/* The Coupon Collector's problem:
   Consider an experiment with K possible outcomes, where outcome i
   occurs with probability p_i. Let N be the number of trials
   needed so that at least c occurences have occured of each outcome.
   When c=1 and p_i = 1/n, this is the Coupon Collector's problem.
 */

public class CouponCollector {

  static int getNumDraws (int K)
  {
    int[] A = new int [K+1];
    int numNotCollected = K;
    int numDraws = 0;
    while (numNotCollected > 0) {
      numDraws ++;
      int i = (int) UniformRandom.uniform (1, K);
      if (A[i] == 0) {
        // This coupon has not been collected.
        A[i] = 1;
        numNotCollected --;
      }
    }
    return numDraws;
  }
  
  // K=#genes or urns, m=#draws
  static double estimateExtremeProb (int K, int m, int numTrials)
  {
    int numSuccesses = 0;
    for (int i=0; i<numTrials; i++) {
      int numDraws = getNumDraws (K);
      if (numDraws < m) {
        numSuccesses ++;
      }
    }
    double avg = (double) numSuccesses / (double) numTrials;
    System.out.println ("K=" + K + " m=" + m + "  ProbEstimate=" + avg);
    return avg;
  }
  
  public static void main (String[] argv)
  {
    // Print out the extreme probability for various values of m.
    for (int m=50; m<= 200; m+=10) {
      estimateExtremeProb (20, m, 10000);
    }
  }

}