Sliding Window Maximum

Problem

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. Each time the sliding window moves right by one position, return the max sliding window.

Examples

The brute-force approach

For each window position, scan all k elements and take the maximum.

result = []
for i in range(len(nums) - k + 1):
    result.append(max(nums[i:i+k]))
return result

O(n × k) — each of the n-k+1 windows requires a full scan of k elements.

Spotting the pattern

This is a Monotonic Queue problem. The key question to ask yourself:

If element at index j is larger than all elements from index i to j-1, can any of those smaller elements ever be the window maximum? What can you do with them?

Answering that is where it clicks, and it's exactly what the guided walkthrough below builds with you: the pattern reasoning, a progressive hint ladder that never spoils the answer, a row-by-row dry run, the optimized solution, and an in-browser editor to run your code against real test cases.