Coupon collector

问题描述.假设某交易卡公司发行N种不同的卡，收集每种卡具有等可能概率，问收集全N种不同的卡需要购买多种张卡？

Coupon Collector Problem. Suppose that a trading card company issues trading cards with N different possible cards: how many do you have to collect before you have all N possibilities, assuming that each possibility is equally likely for each card that you collect?

/***************************************************************************
  * Compilation: javac CouponCollector
  * Execution: java CouponCollector N
  *
  * Given N distinct card types, how many random cards do you need   *  do collect before you have (at least) one of each type? *  This program simulates this random process. *
  * Sample execution:
  * % java CouponCollector 30
  * The number of coupons is 117
  *
  *
  * ***************************************************************************/

public class CouponCollector {
    public static void main(String[] args) {
        int N = Integer.parseInt(args[0]);
        boolean[] found = new boolean[N];
        int count = 0; // number of cards collected
        int valcnt = 0; // number of distinct cards

        while (valcnt < N) {
            int val = (int) (Math.random()*N);
            count++;
            if (!found[val]){
                valcnt++;
                found[val] = true;
            }
    }
        System.out.println("The number of coupons is " + count);

     }
}