Write a programthat can play Tic-Tac-Toe effectively. (See Section 3.1.5.) To do this, you will need to create a game tree T, which is a tree where each position corresponds to a game configuration, which, in this case, is a representation of the Tic-Tac-Toe board. (See Section 8.4.2.) The root corresponds to the initial configuration. For each internal position p in T, the children of p correspond to the game states we can reach from p’s game state in a single legal move for the appropriate player, A (the first player) or B (the second player). Positions at
even depths correspond to moves for A and positions at odd depths correspond to moves for B. Leaves are either final game states or are at a depth beyond which we do not want to explore. We score each leaf with a value that indicates how good this state is for player A. In large games, like chess, we have to use a heuristic
scoring function, but for small games, like Tic-Tac-Toe, we can construct the entire game tree and score leaves as +1, 0, −1, indicating whether player A has a win, draw, or lose in that configuration. A good algorithm for choosing moves is minimax. In this algorithm, we assign a score to each internal position p in T, such that if p represents A’s turn, we compute p’s score as the maximum of the scores of p’s children (which corresponds to A’s optimal play from p). If an internal node p represents B’s turn, then we compute p’s score as the minimum
of the scores of p’s children (which corresponds to B’s optimal play from p).