Enhance readability of Minimax (#10838)

* Enhance readability of Minimax

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

* Reduce line overflow

* Update backtracking/minimax.py

Co-authored-by: Tianyi Zheng <tianyizheng02@gmail.com>

* Update backtracking/minimax.py

Co-authored-by: Tianyi Zheng <tianyizheng02@gmail.com>

* Update backtracking/minimax.py

Co-authored-by: Tianyi Zheng <tianyizheng02@gmail.com>

* Remove line overflow

---------

Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Co-authored-by: Tianyi Zheng <tianyizheng02@gmail.com>

backtracking/minimax.py

@@ -16,6 +16,22 @@ def minimax(
     depth: int, node_index: int, is_max: bool, scores: list[int], height: float
 ) -> int:
     """
+    This function implements the minimax algorithm, which helps achieve the optimal
+    score for a player in a two-player game by checking all possible moves.
+    If the player is the maximizer, then the score is maximized.
+    If the player is the minimizer, then the score is minimized.
+
+    Parameters:
+    - depth: Current depth in the game tree.
+    - node_index: Index of the current node in the scores list.
+    - is_max: A boolean indicating whether the current move
+              is for the maximizer (True) or minimizer (False).
+    - scores: A list containing the scores of the leaves of the game tree.
+    - height: The maximum height of the game tree.
+
+    Returns:
+    - An integer representing the optimal score for the current player.
+
     >>> import math
     >>> scores = [90, 23, 6, 33, 21, 65, 123, 34423]
     >>> height = math.log(len(scores), 2)
@@ -37,19 +53,24 @@ def minimax(
 
     if depth < 0:
         raise ValueError("Depth cannot be less than 0")
-
     if len(scores) == 0:
         raise ValueError("Scores cannot be empty")
 
+    # Base case: If the current depth equals the height of the tree,
+    # return the score of the current node.
     if depth == height:
         return scores[node_index]
 
+    # If it's the maximizer's turn, choose the maximum score
+    # between the two possible moves.
     if is_max:
         return max(
             minimax(depth + 1, node_index * 2, False, scores, height),
             minimax(depth + 1, node_index * 2 + 1, False, scores, height),
         )
 
+    # If it's the minimizer's turn, choose the minimum score
+    # between the two possible moves.
     return min(
         minimax(depth + 1, node_index * 2, True, scores, height),
         minimax(depth + 1, node_index * 2 + 1, True, scores, height),
@@ -57,8 +78,11 @@ def minimax(
 
 
 def main() -> None:
+    # Sample scores and height calculation
     scores = [90, 23, 6, 33, 21, 65, 123, 34423]
     height = math.log(len(scores), 2)
+
+    # Calculate and print the optimal value using the minimax algorithm
     print("Optimal value : ", end="")
     print(minimax(0, 0, True, scores, height))