//
// lotto5.cpp
// CSC 215
// John Rogers
//
// This program computes the odds of 
// winning the lottery, allowing the user
// to repeat the calculations.
//

#include <iostream.h>
#include <ctype.h>

void getInput(long& numberOfBalls, long& numberChosen);
long factorial(long n);
long falling(long n, long k);
char getAnswer();

int main()
{
    long numberOfBalls, numberChosen, odds;
    char answer;
    
    do {

      getInput(numberOfBalls, numberChosen);

      odds = falling(numberOfBalls, numberChosen) / 
             factorial(numberChosen);

      cout << "The odds of winning are " << odds 
           << ":1." << endl;
           
      cout << "Do you wish to repeat for another game? ";
      answer = getAnswer();
      
    } while (answer == 'Y');

    return 0;
}

//
// This prompts for the number of balls in the lottery and
// the number chosen.  It forces the user to enter positive
// values and to make the number chosen less than or equal to
// the number of balls.
//
// It uses call-by-reference parameters to pass two values
// back to the main function.
// 
void getInput(long& numberOfBalls, long& numberChosen)
{
  do {
    cout << "How many balls are in the game?  Enter 1 or more: ";
    cin >> numberOfBalls;
  } while (numberOfBalls < 1);

  do {
    cout << "How many balls are chosen from that? " << endl
         << "This must be between 1 and " << numberOfBalls << ": " ;
    cin >> numberChosen;
  } while (numberChosen > numberOfBalls || numberChosen < 1);

  return;
}

//
// This computes n! recursively.
//
long factorial(long n)
{
  if (n == 0) {
    return 1;
  }
  else {
    return n * factorial(n-1);
  }
}

//
// This computes n to the falling k power
// recursively.  In mathematical text, we write 
// "n to the falling k power" as n^k_ (that is, the
// k is underlined).  Its definition is: 
//
//   n^k_ = n*(n-1)*(n-2)*...*(n-k+1)
//
long falling(long n, long k)
{
  if (k == 0) {
    return 1;
  }
  else {
    return n * falling(n-1, k-1);
  }
}

//
// This waits until the user types in Y or N.
//
char getAnswer()
{
  char answer;
  do {
    cin >> answer;
    answer = toupper(answer);
  } while (answer != 'Y' && answer != 'N');
  return answer;
}