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96 lines
3.0 KiB
Python
96 lines
3.0 KiB
Python
"""
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Minimax helps to achieve maximum score in a game by checking all possible moves
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depth is current depth in game tree.
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nodeIndex is index of current node in scores[].
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if move is of maximizer return true else false
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leaves of game tree is stored in scores[]
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height is maximum height of Game tree
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"""
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from __future__ import annotations
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import math
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def minimax(
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depth: int, node_index: int, is_max: bool, scores: list[int], height: float
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) -> int:
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"""
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This function implements the minimax algorithm, which helps achieve the optimal
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score for a player in a two-player game by checking all possible moves.
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If the player is the maximizer, then the score is maximized.
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If the player is the minimizer, then the score is minimized.
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Parameters:
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- depth: Current depth in the game tree.
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- node_index: Index of the current node in the scores list.
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- is_max: A boolean indicating whether the current move
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is for the maximizer (True) or minimizer (False).
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- scores: A list containing the scores of the leaves of the game tree.
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- height: The maximum height of the game tree.
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Returns:
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- An integer representing the optimal score for the current player.
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>>> import math
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>>> scores = [90, 23, 6, 33, 21, 65, 123, 34423]
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>>> height = math.log(len(scores), 2)
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>>> minimax(0, 0, True, scores, height)
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65
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>>> minimax(-1, 0, True, scores, height)
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Traceback (most recent call last):
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...
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ValueError: Depth cannot be less than 0
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>>> minimax(0, 0, True, [], 2)
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Traceback (most recent call last):
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...
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ValueError: Scores cannot be empty
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>>> scores = [3, 5, 2, 9, 12, 5, 23, 23]
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>>> height = math.log(len(scores), 2)
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>>> minimax(0, 0, True, scores, height)
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12
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"""
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if depth < 0:
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raise ValueError("Depth cannot be less than 0")
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if len(scores) == 0:
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raise ValueError("Scores cannot be empty")
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# Base case: If the current depth equals the height of the tree,
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# return the score of the current node.
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if depth == height:
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return scores[node_index]
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# If it's the maximizer's turn, choose the maximum score
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# between the two possible moves.
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if is_max:
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return max(
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minimax(depth + 1, node_index * 2, False, scores, height),
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minimax(depth + 1, node_index * 2 + 1, False, scores, height),
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)
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# If it's the minimizer's turn, choose the minimum score
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# between the two possible moves.
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return min(
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minimax(depth + 1, node_index * 2, True, scores, height),
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minimax(depth + 1, node_index * 2 + 1, True, scores, height),
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)
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def main() -> None:
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# Sample scores and height calculation
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scores = [90, 23, 6, 33, 21, 65, 123, 34423]
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height = math.log(len(scores), 2)
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# Calculate and print the optimal value using the minimax algorithm
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print("Optimal value : ", end="")
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print(minimax(0, 0, True, scores, height))
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if __name__ == "__main__":
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import doctest
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doctest.testmod()
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main()
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