CS 257 Project 2: Memoized Game Tree Search*

Last year, in New York City, for the first time ever, the highest rated human chess player in the world was defeated in regulation tournament play by a computer program.

Problem 1
A tic-tac-toe board can be represented in Scheme by a vector of length nine. For example, the following tic-tac-toe board
```
O | X | 
---------
  | X | 
---------
  |   | O
```
can be represented by the vector #(O X ? ? X ? ? ? O). Write a function, index, which takes a vector representing a tic-tac-toe board as its argument and returns an integer value which is unique to that board, i.e., no other board has the same value.
Problem 2
A board is a winning position for X if it contains three X's in any row, column, or diagonal. Similiarly, a board is a winning position for O if it contains three O's in any row, column, or diagonal. A static evaluation function for tic-tac-toe is a function which takes a board as its argument, and returns a large positive value (e.g., 100) if the board represents a winning position for X and a large negative value (e.g., -100) if the board represents a winning position for O. If the board does not represent a winning position for either X or O then the static evaluation function should return a positive number (e.g., 0 < n < 100) if the position favors X, and a negative number (e.g., 0 > n > -100) if the position favors O. If the position favors neither X nor O then the evaluation function should return 0.
Click here to get Scheme code which plays tic-tac-toe using minimax game tree search. Except for the fact that there is no static evaluation function, this code is complete.
Write a static evaluation function, evaluate-board, for the game of tic-tac-toe. To work properly, it should satisfy the constraints described above, but the exact details are up to you. Test your static evaluation function and verify that the program plays correct tic-tac-toe (i.e., the program does not lose and will take advantage of any mistakes which you make).
Problem 3

Write a function memoize which will memoize any function which takes a tic-tac-toe board as an argument. Use it to create memoized versions of evaluate-board, empties, and best-move (you can call these evaluate-board-m, empties-m, and best-move-m). Change all references to the old functions in the code so that the program now calls the new memoized versions. Verify that the behavior of the program is exactly the same as before--only faster. Note the presence of the time command surrounding the best-move function. This will print the time needed to compute the best move. You can use it to verify the increase in speed.

What You Should Hand In

Listings of all your code.
Traces of four complete tic-tac-toe games. The first trace should demonstrate that your program plays to a draw when the human makes no mistakes. The second should demonstrate that it is able to win if the human errs. The third and fourth traces should show the same games after memoization.

When You Should Hand It In

The above should be handed in at the beginning of class on Dec. 11.

Of Possible Interest

* This webpage is located at http://cs.unm.edu/~williams/cs257/project2.html

CS 257 Project 2: Memoized Game Tree Search*

Problem 1

Problem 2

Problem 3

What You Should Hand In

When You Should Hand It In

Of Possible Interest