Sliding Subarray Beauty

Problem Description

Given an integer array nums containing n integers, find the beauty of each subarray of size k. The beauty of a subarray is the x-th 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.

Key Insights

• A subarray is a contiguous non-empty sequence of elements within an array.
• The beauty of a subarray depends on the negative integers present in it.
• We can utilize a sliding window approach to efficiently find the x-th smallest negative integer in each subarray.
• A priority queue or a sorted list can help maintain the order of negative integers as we slide the window.

Space and Time Complexity

Time Complexity: O(n * log(k))
Space Complexity: O(k)

Solution

To solve this problem, we will utilize a sliding window approach to examine each subarray of size k. For each subarray, we will maintain a collection of negative integers in a sorted order. This can be efficiently done using a max-heap or a sorted list.

1. Initialize a data structure to store negative integers for the current window.
2. Iterate through the array, adding elements to the window and removing elements that fall out as the window slides.
3. For each subarray, check the count of negative integers:
   • If there are at least x negative integers, retrieve the x-th smallest negative integer.
   • If fewer than x negative integers exist, return 0 for that subarray.
4. Store the results and return them after processing all subarrays.

Code Solutions