Question

The Assignment

Write a Java application (named GoatsAndCars.java) that plays the game automatically. Your application will run 1,000 trials in which the player does not switch, store the results (“car” or “goat”) in an array (prizeArray) and then loop through the array to determine how often the player wins the car.

Then your application will run 1,000 trials in which the player switches, store the results in prizeArray, and record how often the player wins the car.

Finally, your application will compare the two results and report whether switching doors improves the odds of winning the car – or not.

As you work out an algorithm to solve this problem you will no doubt notice that since the game is played 2,000 times, there is a lot of repetition in the code (putting the goats and cars behind the doors 2,000 times, selecting the player’s choice 2,000 times, and so on). Some of this repetitive code can is unavoidable, and after all, that’s what repetition structures are designed for. But some of this repeated code can be eliminated by having the main method call other methods, thereby, for example, having a method that stores the variables in prizeArray.

To improve your applications performance (by a nanosecond or two), and your programming skills, your application will include the following methods (in addition to public static void main():

public static void placePrizes()

public static void doesPlayerWin()

public static void countPrizes()

Answer 1

public class MontyHall
{
    public static void main(String[] args)
    {
        boolean[] withOutChange = new boolean[1000];
        boolean[] withChange = new boolean[1000];
        boolean[] doors = new boolean[3];

        for (int x = 0; x < withOutChange.length; x++)
        {
            placePrizes(doors);
            withOutChange[x] =  playGame(doors, false);
        }

        for (int x = 0; x < withChange.length; x++)
        {
            placePrizes(doors);
            withChange[x] = playGame(doors, true);
        }

        System.out.println("Chances of winning without changing: " + countPrizes(withOutChange) + "%");
        System.out.println("Chances of winning with changing   : " + countPrizes(withChange) + "%");
    } // end of main method

    public static void placePrizes(boolean[] doors)
    {
        for (int x = 0; x < doors.length; x++)
        {
            doors[x] = false;
        }
        int carDoor = (int)(Math.random() * 3);
        System.out.println("CAR DOOR IS: " + carDoor);
        doors[carDoor] = true;
    }  // end of placePrizes method

    public static boolean playGame(boolean[] doors, boolean changeDoor)
    {
        int playerChoice = (int)(Math.random() * 3);
        System.out.println("Players first choice: " + playerChoice);
        int revealedDoor = -1;

        for (int x = 0; x < doors.length; x++)
        {
            if (!doors[x] &&  x != playerChoice)
            {
                revealedDoor = x;
                break;
            }
        }
        System.out.println("revealed door: " + revealedDoor);

        if (changeDoor)
        {
            int randomNumber = -1;
            int originalChoice = playerChoice;
            do
            {
                randomNumber = (int)(Math.random() * 3);
            }
            while(!(randomNumber != originalChoice && randomNumber != revealedDoor));
            playerChoice = randomNumber;
            System.out.println("The players second choice is: " + playerChoice);
        }  // end of if block
        return doesPlayerWin(playerChoice, doors);
    } // end of playGame method

    public static boolean doesPlayerWin(int playerChoice, boolean[] doors)
    {
        if (doors[playerChoice])
        {
            System.out.println("You won!");
            return true;
        }
        else
        {
            System.out.println("You lost...");
            return false;
        }
    } // end of doesPlayerWin method

    public static double countPrizes(boolean[] wins)
    {
        int winsCount = 0;
        for (int x = 0; x < wins.length; x++)
        {
            if (wins[x] == true)
            {
                winsCount++;
            } // end of if statement
        }  // end of for block
        return ((double)winsCount/(double)wins.length) * 100.0;
    }
} // end of class