From 0a6830adf02fce5485de340862b15baeaf7c202c Mon Sep 17 00:00:00 2001
From: MAHY U DEEN SHAHID <mahyudeenshahidiqbal@gmail.com>
Date: Wed, 22 Oct 2025 00:32:45 +0500
Subject: [PATCH 1/2] Add sliding_window_maximum function

Implement sliding window maximum algorithm using deque.
---
 .../arrays/sliding_window_maximum.py          | 57 +++++++++++++++++++
 1 file changed, 57 insertions(+)
 create mode 100644 data_structures/arrays/sliding_window_maximum.py

diff --git a/data_structures/arrays/sliding_window_maximum.py b/data_structures/arrays/sliding_window_maximum.py
new file mode 100644
index 000000000000..213328dcdf74
--- /dev/null
+++ b/data_structures/arrays/sliding_window_maximum.py
@@ -0,0 +1,57 @@
+from collections import deque
+from typing import List
+
+
+def sliding_window_maximum(nums: List[int], k: int) -> List[int]:
+    """
+    Return a list of the maximum values in each sliding window of size k.
+
+    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.
+    k : int
+        The window size.
+
+    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)
+    []
+    """
+    if not nums or k <= 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 - k:
+            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 k
+        if i >= k - 1:
+            result.append(nums[dq[0]])
+
+    return result

From 2ac3757f5ef7f01286baaf1c6f025095dcd5098f Mon Sep 17 00:00:00 2001
From: MAHY U DEEN SHAHID <mahyudeenshahidiqbal@gmail.com>
Date: Wed, 22 Oct 2025 00:43:35 +0500
Subject: [PATCH 2/2] Refactor sliding_window_maximum function signature

Updated type hints and parameter names for clarity.
---
 .../arrays/sliding_window_maximum.py          | 32 ++++++++++---------
 1 file changed, 17 insertions(+), 15 deletions(-)

diff --git a/data_structures/arrays/sliding_window_maximum.py b/data_structures/arrays/sliding_window_maximum.py
index 213328dcdf74..eaa44c3891c3 100644
--- a/data_structures/arrays/sliding_window_maximum.py
+++ b/data_structures/arrays/sliding_window_maximum.py
@@ -1,28 +1,26 @@
 from collections import deque
-from typing import List
 
 
-def sliding_window_maximum(nums: List[int], k: int) -> List[int]:
+def sliding_window_maximum(nums: list[int], window_size: int) -> list[int]:
     """
-    Return a list of the maximum values in each sliding window of size k.
-
+    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]
+    nums : list[int]
         The input list of integers.
-    k : int
-        The window size.
+    window_size : int
+        The size of the sliding window.
 
     Returns
     -------
-    List[int]
+    list[int]
         A list containing the maximum of each sliding window.
 
     Examples
     --------
-    >>> sliding_window_maximum([1,3,-1,-3,5,3,6,7], 3)
+    >>> 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]
@@ -30,18 +28,22 @@ def sliding_window_maximum(nums: List[int], k: int) -> List[int]:
     [4, -2]
     >>> sliding_window_maximum([], 3)
     []
-    >>> sliding_window_maximum([1,2,3], 0)
+    >>> sliding_window_maximum([1, 2, 3], 0)
     []
+
+    Reference
+    ---------
+    https://en.wikipedia.org/wiki/Sliding_window_protocol
     """
-    if not nums or k <= 0:
+    if not nums or window_size <= 0:
         return []
 
     dq: deque[int] = deque()
-    result: List[int] = []
+    result: list[int] = []
 
     for i, num in enumerate(nums):
         # Remove indices that are out of the current window
-        while dq and dq[0] <= i - k:
+        while dq and dq[0] <= i - window_size:
             dq.popleft()
 
         # Remove smaller values as they are not useful
@@ -50,8 +52,8 @@ def sliding_window_maximum(nums: List[int], k: int) -> List[int]:
 
         dq.append(i)
 
-        # Add the current max to the result once the window is of size k
-        if i >= k - 1:
+        # 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