add monotonic queue algorithm (#10531)

* add monotonic queue algorithm

* add monotonic queue algorithm

* add monotonic queue algorithm

* monotonic queue

* updating DIRECTORY.md

* Rename file to correct directory structure

* updating DIRECTORY.md

---------

Co-authored-by: Christian Clauss <cclauss@me.com>
Co-authored-by: cclauss <cclauss@users.noreply.github.com>

Author: Jiang15

DIRECTORY.md

@@ -370,6 +370,7 @@
     * [Circular Queue Linked List](data_structures/queues/circular_queue_linked_list.py)
     * [Double Ended Queue](data_structures/queues/double_ended_queue.py)
     * [Linked Queue](data_structures/queues/linked_queue.py)
+    * [Monotonic Queue](data_structures/queues/monotonic_queue.py)
     * [Priority Queue Using List](data_structures/queues/priority_queue_using_list.py)
     * [Queue By List](data_structures/queues/queue_by_list.py)
     * [Queue By Two Stacks](data_structures/queues/queue_by_two_stacks.py)

data_structures/queues/monotonic_queue.py

@@ -0,0 +1,39 @@
+from __future__ import annotations
+
+from collections import deque
+
+arr = [1, 3, -1, -3, 5, 3, 6, 7]
+window_size = 3
+expect = [3, 3, 5, 5, 6, 7]
+
+
+def max_sliding_window(arr: list[float], window_size: int) -> list[float]:
+    """
+    Given an array of integers nums, there is a sliding window of size k which is moving
+    from the very left of the array to the very right.
+    Each time the sliding window of length window_size moves right by one position.
+    Return the max sliding window.
+    >>> max_sliding_window(arr, window_size) == expect
+    True
+    """
+    max_val = []
+    mono_queue: deque = deque()
+    for i in range(len(arr)):
+        # pop the element if the index is outside the window size k
+        if mono_queue and i - mono_queue[0] >= window_size:
+            mono_queue.popleft()
+        # keep the queue monotonically decreasing
+        # so that the max value is always on the top
+        while mono_queue and arr[i] >= arr[mono_queue[-1]]:
+            mono_queue.pop()
+        mono_queue.append(i)
+        # the maximum value is the first element in queue
+        if i >= window_size - 1:
+            max_val.append(arr[mono_queue[0]])
+    return max_val
+
+
+if __name__ == "__main__":
+    from doctest import testmod
+
+    testmod()