What is the optimal time complexity of solving Sliding Window Maximum?

The optimized solution achieves a time complexity of O(n) by using sorting, mathematical shortcuts, or hash table lookups.

What is the auxiliary space complexity for Sliding Window Maximum?

The space complexity is O(n) since we only use a minimal/constant amount of extra memory for tracking variables (or auxiliary space if dynamic structures are allocated).

What are the typical edge cases we must handle in Sliding Window Maximum?

Key edge cases include empty collections, negative or large bounds causing integer overflow, arrays with only one element, or inputs where target criteria are not met.

How can we optimize the brute force approach for Sliding Window Maximum?

Brute force methods often inspect all possible combinations. We optimize this by sorting the input list to enable binary search, or tracking processed items in a set to avoid redundant nested loop lookups.

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Sliding Window Maximum

Learn how to solve the 'Sliding Window Maximum' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Hard

You are given an array of integers nums and an integer k representing the size of a sliding window which moves 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 value in each sliding window.

Write a function maxSlidingWindow(nums: List[int], k: int) -> List[int].

Constraints

•1 <= len(nums) <= 10^5
•-10^4 <= nums[i] <= 10^4
•1 <= k <= len(nums)

Examples

Example 1

Input

nums = [1, 3, -1, -3, 5, 3, 6, 7], k = 3

Output

[3, 3, 5, 5, 6, 7]

Explanation

Window [1,3,-1] max=3, [3,-1,-3] max=3, [-1,-3,5] max=5, [-3,5,3] max=5, [5,3,6] max=6, [3,6,7] max=7.

Example 2

Input

nums = [1], k = 1

Output

[1]

Explanation

Single element window, max is 1.

Need a Hint?

Maintain a sliding window boundary using two pointers. Expand the right boundary, and contract the left boundary if criteria are violated.

Edge Cases to Watch

Empty list or null input variables
Single item lists/arrays
Extremely large input bounds causing integer or stack overflow

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