr, "Usage: %s <target number> <number of successes> <number of dice>\n", argv[0]);
		retval = 1;
		}
	else {
		int tn = atoi(argv[1]);
		int successes = atoi(argv[2]);
		int dice = atoi(argv[3]);

		if (tn < 2) {
			fprintf(stderr, "The target number must be at least 2.\n");
			retval = 2;
			}
		else if (successes < 1) {
			fprintf(stderr, "The number of successes must be at least 1.\n");
			retval = 3;
			}
		else if (dice < 1) {
			fprintf(stderr, "The number of dice must be at least 1.\n");
			retval = 4;
			}
		else if (successes > dice) {
			fprintf(stderr, "The number of successes is more than the number of dice rolled.\n");
			retval = 5;
			}
		else {
			int i;
			double result = 0.0;
			double chance, inverseChance;

			chance = targetNumberPercentage(tn);
			inverseChance = 1.0 - chance;
			fprintf(stdout, "The chance to roll TN %d on a die is %g%%.\n", tn, chance * 100.0);
			for (i = successes; i <= dice; i++) {
				result += combination(i, dice) * pow(chance, (double) i) * pow(inverseChance, (double) (dice - i));
				}
			fprintf(stdout, "The chance to roll at least %d successes of TN %d on %d dice is %g%%.\n", successes, tn, dice, result * 100.0);
			}
		}
	exit(retval);
	}