Create minmax.py (TheAlgorithms#7409)

* Create minmax.py

* Update minmax.py

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Co-authored-by: Christian Clauss <cclauss@me.com>
Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>

Author: 3 people

backtracking/minmax.py

@@ -0,0 +1,69 @@
+"""
+Minimax helps to achieve maximum score in a game by checking all possible moves.
+
+"""
+from __future__ import annotations
+
+import math
+
+
+def minimax(
+    depth: int, node_index: int, is_max: bool, scores: list[int], height: float
+) -> int:
+    """
+    depth is current depth in game tree.
+    node_index is index of current node in scores[].
+    scores[] contains the leaves of game tree.
+    height is maximum height of game tree.
+
+    >>> scores = [90, 23, 6, 33, 21, 65, 123, 34423]
+    >>> height = math.log(len(scores), 2)
+    >>> minimax(0, 0, True, scores, height)
+    65
+    >>> minimax(-1, 0, True, scores, height)
+    Traceback (most recent call last):
+        ...
+    ValueError: Depth cannot be less than 0
+    >>> minimax(0, 0, True, [], 2)
+    Traceback (most recent call last):
+        ...
+    ValueError: Scores cannot be empty
+    >>> scores = [3, 5, 2, 9, 12, 5, 23, 23]
+    >>> height = math.log(len(scores), 2)
+    >>> minimax(0, 0, True, scores, height)
+    12
+    """
+
+    if depth < 0:
+        raise ValueError("Depth cannot be less than 0")
+
+    if not scores:
+        raise ValueError("Scores cannot be empty")
+
+    if depth == height:
+        return scores[node_index]
+
+    return (
+        max(
+            minimax(depth + 1, node_index * 2, False, scores, height),
+            minimax(depth + 1, node_index * 2 + 1, False, scores, height),
+        )
+        if is_max
+        else min(
+            minimax(depth + 1, node_index * 2, True, scores, height),
+            minimax(depth + 1, node_index * 2 + 1, True, scores, height),
+        )
+    )
+
+
+def main() -> None:
+    scores = [90, 23, 6, 33, 21, 65, 123, 34423]
+    height = math.log(len(scores), 2)
+    print(f"Optimal value : {minimax(0, 0, True, scores, height)}")
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()
+    main()