|
| 1 | +from collections import deque |
| 2 | + |
| 3 | + |
| 4 | +def sliding_window_maximum(numbers: list[int], window_size: int) -> list[int]: |
| 5 | + """ |
| 6 | + Return a list containing the maximum of each sliding window of size window_size. |
| 7 | +
|
| 8 | + This implementation uses a monotonic deque to achieve O(n) time complexity. |
| 9 | +
|
| 10 | + Args: |
| 11 | + numbers: List of integers representing the input array. |
| 12 | + window_size: Size of the sliding window (must be positive). |
| 13 | +
|
| 14 | + Returns: |
| 15 | + List of maximum values for each valid window. |
| 16 | +
|
| 17 | + Raises: |
| 18 | + ValueError: If window_size is not a positive integer. |
| 19 | +
|
| 20 | + Time Complexity: O(n) - each element is added and removed at most once |
| 21 | + Space Complexity: O(k) - deque stores at most window_size indices |
| 22 | +
|
| 23 | + Examples: |
| 24 | + >>> sliding_window_maximum([1, 3, -1, -3, 5, 3, 6, 7], 3) |
| 25 | + [3, 3, 5, 5, 6, 7] |
| 26 | + >>> sliding_window_maximum([9, 11], 2) |
| 27 | + [11] |
| 28 | + >>> sliding_window_maximum([], 3) |
| 29 | + [] |
| 30 | + >>> sliding_window_maximum([4, 2, 12, 3], 1) |
| 31 | + [4, 2, 12, 3] |
| 32 | + >>> sliding_window_maximum([1], 1) |
| 33 | + [1] |
| 34 | + """ |
| 35 | + if window_size <= 0: |
| 36 | + raise ValueError("Window size must be a positive integer") |
| 37 | + if not numbers: |
| 38 | + return [] |
| 39 | + |
| 40 | + result: list[int] = [] |
| 41 | + index_deque: deque[int] = deque() |
| 42 | + |
| 43 | + for current_index, current_value in enumerate(numbers): |
| 44 | + # Remove the element which is out of this window |
| 45 | + if index_deque and index_deque[0] == current_index - window_size: |
| 46 | + index_deque.popleft() |
| 47 | + |
| 48 | + # Remove useless elements (smaller than current) from back |
| 49 | + while index_deque and numbers[index_deque[-1]] < current_value: |
| 50 | + index_deque.pop() |
| 51 | + |
| 52 | + index_deque.append(current_index) |
| 53 | + |
| 54 | + # Start adding to result once we have a full window |
| 55 | + if current_index >= window_size - 1: |
| 56 | + result.append(numbers[index_deque[0]]) |
| 57 | + |
| 58 | + return result |
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