Sliding Subarray Beauty

Sliding Subarray Beauty

What is this problem about?

The "Sliding Subarray Beauty" interview question asks you to process an array using a fixed-size sliding window of length k. For each window, you need to find the x-th smallest integer, but only if that integer is negative. If the x-th smallest integer is non-negative, the "beauty" of that subarray is 0. The "Sliding Subarray Beauty coding problem" requires returning an array of these beauty values for every possible window.

Why is this asked in interviews?

Amazon uses this question to test a candidate's ability to optimize window-based calculations. Finding the x-th smallest element in a set is a "selection" problem. Doing this naively for every window would be O(N * K log K), which is too slow. The challenge is to maintain the window state efficiently. It also tests your knowledge of data ranges—often the values in such problems are small (e.g., -50 to 50), which hints at a specific optimization.

Algorithmic pattern used

This problem follows the "Sliding Window and Hash Table (Frequency Array) interview pattern". Because the range of possible integers is very small (often -50 to 50), you can use a frequency array of size 101 to store the counts of each number currently in the sliding window.

1. As the window moves, increment the count of the entering element and decrement the count of the exiting element.
2. To find the x-th smallest negative number, iterate through the frequency array from the index representing -50 up to the index for -1.
3. Keep a running sum of the frequencies. The first number that pushes the sum to x or higher is your x-th smallest element.

Example explanation

Array: [1, -1, -3, -2, 3], k=3, x=2

1. Window 1: [1, -1, -3]. Sorted: [-3, -1, 1]. 2nd smallest is -1. Beauty = -1.
2. Window 2: [-1, -3, -2]. Sorted: [-3, -2, -1]. 2nd smallest is -2. Beauty = -2.
3. Window 3: [-3, -2, 3]. Sorted: [-3, -2, 3]. 2nd smallest is -2. Beauty = -2. Final result: [-1, -2, -2]. If x was 3 for Window 3, the 3rd smallest is 3 (positive), so beauty would be 0.

Common mistakes candidates make

A frequent mistake is re-sorting the entire window at every step, which is highly inefficient. Another error is not correctly handling the frequency array indices (mapping negative numbers to positive indices). Some candidates also forget the condition that only negative numbers contribute to "beauty," returning positive values instead of 0.

Interview preparation tip

Always check the constraints on value ranges. If the numbers are small, a frequency array (Bucket Sort style) is often much faster than a heap or a balanced BST for finding order statistics. This "Sliding Subarray Beauty interview question" is a perfect example of when to use a frequency array to achieve O(N * range) time complexity.