用 Java 模拟三门问题

美国以前有一个综艺节目。参赛者会看见三扇关闭了的门，其中一扇的后面有一辆汽车，选中后面有车的那扇门可赢得该汽车，另外两扇门后面则各藏有一只山羊。当参赛者选定了一扇门，但未去开启它的时候，节目主持人开启剩下两扇门的其中一扇，露出其中一只山羊。主持人其后会问参赛者要不要换另一扇仍然关上的门。问题是：换另一扇门会否增加参赛者赢得汽车的机会率？

以下为模拟三门问题的Java代码。

 

import java.util.Scanner;
import java.text.DecimalFormat;
import java.text.DecimalFormatSymbols;

//三门
class ThreeDoor {
  String[] threeDoor = new String[3]; //三门

  //设置门后的奖品
  public void setPrize() {
    int carPosition = (int)(Math.random()*100)%3;

    threeDoor[0] = "Goat";
    threeDoor[1] = "Goat";
    threeDoor[2] = "Goat";
    threeDoor[carPosition] = "Car";
  }
}

//玩家
class Player {
  int firstChoicePosition = 0;  //首次选择的门
  int lastChoicePosition = 0;   //最终选择的门

  //选择一个门
  public void choiceDoor() {
    firstChoicePosition = (int)(Math.random()*100)%3;
    lastChoicePosition = firstChoicePosition;
  }

  //更换为另一个门
  public void changeDoor(int firstGoatPosition) {
    lastChoicePosition = 3 - firstChoicePosition - firstGoatPosition;
  }
}

//主持人
class Presenter {
  int firstGoatPosition = 0;  //主持人打开的门

  //打开后面为山羊的门
  public void openFirstGoatPosition (String[] threeDoor,int playerFirstChoicePosition) {
    if(threeDoor[playerFirstChoicePosition].equals("Car")) {
      do {
        firstGoatPosition = (int)(Math.random()*100)%3;
      } while (firstGoatPosition == playerFirstChoicePosition);
    } else {
      for(int i=0;i<3;i++)
        if(!threeDoor[i].equals("Car") && i!=playerFirstChoicePosition)
          firstGoatPosition = i;
    }
  }
}

//计分牌
class Scorer {
  int playCount = 0;        //玩的总次数
  int choiceCarCount = 0;   //获得车的次数
  int choiceGoatCount = 0;  //获得山羊的次数

  //计分
  public void score(String[] threeDoor,int playLastChoicePosition) {
    playCount++;
    if(threeDoor[playLastChoicePosition].equals("Car"))
      choiceCarCount++;
    else
      choiceGoatCount++;
  }

  //计算获得车的概率
  public void statistics() {
    DecimalFormat df = new DecimalFormat("##.00%");
    System.out.println("Choice Goat Count: " + choiceGoatCount);
    System.out.println("Choice Car  Count: " + choiceCarCount);
    System.out.println("Choice Car  Rate : " + df.format((float)choiceCarCount/playCount));
  }
}

//设置模式
class Moder {
  String mode = "";       //模式，A：换门，B：不换门
  int playTotalCount = 0; //玩的总次数

  //设置模式
  public void setMode() {
    Scanner sc = new Scanner(System.in);

    //设置选门模式
    while(!mode.equals("A") && !mode.equals("B")) {
      System.out.println("Plase input mode: A[Change]  B[Don't Change]");
      mode = sc.nextLine();
      if(!mode.equals("A") && !mode.equals("B"))
        System.out.println("Input Error, Input again.");
    }

    //设置玩的总次数
    while(playTotalCount<=0) {
      System.out.println("Plase input play total count: ");
      try {
        Scanner scCnt = new Scanner(System.in);
        playTotalCount = scCnt.nextInt();
      } catch(Exception e) {
        playTotalCount = 0;
      }
      if(playTotalCount<=0)
        System.out.println("Input Error, Input again.");
    }

    System.out.println();
  }

  //显示设置的模式
  public void showMode() {
    if(mode.equals("A"))
      System.out.println("Mode: [Change]");
    else
      System.out.println("Mode: [Don't Change]");

    System.out.println("Play Total Count: " + playTotalCount);
    System.out.println();
  }
}

//main程序
class ThreeDoorDemo {
  public static void main(String[] args) {
    ThreeDoor threeDoor = new ThreeDoor();  //三门
    Player player = new Player();           //玩家
    Presenter presenter = new Presenter();  //主持人
    Scorer scorer = new Scorer();           //计分者
    Moder moder = new Moder();              //设置模式者

    moder.setMode();  //设置模式
    moder.showMode(); //显示模式

    //循环玩多次
    for(int i=0; i<moder.playTotalCount; i++) {
      threeDoor.setPrize(); //设置门后奖品
      player.choiceDoor();  //玩家选择一个门
      //主持人打开一扇是山羊的门
      presenter.openFirstGoatPosition(threeDoor.threeDoor,player.firstChoicePosition);
      if(moder.mode.equals("A"))
        player.changeDoor(presenter.firstGoatPosition); //玩家换另外一扇门
      //计分
      scorer.score(threeDoor.threeDoor,player.lastChoicePosition);
    }

    scorer.statistics();  //统计获得汽车的概率
  }
}