Add sliding window maximum using monotonic deque

other/sliding_window_maximum.py

@@ -0,0 +1,58 @@
+from collections import deque
+
+
+def sliding_window_maximum(numbers: list[int], window_size: int) -> list[int]:
+    """
+    Return a list containing the maximum of each sliding window of size window_size.
+
+    This implementation uses a monotonic deque to achieve O(n) time complexity.
+
+    Args:
+        numbers: List of integers representing the input array.
+        window_size: Size of the sliding window (must be positive).
+
+    Returns:
+        List of maximum values for each valid window.
+
+    Raises:
+        ValueError: If window_size is not a positive integer.
+
+    Time Complexity: O(n) - each element is added and removed at most once
+    Space Complexity: O(k) - deque stores at most window_size indices
+
+    Examples:
+    >>> sliding_window_maximum([1, 3, -1, -3, 5, 3, 6, 7], 3)
+    [3, 3, 5, 5, 6, 7]
+    >>> sliding_window_maximum([9, 11], 2)
+    [11]
+    >>> sliding_window_maximum([], 3)
+    []
+    >>> sliding_window_maximum([4, 2, 12, 3], 1)
+    [4, 2, 12, 3]
+    >>> sliding_window_maximum([1], 1)
+    [1]
+    """
+    if window_size <= 0:
+        raise ValueError("Window size must be a positive integer")
+    if not numbers:
+        return []
+
+    result: list[int] = []
+    index_deque: deque[int] = deque()
+
+    for current_index, current_value in enumerate(numbers):
+        # Remove the element which is out of this window
+        if index_deque and index_deque[0] == current_index - window_size:
+            index_deque.popleft()
+
+        # Remove useless elements (smaller than current) from back
+        while index_deque and numbers[index_deque[-1]] < current_value:
+            index_deque.pop()
+
+        index_deque.append(current_index)
+
+        # Start adding to result once we have a full window
+        if current_index >= window_size - 1:
+            result.append(numbers[index_deque[0]])
+
+    return result