Start by implementing a function that calculates the x-sum for any given subarray. Then iterate through nums using a sliding window of length k, applying the x-sum function at each step. Collect results in an output array to return the final sequence efficiently, avoiding redundant computations through hash-based counting of elements.
Problem Statement
You are given an integer array nums and two integers k and x. The task is to compute the x-sum for every contiguous subarray of length k. The x-sum of a subarray is the sum of its x largest distinct elements, or the sum of all elements if there are fewer than x distinct values.
Return an array of integers where each element corresponds to the x-sum of the subarray of nums starting at that index. Ensure that your solution accounts for repeated values and efficiently handles the scanning of overlapping subarrays using hash-based counting.
Examples
Example 1
Input: nums = [1,1,2,2,3,4,2,3], k = 6, x = 2
Output: [6,10,12]
Example 2
Input: nums = [3,8,7,8,7,5], k = 2, x = 2
Output: [11,15,15,15,12]
Since k == x , answer[i] is equal to the sum of the subarray nums[i..i + k - 1] .
Constraints
- 1 <= n == nums.length <= 50
- 1 <= nums[i] <= 50
- 1 <= x <= k <= nums.length
Solution Approach
Sliding Window with Hash Map
Use a sliding window of size k and maintain a hash map to count occurrences of elements within the window. Update the map incrementally as the window moves, which allows computing the x-sum without rescanning the entire subarray each time.
Sorting Distinct Elements in Window
For each window, extract the distinct elements from the hash map, sort them in descending order, and sum the top x elements. This approach ensures the x-sum is correctly calculated according to the definition and handles arrays with fewer than x distinct elements.
Optimization with Heap
Optionally, use a max heap to track the largest x distinct elements in the window dynamically. This avoids sorting every time and speeds up x-sum computation for larger arrays or repeated values, while still leveraging hash-based counts to handle duplicates.
Complexity Analysis
| Metric | Value |
|---|---|
| Time | Depends on the final approach |
| Space | Depends on the final approach |
Time complexity is O(n * x log x) if sorting distinct elements per window or O(n log x) with a heap optimization. Space complexity is O(k) for the hash map storing window counts.
What Interviewers Usually Probe
- Notice how the window shifts and affects element counts.
- Expect candidates to handle duplicate values correctly in x-sum computation.
- Look for incremental updates instead of recomputing sums from scratch each time.
Common Pitfalls or Variants
Common pitfalls
- Failing to account for subarrays with fewer than x distinct elements.
- Resorting the entire window each time instead of using incremental counts.
- Overcounting elements when duplicates exist within the sliding window.
Follow-up variants
- Compute x-sum for all subarrays of variable length instead of fixed k.
- Return the y-sum of subarrays based on the smallest distinct elements rather than the largest.
- Handle streaming input where the array is not fully available upfront, maintaining a rolling x-sum.
How GhostInterview Helps
- Provides step-by-step guidance for implementing x-sum calculation correctly for each k-length subarray.
- Highlights incremental hash map updates to avoid recomputation in sliding windows.
- Offers tips for handling edge cases like fewer than x distinct elements or duplicate values efficiently.
Topic Pages
Related GhostInterview Pages
- LeetCode Interview Copilot - Use GhostInterview as a live solver when you want direct help with LeetCode-style coding questions.
- Coding Interview Assistant - See how GhostInterview supports array, string, linked list, graph, and tree interview workflows.
- How GhostInterview Works - Review the screenshot, reasoning, and answer flow before using the solver in a live interview.
FAQ
What is the x-sum in Find X-Sum of All K-Long Subarrays I?
The x-sum is the sum of the x largest distinct elements in a subarray, or the sum of all elements if there are fewer than x distinct values.
Can I use a heap to optimize the x-sum calculation?
Yes, a max heap can maintain the largest x distinct elements dynamically, reducing the need to sort each window.
How do I handle duplicates when computing x-sum?
Use a hash map to count occurrences of elements within the window and only consider distinct elements when calculating the sum.
What should I do if the subarray has fewer than x distinct elements?
Simply sum all elements in that subarray as the x-sum definition defaults to the total in that case.
Does this problem rely on sliding window or hash lookup pattern?
Yes, the problem pattern focuses on array scanning combined with hash lookup to efficiently calculate x-sums for overlapping subarrays.
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Calculate the x-sum for every k-length subarray using efficient array scanning and hash-based counting techniques.
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