//
// Program name:  roll_dice_v2
//
// Program to estimate how many times one must roll a 6-sided die 
//   before seeing all its faces.
//
// The program performs repeated "trials".  In each trial, it simulates
// rolling a die, and tracks how many rolls are required before
// all faces have been seen.  It then computes an average number
// of rolls over all trials.
//
// Input:  (from standard input) positive integer specifying how many 
//   trials to perform.
// Output:  (on standard output) the average, over all trials, of the 
//   number of rolls required before all faces of the die have been 
//   seen.
//

#include <iostream.h>
#include <stdlib.h>		// has EXIT_SUCCESS, EXIT_FAILURE,
				//   rand()
#include <algorithm>		// has fill()

// Function prototypes.
int roll(int numFaces);
int doTrial(void);

// Main program.
int main()
{
  int sumOfResults = 0;		// sum of rolls required for each trial
  int numTrials;

  cout << "How many trials do you want to perform?\n";
  cin >> numTrials;

  if (numTrials <= 0)
    {
      cout << "Number must be positive!\n";
      exit(EXIT_FAILURE);
    }

  for (int i = 0; i < numTrials; ++i)
    {
      int rolls = doTrial();
      sumOfResults += rolls;
      cout << rolls << " rolls were required in trial " 
           << i << endl;
    }

  cout << "Average number of trials was "
       << double(sumOfResults) / double(numTrials) << endl;

  return EXIT_SUCCESS;
}

// Function definitions.

// Post:  returns number of rolls required by this trial.
int doTrial(void)
{
  const int FacesOnDie = 6;	// total number of faces on die
  bool seen[FacesOnDie];	// seen[i] is true if we've see face
				// i, false otherwise.

  int rolls = 0;		// number of rolls so far
  int numSeen = 0;		// number of distinct faces so far

  int thisRoll;		// face displayed by current roll

  // Initialize seen array.
  fill (seen, seen + FacesOnDie, false);

  // Roll the die repeatedly until we've seen all faces.
  while (numSeen < FacesOnDie)
    {
      // "Roll the die":  generate a random number between
      //   1 and FacesOnDie.
      thisRoll = 1 + roll(FacesOnDie);
      ++rolls;

      // cout << "the number is " << thisRoll << endl;

      if (!seen[thisRoll-1])
	{
	  // We haven't seen this face before.
	  seen[thisRoll-1] = true;
	  ++numSeen;
	}
    }

  return rolls;
}

// Function to "roll a die".
// Pre:  numFaces is positive.
// Post:  returns a random integer between 0 and numFaces-1.
int roll(int numFaces)
{
  return int(((double(numFaces) * rand())/(RAND_MAX + 1.0)));
}