Start by quickly sliding a window of size k across the array while maintaining a hash map of element counts. For each window, determine the sum of the smallest x distinct numbers or the full sum if fewer than x distinct elements exist. This approach balances speed and accuracy using the array scanning plus hash lookup pattern.
Problem Statement
Given an integer array nums and integers k and x, compute a list where each element represents the x-sum of a k-length subarray of nums. The x-sum is defined as the sum of the smallest x distinct elements in the subarray, or the sum of all elements if there are fewer than x distinct elements.
Return an array of length n - k + 1 containing the x-sums for all contiguous subarrays of length k. Implement a solution that efficiently handles large n up to 105 and uses the sliding window plus hash lookup pattern to avoid recalculating sums unnecessarily.
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
- nums.length == n
- 1 <= n <= 105
- 1 <= nums[i] <= 109
- 1 <= x <= k <= nums.length
Solution Approach
Sliding Window Initialization
Initialize a window of size k and build a hash map counting occurrences of each element. Sort the keys to quickly access the smallest x distinct elements and compute the initial x-sum.
Window Sliding and Hash Update
Slide the window one element at a time. Decrease the count of the outgoing element and remove it if count reaches zero. Add the incoming element to the hash map and update its count. Recalculate x-sum using the updated hash map.
Optimize Sum Calculation
Instead of fully sorting each window, maintain a min-heap or ordered structure for distinct elements to efficiently extract the smallest x values. This reduces repeated sorting overhead and maintains the array scanning plus hash lookup pattern.
Complexity Analysis
| Metric | Value |
|---|---|
| Time | Depends on the final approach |
| Space | Depends on the final approach |
Time complexity depends on maintaining the hash map and min-heap or ordered structure, roughly O(n log x) for all n-k+1 windows. Space complexity is O(k) for the hash map and auxiliary data structures.
What Interviewers Usually Probe
- Expect clarification on handling fewer than x distinct elements in a window.
- Check if candidate uses sliding window properly instead of recalculating sums naively.
- Look for correct use of hash map or counting structure to track element frequencies.
Common Pitfalls or Variants
Common pitfalls
- Recomputing sums from scratch for each window instead of updating incrementally.
- Failing to handle windows with fewer than x distinct elements correctly.
- Neglecting edge cases when elements repeat and the smallest x distinct elements change.
Follow-up variants
- Compute the largest x distinct elements instead of the smallest for each k-length subarray.
- Return the average of the x smallest distinct elements for each window instead of the sum.
- Use a circular array where windows wrap around the end of the array.
How GhostInterview Helps
- Identifies sliding window opportunities and maintains element counts automatically for x-sum calculation.
- Highlights potential pitfalls like handling fewer than x distinct elements or repeated values.
- Provides optimized array scanning and hash lookup techniques to reduce time complexity without manual trial-and-error.
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 II?
The x-sum is the sum of the smallest x distinct elements in a k-length subarray, or the sum of all elements if there are fewer than x distinct elements.
Can I use a naive approach to solve this problem?
Naive recomputation for each subarray is too slow for large arrays; a sliding window plus hash lookup is required for efficiency.
How do I handle repeated elements in the subarray?
Track counts in a hash map and only consider distinct elements when calculating the x-sum, updating counts as the window slides.
Is sorting required for every window?
Full sorting is unnecessary; maintaining a min-heap or ordered structure for distinct elements suffices for efficient smallest x element retrieval.
What pattern does this problem exemplify?
It exemplifies array scanning plus hash lookup, combining sliding window techniques with frequency tracking for optimal performance.
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Compute the x-sum of every subarray of length k efficiently using array scanning combined with hash lookup techniques.
Open problem page#3505 Minimum Operations to Make Elements Within K Subarrays EqualCompute the minimum operations to ensure at least k non-overlapping subarrays of size x have all equal elements efficiently using hash scanning.
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Open problem page