Sliding Window Maximum

Problem

https://leetcode.com/problems/sliding-window-maximum/

You are 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. You can only see the k numbers in the window. Each time the sliding window moves right by one position.

Return the max sliding window.

Example 1:

Input: nums = [1,3,-1,-3,5,3,6,7], k = 3
Output: [3,3,5,5,6,7]
Explanation:
Window position                Max
---------------               -----
[1  3  -1] -3  5  3  6  7       3
 1 [3  -1  -3] 5  3  6  7       3
 1  3 [-1  -3  5] 3  6  7       5
 1  3  -1 [-3  5  3] 6  7       5
 1  3  -1  -3 [5  3  6] 7       6
 1  3  -1  -3  5 [3  6  7]      7

Example 2:

Input: nums = [1], k = 1
Output: [1]

Constraints:

• 1 <= nums.length <= 10:sup:`5`

• -10:sup:`4`<= nums[i] <= 10:sup:`4`

• 1 <= k <= nums.length

Pattern

Array, Queue, Sliding Window, Heap (Priority Queue), Monotonic Queue

Approaches

Monotonic Deque

Code

from collections import deque


def maxSlidingWindow(nums: list[int], k: int) -> list[int]:
    output = []
    q = deque()

    left = 0
    right = 0
    while right < len(nums):
        while len(q) > 0 and nums[q[-1]] < nums[right]:
            q.pop()
        q.append(right)

        if left > q[0]:
            q.popleft()

        if (right + 1) >= k:
            output.append(nums[q[0]])
            left += 1

        right += 1

    return output

Test

>>> from sliding_window_maximum__monotonic_deque import maxSlidingWindow
>>> maxSlidingWindow([1, 3, -1, -3, 5, 3, 6, 7], 3)
[3, 3, 5, 5, 6, 7]
>>> maxSlidingWindow([1], 1)
[1]

sliding_window_maximum__monotonic_deque.maxSlidingWindow(nums: list[int], k: int) → list[int]