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ICS-202 Data Structures
Task:
The objective of this lab is to study the minmax algorithm for game trees. For the purpose of this lab, we consider the following definition of the value of a vertex in game trees:
The Minmax Algorithm for Tic-Tac-Toe:
We consider games with two players in which one person’s gains are the result of another person’s losses (called zero-sum games). The minmax algorithm is a specialized search algorithm which returns the optimal sequence of moves for a player in a zero-sum game. In the game tree that results from the algorithm, each level represents a move by either of two players, say A- and B- player. Below is a game tree for tic-tac-toe game
The minmax algorithm explores the entire game tree using a depth-first search. At each node in the tree where A-player has to move, A-player would like to play the move that maximizes the payoff. Similarly, B-player will minimize the payoff to A-player. The maximum and minimum scores are taken at alternating levels of the tree, since A and B alternate turns.
The minimax algorithm computes the minimax decision for the leaves of the game tree and then backs up through the tree to give the final value to the current state.
Lab Exercises
Download the program TicTacTreeTest.java
Write a program that takes a tic-tac-toe game position from the user. It then computes the game-tree from that point onwards and assigns scores to each node in the tree. It then suggests the best move to make based on whether you are an ‘X’ player or an ‘O’ player.
For example, if the user input is: X..OXXO.O, (the given position represented as a string), and you are player ‘O’, then the program output is
You should place an ‘X’ at row 2, column 1.
ICS-202 Data Structures
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