//-------------------------------------------------------------------
//	bindist.cpp
//
//	This program displays a probability distribution and graph 
//	for the Binomial Distribution with parameters  n  and  p . 
//	
//		to compile:  $ g++ bindist.cpp -o bindist
//		to execute:  $ ./bindist
//
//	programmer: ALLAN CRUSE
//	written on: 21 FEB 2011
//-------------------------------------------------------------------

#include <stdio.h>	// for printf()  
#include <math.h>	// for sqrt()

#define N_MAX	50	 

double	p = 0.50;
double	mu, sigma;

double	power_of_p[ N_MAX+1 ];
double	power_of_q[ N_MAX+1 ];

unsigned long long	pascal[ N_MAX+1 ][ N_MAX+1 ];

void initialize_powers( void )
{
	power_of_p[ 0 ] = 1.0;
	power_of_q[ 0 ] = 1.0;
	for (int k = 1; k <= N_MAX; k++)
		{
		power_of_p[ k ] = power_of_p[ k-1 ] * p;
		power_of_q[ k ] = power_of_q[ k-1 ] * (1.0 - p);
		}
}

void initialize_pascal( void )
{
	for (int n = 0; n <= N_MAX; n++)
		{
		pascal[ n ][ 0 ] = 1LL;
		for (int k = 1; k <= n; k++)
			pascal[ n ][ k ] = 
				pascal[ n-1 ][ k-1 ] + pascal[ n-1 ][ k ];
		}
}

unsigned long long bincoeff( int n, int k )
{
	if (( n < 0 )||( k < 0 )||( n < k )) return 0LL;
	return	pascal[ n ][ k ];
}

int main( int argc, char **argv )
{
	// initialize global variables
	int	n = N_MAX;
	mu = n * p;
	sigma = sqrt( mu * (1.0 - p) );
	initialize_pascal();
	initialize_powers();

	// exhibit the binomial distribution function
	printf( "\n" );
	printf( " Binomial probability distribution" );
	printf( " for n=%d, p=%1.5f \n\n", n, p );
	for (int k = 0; k <= n; k++)
		{
		double	prob = bincoeff( n, k ) * 1.0;
		prob *= power_of_p[ k ];
		prob *= power_of_q[ n-k ];
		printf( " k=%-3d ", k );
		printf( "prob=%1.5f ", prob );
		int	m = (int)(300.0 * prob);
		for (int j = 0; j < m; j++) printf( "*" );
		printf( "\n" );
		}	

	// report this distribution's statistical parameters
	printf( "\n n=%d  mu=%1.5f  sigma=%1.5f \n\n", n, mu, sigma );
}