#include "combinatorics.h"

// Function definitions

largeint combinations(largeint n, largeint r)
{
	largeint max_den = max(r, n - r);

	largeint numerator = 1;
	for ( largeint i = n; i > max_den; --i )
		numerator *= i;

	return numerator / factorial( min(r, n - r) );
}

#if 0
	// Inneficient way: easily overflows largeints
	largeint factorial_n = factorial(n);
	largeint factorial_r = factorial(r);
	largeint factorial_n_r = factorial(n - r);
	return factorial_n / (factorial_r * factorial_n_r);

	// Does the same than the four previous sentences
//	return factorial(n) / (factorial(r) * factorial(n - r));
#endif


largeint factorial(largeint n)
{
	largeint result = 1;
	for ( largeint i = 1; i <= n; ++i )
		result = result * i;

	return result;
}