//-------------------------------------------------------------------
//	eulernum.cpp
//
//	This program introduces the number  e  (Euler's Number) as 
//	the limiting value for an infinite sequence of averages in
//	an experiment where real numbers are chosen at random from 
//	the unit-interval [0,1] until their sum exceeds 1.  As the
//	experiment is repeated, the average number of the summands
//	required approaches  e = 2.718... , as is illustrated here
//	via computer simulations using one hundred million trials.
//
//		to compile:  $ g++ eulernum.cpp -o eulernum
//		to execute:  $ ./eulernum
//
//	NOTE: The program takes several seconds to finish running.
//
//	ACKNOWLEDGEMENT: We wish to thank Professor Paul Zeitz for 
//	introducing us to this intriguing problem. 
//
//	programmer: ALLAN CRUSE
//	written on: 06 FEB 2011
//-------------------------------------------------------------------

#include <stdio.h>	// for printf()  
#include <stdlib.h>	// for drand48(), srand48() 
#include <time.h>	// for time()

#define N_TRIALS	100000000	// one hundred million

double summands( void )
{
	double	rep = 0.0, sum = 0.0;

	do	{
		sum += drand48();
		rep += 1.0;
		}
	while ( sum < 1.0 );
	return	rep;
}


int main( int argc, char **argv )
{
	printf( "\n An introduction to Euler's Number  e  = 2.718...\n\n" );

	srand48( time( NULL ) );
	for (int demo = 0; demo < 3; demo++)
		{
		double	total = 0.0;
		double	tries = 0.0;
		for (int i = 0; i < N_TRIALS; i++)
			{
			total += summands();
			tries += 1.0;
			switch ( i+1 )
				{
				case 1000:
				case 10000:
				case 100000:
				case 1000000:
				case 10000000:
				case 100000000:
				printf( " After %u trials, ", i+1 );
				printf( "the average number of summands " ); 
				printf( "was %1.3f \n", total / tries ); 
				}
			}
		printf( "\n" );
		}
}