Added minimax algorithm

machine_learning/minimax.py

@@ -0,0 +1,66 @@
+import math
+
+
+def minimax(
+    depth: int, node_index: int, is_maximizing_player: bool, scores: list, height: int
+) -> float:
+    """
+    Minimax algorithm to determine the optimal move for a player in a two-player
+    zero-sum game.
+
+    Parameters:
+    - depth (int): Current depth in the game tree. Used to track recursion level.
+    - node_index (int): Index of the current node in the scores array, representing
+    leaf nodes.
+    - is_maximizing_player (bool): True if the current player is the maximizing player
+    , False otherwise.
+    - scores (list): A list of integers representing the scores at the leaf nodes
+    of the game tree.
+    - height (int): The maximum depth of the game tree, based on the number of leaf
+    nodes in a binary structure.
+
+    Returns:
+    - int: The best score that the current player can achieve from this node.
+    """
+    # Base case: If the maximum depth is reached, return the score at this node.
+    if depth == height:
+        return scores[node_index]
+
+    # Maximizing player's move
+    if is_maximizing_player:
+        best_score = -math.inf  # Start with the worst possible score for maximizer
+        # Simulate two possible moves (binary tree branches)
+        for i in range(2):
+            # Recursive call for the next level of depth
+            val = minimax(depth + 1, node_index * 2 + i, False, scores, height)
+            best_score = max(
+                best_score, val
+            )  # Maximizer chooses the highest score available
+        return best_score
+
+    # Minimizing player's move
+    else:
+        best_score = math.inf  # Start with the worst possible score for minimizer
+        for i in range(2):
+            # Recursive call for the next level of depth
+            val = minimax(depth + 1, node_index * 2 + i, True, scores, height)
+            best_score = min(
+                best_score, val
+            )  # Minimizer chooses the lowest score available
+        return best_score
+
+
+def main() -> None:
+    # Scores array representing the leaf nodes of a binary tree (depth = 3)
+    scores = [3, 5, 2, 9, 12, 5, 23, 23]
+    # Calculate the height of the binary tree based on the number of leaf nodes
+    height = math.ceil(math.log2(len(scores)))
+
+    # Print the optimal outcome for the maximizing player
+    print(
+        "Optimal value for the maximizing player:", minimax(0, 0, True, scores, height)
+    )
+
+
+if __name__ == "__main__":
+    main()

machine_learning/minimax_alpha_beta_pruning.py

@@ -0,0 +1,80 @@
+import math
+
+
+def minimax_with_pruning(
+    depth: int,
+    node_index: int,
+    is_maximizing_player: bool,
+    scores: list,
+    height: int,
+    alpha: float,
+    beta: float,
+) -> float:
+    """
+    Minimax algorithm with alpha-beta pruning to determine the optimal
+    move with improved efficiency.
+
+    Parameters:
+    - depth (int): Current depth in the game tree, used to track recursion level.
+    - node_index (int): Index of the current node in the scores array, representing
+    leaf nodes.
+    - is_maximizing_player (bool): True if the current player is the maximizing player
+    , False otherwise.
+    - scores (list): A list of integers representing the scores at the
+    leaf nodes of the game tree.
+    - height (int): The maximum depth of the game tree, based on the number of
+    leaf nodes in a binary structure.
+    - alpha (int): The best value that the maximizer can guarantee at the
+    current level or above.
+    - beta (int): The best value that the minimizer can guarantee at the
+    current level or above.
+
+    Returns:
+    - int: The best score that the current player can achieve from this node.
+    """
+    # Base case: If we reach the leaf node level, return its score
+    if depth == height:
+        return scores[node_index]
+
+    # Maximizing player's move
+    if is_maximizing_player:
+        best_score = -math.inf  # Start with the worst possible score for maximizer
+        for i in range(2):  # Two branches at each level in binary tree
+            val = minimax_with_pruning(
+                depth + 1, node_index * 2 + i, False, scores, height, alpha, beta
+            )
+            best_score = max(best_score, val)  # Maximizer selects the maximum value
+            alpha = max(alpha, best_score)  # Update alpha (best option for maximizer)
+            if beta <= alpha:
+                break  # Beta cut-off
+        return best_score
+
+    # Minimizing player's move
+    else:
+        best_score = math.inf  # Start with the worst possible score for minimizer
+        for i in range(2):
+            val = minimax_with_pruning(
+                depth + 1, node_index * 2 + i, True, scores, height, alpha, beta
+            )
+            best_score = min(best_score, val)  # Minimizer selects the minimum value
+            beta = min(beta, best_score)  # Update beta (best option for minimizer)
+            if beta <= alpha:
+                break  # Alpha cut-off
+        return best_score
+
+
+def main() -> None:
+    # Scores array representing the leaf nodes of a binary tree (depth = 3)
+    scores = [3, 5, 2, 9, 12, 5, 23, 23]
+    # Calculate the height of the binary tree based on the number of leaf nodes
+    height = math.ceil(math.log2(len(scores)))
+
+    # Print the optimal outcome for the maximizing player with alpha-beta pruning
+    print(
+        "Optimal value for the maximizing player with pruning:",
+        minimax_with_pruning(0, 0, True, scores, height, -math.inf, math.inf),
+    )
+
+
+if __name__ == "__main__":
+    main()