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* feat: add sliding window maximum using monotonic deque * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci * feat: add sliding window maximum using monotonic deque --------- Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
59 lines
1.8 KiB
Python
59 lines
1.8 KiB
Python
from collections import deque
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def sliding_window_maximum(numbers: list[int], window_size: int) -> list[int]:
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"""
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Return a list containing the maximum of each sliding window of size window_size.
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This implementation uses a monotonic deque to achieve O(n) time complexity.
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Args:
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numbers: List of integers representing the input array.
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window_size: Size of the sliding window (must be positive).
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Returns:
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List of maximum values for each valid window.
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Raises:
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ValueError: If window_size is not a positive integer.
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Time Complexity: O(n) - each element is added and removed at most once
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Space Complexity: O(k) - deque stores at most window_size indices
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Examples:
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>>> sliding_window_maximum([1, 3, -1, -3, 5, 3, 6, 7], 3)
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[3, 3, 5, 5, 6, 7]
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>>> sliding_window_maximum([9, 11], 2)
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[11]
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>>> sliding_window_maximum([], 3)
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[]
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>>> sliding_window_maximum([4, 2, 12, 3], 1)
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[4, 2, 12, 3]
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>>> sliding_window_maximum([1], 1)
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[1]
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"""
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if window_size <= 0:
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raise ValueError("Window size must be a positive integer")
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if not numbers:
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return []
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result: list[int] = []
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index_deque: deque[int] = deque()
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for current_index, current_value in enumerate(numbers):
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# Remove the element which is out of this window
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if index_deque and index_deque[0] == current_index - window_size:
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index_deque.popleft()
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# Remove useless elements (smaller than current) from back
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while index_deque and numbers[index_deque[-1]] < current_value:
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index_deque.pop()
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index_deque.append(current_index)
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# Start adding to result once we have a full window
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if current_index >= window_size - 1:
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result.append(numbers[index_deque[0]])
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return result
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