Add Minimax algorithm implementation in game_theory folder

game_theory/min_max.py

@@ -0,0 +1,53 @@
+import math
+
+
+class MinimaxGame:
+    def __init__(self, scores):
+        """
+        Initialize the MinimaxGame with a list of scores.
+
+        :param scores: List of terminal node scores
+        """
+        self.scores = scores
+        self.tree_depth = int(math.log2(len(scores)))
+
+    def minimax(self, current_depth=0, node_index=0, is_max_turn=True):
+        """
+        Recursive implementation of the minimax algorithm.
+
+        :param current_depth: Current depth in the game tree
+        :param node_index: Index of the current node in the tree
+        :param is_max_turn: Boolean indicating if it's the maximizing player's turn
+        :return: The optimal value for the current player
+        """
+        # Base case: we've reached a terminal node
+        if current_depth == self.tree_depth:
+            return self.scores[node_index]
+
+        # Recursive case
+        if is_max_turn:
+            return max(
+                self.minimax(current_depth + 1, node_index * 2, False),
+                self.minimax(current_depth + 1, node_index * 2 + 1, False),
+            )
+        else:
+            return min(
+                self.minimax(current_depth + 1, node_index * 2, True),
+                self.minimax(current_depth + 1, node_index * 2 + 1, True),
+            )
+
+    def find_optimal_value(self):
+        """
+        Find and return the optimal value for the maximizing player.
+
+        :return: The optimal value
+        """
+        return self.minimax()
+
+
+# Driver code
+if __name__ == "__main__":
+    scores = [3, 5, 2, 9, 12, 5, 23, 23]
+    game = MinimaxGame(scores)
+    optimal_value = game.find_optimal_value()
+    print(f"The optimal value is: {optimal_value}")