From f8715831edb11fb7ab81147ae63f37fddad79f4f Mon Sep 17 00:00:00 2001
From: Parag Sharma <sharmaparag2004@gmail.com>
Date: Mon, 12 Jan 2026 19:48:34 +0530
Subject: [PATCH 1/3] feat: add sliding window maximum using monotonic deque

---
 other/sliding_window_maximum.py | 59 +++++++++++++++++++++++++++++++++
 1 file changed, 59 insertions(+)
 create mode 100644 other/sliding_window_maximum.py

diff --git a/other/sliding_window_maximum.py b/other/sliding_window_maximum.py
new file mode 100644
index 000000000000..4fd818e3fed2
--- /dev/null
+++ b/other/sliding_window_maximum.py
@@ -0,0 +1,59 @@
+from collections import deque
+from typing import Deque, List
+
+
+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
\ No newline at end of file

From ecf074dd3830f175d47dca9dd7f1569f520800f1 Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Mon, 12 Jan 2026 14:20:17 +0000
Subject: [PATCH 2/3] [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci
---
 other/sliding_window_maximum.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/other/sliding_window_maximum.py b/other/sliding_window_maximum.py
index 4fd818e3fed2..1c38e878bc58 100644
--- a/other/sliding_window_maximum.py
+++ b/other/sliding_window_maximum.py
@@ -56,4 +56,4 @@ def sliding_window_maximum(numbers: List[int], window_size: int) -> List[int]:
         if current_index >= window_size - 1:
             result.append(numbers[index_deque[0]])
 
-    return result
\ No newline at end of file
+    return result

From e4f9d6d8cb190301a0c453c267a35027637f0b48 Mon Sep 17 00:00:00 2001
From: Parag Sharma <sharmaparag2004@gmail.com>
Date: Mon, 12 Jan 2026 20:18:17 +0530
Subject: [PATCH 3/3] feat: add sliding window maximum using monotonic deque

---
 other/sliding_window_maximum.py | 7 +++----
 1 file changed, 3 insertions(+), 4 deletions(-)

diff --git a/other/sliding_window_maximum.py b/other/sliding_window_maximum.py
index 1c38e878bc58..1c2c3c8e37e6 100644
--- a/other/sliding_window_maximum.py
+++ b/other/sliding_window_maximum.py
@@ -1,8 +1,7 @@
 from collections import deque
-from typing import Deque, List
 
 
-def sliding_window_maximum(numbers: List[int], window_size: int) -> List[int]:
+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.
 
@@ -38,8 +37,8 @@ def sliding_window_maximum(numbers: List[int], window_size: int) -> List[int]:
     if not numbers:
         return []
 
-    result: List[int] = []
-    index_deque: Deque[int] = deque()
+    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