Added min_max algorithm in game_theory module

game_theory/README.md

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+# Game Theory Algorithms
+
+This repository contains implementations of various algorithms related to game theory.
+
+## Algorithms
+
+- **Minimax Algorithm**
+  - [Minimax (Wikipedia)](https://en.wikipedia.org/wiki/Minimax)
+

game_theory/min_max.py

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+import math
+from typing import List
+
+
+class MinMax:
+    """
+    A class to represent a game using the Minimax algorithm.
+
+    Attributes:
+    ----------
+    scores : List[int]
+        List of terminal node scores.
+    tree_depth : int
+        Depth of the game tree.
+
+    Methods:
+    -------
+    minimax(current_depth: int = 0, node_index: int = 0, is_max_turn: bool = True) -> int:
+        Recursive implementation of the minimax algorithm.
+    find_optimal_value() -> int:
+        Find and return the optimal value for the maximizing player.
+
+    Examples:
+    ---------
+    >>> game = MinMax([3, 5, 2, 9, 12, 5, 23, 23])
+    >>> game.find_optimal_value()
+    12
+    """
+
+    def __init__(self, scores: List[int]) -> None:
+        """
+        Initialize the MinMax game with a list of scores.
+
+        Parameters:
+        ----------
+        scores : List[int]
+            List of terminal node scores.
+        """
+        self.scores = scores
+        self.tree_depth = int(math.log2(len(scores)))
+
+    def minimax(
+        self, current_depth: int = 0, node_index: int = 0, is_max_turn: bool = True
+    ) -> int:
+        """
+        Recursive implementation of the minimax algorithm.
+
+        Parameters:
+        ----------
+        current_depth : int
+            Current depth in the game tree.
+        node_index : int
+            Index of the current node in the tree.
+        is_max_turn : bool
+            Boolean indicating if it's the maximizing player's turn.
+
+        Returns:
+        -------
+        int
+            The optimal value for the current player.
+
+        Examples:
+        ---------
+        >>> game = MinMax([3, 5, 2, 9, 12, 5, 23, 23])
+        >>> game.minimax(0, 0, True)
+        12
+        """
+
+        if current_depth == self.tree_depth:
+            return self.scores[node_index]
+
+        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) -> int:
+        """
+        Find and return the optimal value for the maximizing player.
+
+        Returns:
+        -------
+        int
+            The optimal value.
+
+        Examples:
+        ---------
+        >>> game = MinMax([3, 5, 2, 9, 12, 5, 23, 23])
+        >>> game.find_optimal_value()
+        12
+        """
+        return self.minimax()
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()
+
+    scores = [3, 5, 2, 9, 12, 5, 23, 23]
+    game = MinMax(scores)
+    optimal_value = game.find_optimal_value()
+    print(f"The optimal value is: {optimal_value}")