//=================================================== file = birthday.c =====
//=  Program to solve the Birthday paradox                                  =
//===========================================================================
//=  Notes:                                                                 =
//=    1) Solves for probability of two people in a room of K people        =
//=       having the same birthday (birthday is one of N distinct values    =
//=       such as 1 of 365 days of the year)                                =
//=    2) Input values of K and N must be greater than 0                    =
//=    3) The birthday problem is described here,                           =
//=       http://www.mste.uiuc.edu/reese/birthday/intro.html                =
//=-------------------------------------------------------------------------=
//=  Example execution:                      			                          =
//=                                                                         =
//=   --------------------------------------- birthday.c -----              =
//=   -  Program to solve the birthday paradox               -              =
//=   --------------------------------------------------------              =
//=   Number of people in room (K) =======================> 23              =
//=   Number of possible birthdays (N) ===================> 365             =
//=                                                                         =
//=   Probability of two same birthdays = 0.507297                          =
//=   --------------------------------------------------------              =
//=-------------------------------------------------------------------------=
//=  Build: bcc32 birthday.c, cl birthday.c, gcc birthday.c                 =
//=-------------------------------------------------------------------------=
//=  Execute: birthday                                                      =
//=-------------------------------------------------------------------------=
//=  Author: Zornitza Genova                                                =
//=          University of South Florida                                    =
//=          WWW: http://www.csee.usf.edu/~zgenova                          =
//=          Email: zgenova@csee.usf.edu                                    =
//=-------------------------------------------------------------------------=
//=  History: ZG (07/17/01) - Genesis                                       =
//===========================================================================

//----- Include files -------------------------------------------------------
#include <stdio.h>                   // Needed for printf() and scanf()
#include <stdlib.h>                  // Needed for ato*()

//===== Main program ========================================================
void main(void)
{
  unsigned int                K;     // Number of people in the room
  unsigned int                N;     // Number of possible birthdays
  double                   prob;     // Probability of two same birthdays
  unsigned int                i;     // Loop counter
  unsigned char   instring[255];     // Temporary input string

  // Output banner
  printf("--------------------------------------- birthday.c -----\n");
  printf("-  Program to solve the birthday paradox               -\n");
  printf("--------------------------------------------------------\n");

  // Prompt for input
  printf("Number of people in room (K) =======================> ");
  scanf("%s", instring);
  K = atoi(instring);
  printf("Number of possible birthdays (N) ===================> ");
  scanf("%s", instring);
  N = atoi(instring);

  // Compute the probability of two same birthdays in the room
  prob = 1.0;
  for(i=1; i<=K; i++)
	  prob = prob * ((double) (N - i + 1) / N);
  prob = 1.0 - prob;

  // Output the result
  printf("\n");
  printf("Probability of two same birthdays = %f \n", prob);
  printf("--------------------------------------------------------\n");
}