Watch 10 video solutions for Sliding Subarray Beauty, a medium level problem involving Array, Hash Table, Sliding Window. This walkthrough by Prakhar Agrawal has 2,871 views views. Want to try solving it yourself? Practice on FleetCode or read the detailed text solution.
Given an integer array nums containing n integers, find the beauty of each subarray of size k.
The beauty of a subarray is the xth smallest integer in the subarray if it is negative, or 0 if there are fewer than x negative integers.
Return an integer array containing n - k + 1 integers, which denote the beauty of the subarrays in order from the first index in the array.
A subarray is a contiguous non-empty sequence of elements within an array.
Example 1:
Input: nums = [1,-1,-3,-2,3], k = 3, x = 2 Output: [-1,-2,-2] Explanation: There are 3 subarrays with size k = 3. The first subarray is[1, -1, -3]and the 2nd smallest negative integer is -1. The second subarray is[-1, -3, -2]and the 2nd smallest negative integer is -2. The third subarray is[-3, -2, 3]and the 2nd smallest negative integer is -2.
Example 2:
Input: nums = [-1,-2,-3,-4,-5], k = 2, x = 2 Output: [-1,-2,-3,-4] Explanation: There are 4 subarrays with size k = 2. For[-1, -2], the 2nd smallest negative integer is -1. For[-2, -3], the 2nd smallest negative integer is -2. For[-3, -4], the 2nd smallest negative integer is -3. For[-4, -5], the 2nd smallest negative integer is -4.
Example 3:
Input: nums = [-3,1,2,-3,0,-3], k = 2, x = 1 Output: [-3,0,-3,-3,-3] Explanation: There are 5 subarrays with size k = 2. For[-3, 1], the 1st smallest negative integer is -3. For[1, 2], there is no negative integer so the beauty is 0. For[2, -3], the 1st smallest negative integer is -3. For[-3, 0], the 1st smallest negative integer is -3. For[0, -3], the 1st smallest negative integer is -3.
Constraints:
n == nums.length 1 <= n <= 1051 <= k <= n1 <= x <= k -50 <= nums[i] <= 50 Problem Overview: Given an integer array nums, a window size k, and an integer x, evaluate every contiguous subarray of length k. The “beauty” of a window is the x-th smallest negative number inside it. If the window contains fewer than x negative values, the beauty is 0. The task is to compute this value for every sliding window across the array.
Approach 1: Brute Force with Sorting (O(n * k log k) time, O(k) space)
For each starting index, copy the next k elements to form the current window. Filter or scan for negative numbers, sort them, and pick the x-th smallest negative value. If the window has fewer than x negatives, return 0. This approach directly follows the problem definition and is useful for verifying correctness. The downside is performance: sorting up to k elements for every window results in O(n * k log k) time, which becomes slow for large inputs.
Approach 2: Sliding Window with Multisets (O(n log k) time, O(k) space)
The optimized approach maintains a dynamic view of the current window using a sliding window technique from Sliding Window. Instead of rebuilding the window each time, insert the incoming element and remove the outgoing element as the window shifts. A multiset (or balanced ordered structure) keeps window elements sorted automatically. This allows efficient insertion and deletion in O(log k) time.
To compute the beauty, focus only on negative numbers. Iterate through the ordered structure (or maintain a subset of negatives) and retrieve the x-th smallest negative element. If fewer than x negatives exist, return 0. Because each element is inserted and removed once, the total complexity becomes O(n log k). This method combines ordered storage with incremental updates and fits naturally with array processing problems involving arrays and frequency tracking techniques similar to hash tables.
Recommended for interviews: Start by explaining the brute force solution to demonstrate understanding of the definition of window beauty. Then move to the sliding window with multiset optimization. Interviewers expect you to avoid recomputing the entire window each time and instead maintain state as the window moves. The optimized approach shows strong knowledge of sliding window patterns and ordered data structures.
| Approach | Time | Space | When to Use |
|---|---|---|---|
| Brute Force with Sorting | O(n * k log k) | O(k) | Useful for small inputs or validating logic before optimizing |
| Sliding Window with Multiset | O(n log k) | O(k) | General case for large arrays where windows shift frequently |