This problem requires scanning the array while keeping track of marked indices using a hash lookup. Each query updates markings and affects subsequent unmarked sums. A careful combination of array scanning, hash table management, and sorting ensures all queries are processed efficiently without double counting.
Problem Statement
You are given a 0-indexed array nums of positive integers and a 2D array queries where each query specifies an index and a count ki. Initially, all elements are unmarked. For each query, you mark the element at the given index and the ki smallest unmarked elements, then compute the sum of remaining unmarked elements after marking.
Return an array where each element corresponds to the sum of unmarked elements after performing the respective query. The challenge is efficiently tracking which elements are already marked and avoiding repeated scanning of the entire array for each query.
Examples
Example 1
Input: nums = [1,2,2,1,2,3,1], queries = [[1,2],[3,3],[4,2]]
Output: [8,3,0]
We do the following queries on the array:
Example 2
Input: nums = [1,4,2,3], queries = [[0,1]]
Output: [7]
We do one query which is mark the element at index 0 and mark the smallest element among unmarked elements. The marked elements will be nums = [ 1 ,4, 2 ,3] , and the sum of unmarked elements is 4 + 3 = 7 .
Constraints
- n == nums.length
- m == queries.length
- 1 <= m <= n <= 105
- 1 <= nums[i] <= 105
- queries[i].length == 2
- 0 <= indexi, ki <= n - 1
Solution Approach
Use a Hash Table to Track Marked Indices
Create a boolean or hash table array the same length as nums to record which indices are marked. This prevents double-counting when processing queries and allows constant-time checks during each query operation.
Process Queries with Sorted Access
Sort a copy of nums along with their original indices. For each query, select the ki smallest unmarked elements quickly using the sorted array while updating the hash table, reducing repeated scanning overhead.
Compute Unmarked Sums Efficiently
Maintain a running total of unmarked elements or update the sum incrementally after marking. This avoids recomputing the sum of the entire array after each query and ties directly to the failure mode of naive repeated summation.
Complexity Analysis
| Metric | Value |
|---|---|
| Time | Depends on the final approach |
| Space | Depends on the final approach |
Time complexity depends on sorting nums once (O(n log n)) and processing m queries with O(1) hash checks per element. Space complexity is O(n) for the hash table tracking marked elements.
What Interviewers Usually Probe
- They may ask how you avoid double-counting marked elements across queries.
- They may hint at using additional data structures like hash tables to track marks.
- They may suggest considering sorting to quickly find the ki smallest unmarked elements.
Common Pitfalls or Variants
Common pitfalls
- Recomputing the sum of unmarked elements from scratch after every query.
- Marking elements without checking if they are already marked, causing errors.
- Ignoring the optimal combination of array scanning and hash lookup, leading to TLE.
Follow-up variants
- Instead of marking the smallest ki elements, mark the largest ki elements and compute sums.
- Allow queries that mark ranges instead of single indices, requiring interval tracking.
- Modify nums dynamically between queries, needing a flexible update strategy.
How GhostInterview Helps
- GhostInterview identifies the correct array scanning plus hash lookup pattern for this problem and warns of double-counting pitfalls.
- It suggests an incremental sum strategy to avoid repeated full-array computations after each query.
- It flags inefficient naive approaches and guides toward using sorting combined with hash tables to maintain performance.
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 main pattern used in Mark Elements on Array by Performing Queries?
The key pattern is array scanning combined with hash table lookup to track marked elements efficiently.
Can I avoid sorting to solve this problem?
Sorting is optional but helps quickly identify the ki smallest unmarked elements; skipping it may require more complex selection logic.
How do I track which elements are already marked?
Use a boolean array or hash table indexed by element positions to record which elements are marked to prevent double-counting.
What is the time complexity for processing all queries?
Sorting costs O(n log n) once, then each query uses O(ki) hash lookups; overall complexity depends on the sum of all ki across queries.
Why does naive repeated sum computation fail?
Recomputing the sum of unmarked elements from scratch after each query results in O(n * m) time, which exceeds limits for large arrays.
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