Solution: Sliding Window Maximum

Explore the sliding window maximum problem by learning how to efficiently find the maximum in each subarray of a given size. Understand naive and optimized approaches using a deque that maintains indexes of potential maximums, enabling O(n) time complexity. This lesson helps you implement the sliding window technique to handle varying input array patterns and master time and space trade-offs.

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Statement
Solution
- Naive approach
- Optimized approach using sliding window

Statement

You are given an array of integers nums and a sliding window of size w that moves from left to right across the array, shifting one position at a time.

Your task is to find the maximum value within the current window at each step and return it.

Constraints:

$1 \leq$ nums.length $\leq 10^3$
$-10^4 \leq$ nums[i] $\leq 10^4$
$1 \leq$ w $\leq$ nums.length

Solution

So far, you’ve probably brainstormed some approaches on how to solve this problem. Let’s explore some of these approaches and figure out which one to follow while considering time complexity and any implementation constraints.

Naive approach

A naive approach is to slide the window over the input list and find the maximum in each window separately. We iterate over the input list, calculating the maximum element in each window linearly, and then adding it to the output list. In each subsequent iteration, we update the current window by removing the first element from the current window and adding the incoming element of the input list. Once we are done iterating the input list, we return the output list, containing the maximums of all $(n−w+1)$ windows.

The time complexity of this approach is $O(n \times w)$ ...