//-------------------------------------------------------------------
//	buffon.cpp
//
//	This program performs an automated simulation of the famous
//	Buffon Needle Problem: a needle 2-inches long is dropped at
//	random onto a floor made of 4-inch wide planks.  How likely
//	is it that the needle will fall across a crack?  We use the
//	built-in random number library function to simulate a drop,
//	and we "drop" our needle a great many times to estimate the  
//	probability that the needle will fall across a crack on any
//	individual trial, based of the statistical Law of Averages. 
//
//	   	      compile using:  $ make buffon
//		      execute using:  $ buffon
//
//	Note: This program was developed and tested using Linux 2.6.
//
//	programmer: ALLAN CRUSE
//	written on: 31 AUG 2005
//-------------------------------------------------------------------

#include <stdio.h>	// for printf() 
#include <stdlib.h>	// for rand(), srand()
#include <math.h>	// for sin()
#include <time.h>	// for time()

#define PI 3.14159

double random_real( void )
{
	return	(double)rand() / (double)RAND_MAX;
}

int main( int argc, char **argv )
{
	printf( "\n\tDoing a simulation of Buffon's Needle Problem\n" );
	
	int	trials = 10000000;	// we use ten million trials
	int	across = 0;		// initial value for counter
	srand( time( NULL ) );		// time seed for randomizing

	for (int i = 0; i < trials; i++)
		{
		double	theta = PI * random_real();
		double	ydist = 4.0 * random_real();
		if ( ydist < 2.0 * sin( theta ) ) ++across;
		}
	printf( "\n" );
	printf( "\tNumber of needles dropped on floor = %8d \n", trials );
	printf( "\tNumber of those that cross a crack = %8d \n", across );
	
	double	probability = (double)across / (double)trials;
	printf( "\n\tSo probability of crossing a crack is " );
	printf( "%0.5f \n", probability );

	double	one_over_pi = (double)1.0 / (double)PI;
	printf( "\n\tFor a comparison: reciprocal of PI is " );
	printf( "%0.5f \n\n", one_over_pi );
}