Note: You may test getComputerSmartMove$()$ method in zyBook

Nim.java darr $q,$

The Game of Nim

Problem Description:

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 marbles. The other player takes a turn. The player who takes the last marble loses.

Write a program to simulate a game of computer vs$.$ human being. Generate a random number between $10-100$ to denote the initial size of the pile. Simulate a coin toss to determine who goes first, the computer or the human. Simulate a coin toss to decide if the computer plays smart or stupid mode. In stupid mode, the computer simply takes a random legal number between $1$ and $\frac{n}{2}$ 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 $63.$ If the human player knows the winning strategy and takes the first turn, he can win against the computer.

Program Requirements:

The program must define and use the following methods,

int getComputerStupidMove$($int num$)//$ return number of marbles to be moved in stupid mode if current marble number is num.

int getComputerSmartMove$($int num$)//$ return number of marbles to be moved in smart mode if current marble number is num.

boolean computerTurn$()//$ return true if it is computer's turn and false if human player's turn

boolean smartMode$()//$ return true if it is in smart mode and false if in stupid mode

Nim.Java

The Game of Nim

Problem Description:

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 marbles. The other player takes a turn. The player who takes the last marble loses.

Write a program to simulate a game of computer vs$.$ human being. Generate a random number between $10-100$ to denote the initial size of the pile. Simulate a coin toss to determine who goes first, the computer or the human. Simulate a coin toss to decide if the computer plays smart or stupid mode. In stupid mode, the computer simply takes a random legal number between $1$ and $\frac{n}{2}$ 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 $63.$ If the human player knows the winning strategy and takes the first turn, he can win against the computer.

Program Requirements:

The program must define and use the following methods,

int getComputerStupidMove$($int num$)$

$//$ return number of marbles to be moved in stupid mode if current marble number is num.

int getComputerSmartMove$($int num$)//$ return number of marbles to be moved in smart mode if current marble number is num.

boolean computerTurn$()$

$//$ return true if it is computer's turn and false if human player's turn

boolean smartMode$()$

$//$ return true if it is in smart mode and false if in stupid mode

Sample output:

Sample output:

GRASP exec: java GameOfNim

The computer is in stupid mode.

The computer will go first.

Total marbles: $36$

There are $36$ marbles left.

The computer took $16$ marble$($s$).$

There are $20$ marbles left.

Take a number between $10$ and $1$: $10$

You took $10$ marble$($s$).$

There are $10$ marbles left.

The computer took $1$ marble$($s$).$

There are $9$ marbles left.

Take a number between $4$ and $1$: $3$

You took $3$ marble $($s$).$

There are $6$ marbles left.

The computer took $1$ marble$($s$).$

There are $5$ marbles left.

Take a number between $2$ and $1$: $2$

You took $2$ marble$($s$).$

There are $3$ marbles left.

The computer took $1$ marble$($s$).$

There are $2$ marbles left.

You can only take $1$ marble: $1$

You took $1$ marble$($s$).$

There is $1$ marble left.

Computer took the last marble. Player wins!

$----$jGRASP: operation complete.What does this mean