The game ofNim. This is a well-known game with a number of variants. We will con

Question

The game ofNim. This is a well-known game with a number of variants. We will consider the following variant, which has an interesting winning strategy. Two players alternately take marbles from a pile. In each move, a player chooses how many marbles to take. The player must take at least one but at most half of the mar ­bles. Then the other player takes a turn. The player who takes the last marble loses.

"Write a program in which the computer plays against a human opponent. Generate a random integer between 10 and 100 to denote the initial size of the pile. Generate a random integer between 0 and 1 to decide whether the computer or the human takes the first turn. Generate a random integer between 0 and 1 to decide whether the computer plays smart or stupid. In stupid mode, the computer simply takes a random legal value (between 1 and »/2) from the pile whenever it has a turn. In smart mode the computer takes off enough marbles to make the size of the pile a power of two minus 1 -that is, 3, 7,15, 31, or 63. That is always a legal move, except if the size of the pile is currently one less than a power of 2. In that case, the computer makes a random legal move.

Note that the computer cannot be beaten in smart mode when it has the first move, unless the pile size happens to be 15, 31, or 63. Of course, a human player who has the first turn and knows the winning strategy can win against the computer.

When you implement this program, be sure to use classes Pile, Player, and Came. A player can be either stupid, smart, or human. (Human Player objects prompt for input.)

Please send me the source code and make a flowchart.

Explanation / Answer

import java.util.Random; public class Game { public static void main(String args[]) { //declare variables Pile marbles = new Pile(); Random random = new Random(); Player player1; Player player2; int marblesToRemove = 0; //determine who goes first if(random.nextInt(2) == 0) { System.out.println("User goes first "); player1 = new Player(2); player2 = new Player(); } else { System.out.println("Computer goes first "); player1 = new Player(); player2 = new Player(2); } //keep going until all the marbles are gone while(marbles.getMarbles() > 0) { //check if player two wins if(marbles.getMarbles() == 1) { System.out.println("Player 2 Wins!!!"); break; } //prompt/calculate number of marbles to remove System.out.println("Number of marbles left: " + marbles.getMarbles()); System.out.println("Player 1's turn:"); marblesToRemove = player1.chooseNextMove(marbles.getMarbles()); System.out.println("Player 1 removed " + marblesToRemove); System.out.println(); //remove the marbles marbles.removeMarbles(marblesToRemove); //check if player one wins if(marbles.getMarbles() == 1) { System.out.println("Player 1 Wins!!!"); break; } //prompt/calculate number of marbles to remove System.out.println("Number of marbles left: " + marbles.getMarbles()); System.out.println("Player 2's turn:"); marblesToRemove = player2.chooseNextMove(marbles.getMarbles()); System.out.println("Player 2 removed " + marblesToRemove); System.out.println(); //remove marbles marbles.removeMarbles(marblesToRemove); } } } import java.util.Random; public class Pile { //fields int numMarbles = 0; //generate the number of marbles public Pile() { Random random = new Random(); numMarbles = random.nextInt(89) + 11; } //get method public int getMarbles() { return numMarbles; } //remove method public void removeMarbles(int marblesToRemove) { numMarbles -= marblesToRemove; } } import java.util.Random; import java.util.Scanner; public class Player { int playerType = 0; // 0 dumb, 1 smart, 2 player Random random = new Random(); Scanner input; //constructor where player type is specified public Player(int type){ if (type < 0 || type > 2) playerType = 2; else playerType = type; input = new Scanner(System.in); } //constructor where player type is specified public Player() { playerType = random.nextInt(2); input = new Scanner(System.in); } //pick next move public int chooseNextMove(int marblesLeft) { //setup variables int marblesToRemove = 0; //remove the second to last marble if(marblesLeft == 3) return 1; //if dumb, pick random number if(playerType == 0) { marblesToRemove = random.nextInt((marblesLeft/2) - 1) + 1; } //if smart get to specific numbers else if (playerType == 1) { if(marblesLeft > 63) marblesToRemove = marblesLeft - 63; else if(marblesLeft > 31) marblesToRemove = marblesLeft - 31; else if(marblesLeft > 15) marblesToRemove = marblesLeft - 15; else if(marblesLeft > 7) marblesToRemove = marblesLeft - 7; else if(marblesLeft > 3) marblesToRemove = marblesLeft - 3; else if(marblesLeft == 2) marblesToRemove = 1; //pick random number else marblesToRemove = random.nextInt((marblesLeft/2) - 1 ) + 1; } else { //prompt user System.out.println("Please enter a number of marbles to remove between 1 and " + (marblesLeft / 2)); marblesToRemove = input.nextInt(); //error check while(marblesToRemove > marblesLeft / 2 || marblesToRemove < 0) { System.out.println("That is not a valid entry, please try again (1 - " + (marblesLeft / 2) + ")"); marblesToRemove = input.nextInt(); } } //return values return marblesToRemove; } }

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