/* pick.c -- evaluate N!/(n! (N-n)!)
 * 
 * long	p;
 * int	N, n;
 * p = pick(N, n);
 *
 * pick returns the number of ways of picking n distinct elements from a
 * total of N.
 */
#include <math.h>
#include "common.h"
#include "logs.h"

double	log();				/* natural logarithms		*/
int	gcf();				/* greatest common factor	*/

long
pick(N, n)
int		N, n;
{
    register int	i;
    register int	f;
    register int	g;
    register long	p = 1L;

    if (				/* make sure values valid	*/
	(n < 0) ||
	(N < 0) ||
	(N < n)
    ) return(0L);
    if (n > N-n) n = N-n;
    for(i=1; i<=n; i++) {
	f = N+1 - i;
	g = gcf(f, i);
	f /= g;
	p /= i/g;
	p *= f;
    }
    return(p);
}

/* logpick -- evaluate ln( N!/(n! (N-n)!) )
 * 
 * double	lp;
 * int		N, n;
 * lp = logpick(N, n);
 *
 * pick returns the natural logarithm of the number of ways of picking
 * n distinct elements from a total of N.  It can be used where pick
 * would overflow.
 */
double
logpick(N, n)
int		N, n;
{
    register int	i;
    register int	f;
    register double	lp = LOG1;

    if (				/* make sure values valid	*/
	(n < 0) ||
	(N < 0) ||
	(N < n)
    ) return(LOG0);
    if (n > N-n) n = N-n;
    for(i=1; i<=n; i++) {
	f = N+1 - i;
	lp += logint(f) - logint(i);
    }
    if (lp < LOG1) lp = LOG1;
    return(lp);
}