C#之桶中取黑白球问题

《编程之美》284页，问题4.6：桶中取黑白球。

有一个桶，里面有白球、黑球各100个，人们必须按照以下规则把球取出来：

1. 每次从桶中拿两个球；

2. 如果两球同色，再放入一个黑球；

3. 如果两球异色，再放入一个白球；

问：最后桶里面只剩下一个黑球的概率是多少？

于是我开始分析，桶里装球，每次摸球是随机的，所以不能用队列和栈，那就用万能的动态列表来做桶吧。按照题目描述的顺序，写出取球的过程，最后剩的是黑球返回1，白球返回2，其他情况（没球了）返回3，然后根据概率在大数据量下将会趋于稳定的性质无限取球，最后趋于稳定的那个数就是答案。

代码如下（注释的部分为调试程序过程中用到的测试代码，用来显示操作过程中取球、放球、以及桶中球的详细变化过程）：

using System;
using System.Collections.Generic;
using System.Linq;

namespace BucketBall
{
    class Program
    {
        static void Main(string[] args)
        {
            int count = ;
            int targetCount = ;
            int result;
            double probability;
            while (true)
            {
                List<string> bucketBalls = new List<string>();
                result = Play(bucketBalls);
                //Console.WriteLine("result:" + result);
                if (result == )
                {
                    targetCount++;
                    //Console.WriteLine("targetCount:" + targetCount);
                }
                count++;
                //Console.WriteLine("count:" + count);
                probability = Math.Round((double)1.0 * targetCount / count, );
                Console.WriteLine(probability);
                //Console.Read();
            }
        }
        private static int Play(List<string> bucketBalls)
        {
            for (int i = ; i <= ; i++)
            {
                bucketBalls.Add("BlackBall");
                bucketBalls.Add("WhiteBall");
            }
            //PrintList(bucketBalls);
            Random ran = new Random();
            while (bucketBalls.Count() > )
            {

                var balls = Take(bucketBalls, , ran);
                //Console.WriteLine("Take the balls " + balls[0] + " " + balls[1]);
                //PrintList(bucketBalls);
                if (balls[] == balls[])
                {
                    Put(bucketBalls, "BlackBall");
                    //Console.WriteLine("Put the BlackBall");
                    //PrintList(bucketBalls);
                }
                else
                {
                    Put(bucketBalls, "WhiteBall");
                    //Console.WriteLine("Put WhiteBall over!");
                    //PrintList(bucketBalls);
                }
                //Console.WriteLine(bucketBalls.Count());
            }
            if (bucketBalls.Count() == )
            {
                //Console.WriteLine("result is " + bucketBalls[0]);
                return bucketBalls[] == "BlackBall" ?  : ;
            }
            else
            {
                return ;
            }
        }

        private static void PrintList(List<string> bucketBalls)
        {
            Console.WriteLine();
            foreach (var ball in bucketBalls)
            {
                Console.Write(ball + " ");
            }
            Console.WriteLine();
        }

        private static void Put(List<string> bucketBalls, string v)
        {
            bucketBalls.Add(v);
        }

        private static List<string> Take(List<string> bucketBalls, int v, Random ran)
        {
            List<string> balls = new List<string>();
            int pos;
            for (int i = ; i <= v; i++)
            {
                pos = ran.Next(, bucketBalls.Count());
                balls.Add(bucketBalls[pos]);
                bucketBalls.RemoveAt(pos);
            }
            return balls;
        }
    }
}

我因为不小心将一处的“WhiteBall”写成了“WhileBall”而一度修改却得不到正确的答案，最终一步一步的通过上面的测试代码，才将出错范围最终锁定在了初始化bucketBalls的for循环内，最终发现我将“WhiteBall”写成了“WhileBall”。改过来以后，运行结果终于正确了。下面是去掉测试代码的最终版：

using System;
using System.Collections.Generic;
using System.Linq;

namespace BucketBall
{
    class Program
    {
        static void Main(string[] args)
        {
            int count = ;
            int targetCount = ;
            int result;
            double probability;
            while (true)
            {
                List<string> bucketBalls = new List<string>();
                result = Play(bucketBalls);
                if (result == )
                {
                    targetCount++;
                }
                count++;
                probability = Math.Round((double)1.0 * targetCount / count, );
                Console.WriteLine(probability);
            }
        }
        private static int Play(List<string> bucketBalls)
        {
            for (int i = ; i <= ; i++)
            {
                bucketBalls.Add("BlackBall");
                bucketBalls.Add("WhiteBall");
            }
            Random ran = new Random();
            while (bucketBalls.Count() > )
            {

                var balls = Take(bucketBalls, , ran);
                if (balls[] == balls[])
                {
                    Put(bucketBalls, "BlackBall");
                }
                else
                {
                    Put(bucketBalls, "WhiteBall");
                }
            }
            if (bucketBalls.Count() == )
            {
                return bucketBalls[] == "BlackBall" ?  : ;
            }
            else
            {
                return ;
            }
        }

        private static void Put(List<string> bucketBalls, string v)
        {
            bucketBalls.Add(v);
        }

        private static List<string> Take(List<string> bucketBalls, int v, Random ran)
        {
            List<string> balls = new List<string>();
            int pos;
            for (int i = ; i <= v; i++)
            {
                pos = ran.Next(, bucketBalls.Count());
                balls.Add(bucketBalls[pos]);
                bucketBalls.RemoveAt(pos);
            }
            return balls;
        }
    }
}

通过运行结果可以看出来，概率一直很稳定，为1：

所以答案是在白球和黑球各100个的前提下取球放球，最后都只剩下黑球，概率为1。

修改程序中的初始化参数还可以用来求解课后题中的拓展情况，不用动脑。大家可以试试。

总结过程中遇到的问题：

1、字符串赋值的时候一定要仔细，别写错了！

2、Random.Next()函数返回值的范围包括 minValue 但不包括 maxValue。如果 minValue 等于 maxValue，则返回 minValue。