Implement sliding window maximum algorithm using deque

data_structures/arrays/sliding_window_maximum.py

@@ -0,0 +1,59 @@
+from collections import deque
+
+
+def sliding_window_maximum(nums: list[int], window_size: int) -> list[int]:
+    """
+    Return a list of the maximum values in each sliding window of the given size.
+    This algorithm runs in O(n) time using a deque to keep track of useful elements.
+
+    Parameters
+    ----------
+    nums : list[int]
+        The input list of integers.
+    window_size : int
+        The size of the sliding window.
+
+    Returns
+    -------
+    list[int]
+        A list containing the maximum of each sliding window.
+
+    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([4, -2], 1)
+    [4, -2]
+    >>> sliding_window_maximum([], 3)
+    []
+    >>> sliding_window_maximum([1, 2, 3], 0)
+    []
+
+    Reference
+    ---------
+    https://en.wikipedia.org/wiki/Sliding_window_protocol
+    """
+    if not nums or window_size <= 0:
+        return []
+
+    dq: deque[int] = deque()
+    result: list[int] = []
+
+    for i, num in enumerate(nums):
+        # Remove indices that are out of the current window
+        while dq and dq[0] <= i - window_size:
+            dq.popleft()
+
+        # Remove smaller values as they are not useful
+        while dq and nums[dq[-1]] < num:
+            dq.pop()
+
+        dq.append(i)
+
+        # Add the current max to the result once the window is of size window_size
+        if i >= window_size - 1:
+            result.append(nums[dq[0]])
+
+    return result