Enhance readability of Minimax (TheAlgorithms#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>

Author: 3 people

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)
@@ -37,28 +53,36 @@ 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),
  )
 
 
 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))