Optimize inversion for streaming input
Last updated: October 29, 2025
Quick Overview
Given a stream of integers, implement a function that efficiently counts the number of inversions in the input as it arrives. An inversion is defined as a pair of indices (i, j) such that i < j and arr[i] > arr[j]. The function should output the total count of inversions after processing each new integer in the stream.
Redfin
October 29, 20251
14
4,112 solved
Given a stream of integers, implement a function that efficiently counts the number of inversions in the input as it arrives. An inversion is defined as a pair of indices (i, j) such that i < j and arr[i] > arr[j]. The function should output the total count of inversions after processing each new integer in the stream.
Redfin uses this problem in the Technical Screen to evaluate your algorithmic thinking. They expect you to discuss multiple approaches, analyze trade-offs between them, and implement the optimal solution with clean, readable code.
What the Interviewer Expects
- Recognize the underlying problem pattern (sliding window, two pointers, BFS/DFS, etc.)
- Discuss multiple approaches and trade-offs before coding
- Implement an optimal solution with clean, production-quality code
- Handle all edge cases including boundary conditions and invalid input
- Optimize both time and space complexity with clear justification
- Test your solution systematically with well-chosen examples
Key Topics to Cover
How to Approach This
- Clarify input constraints and edge cases before writing code.
- Walk through your approach verbally and confirm with the interviewer before coding.
- Start with a brute force solution, then optimize. Mention time and space complexity.
- Test your solution with examples, including edge cases like empty input or duplicates.
- Consider common patterns: sliding window, two pointers, hash map, BFS/DFS, dynamic programming.
Possible Follow-up Questions
- Can you solve this in a single pass?
- Can you solve this iteratively instead of recursively (or vice versa)?
- What happens if the input contains duplicates?
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Problem Analysis
The problem requires us to count the number of inversions in a stream of integers. An inversion is defined as a pair of indices (i, j) such that i < j and arr[i] > arr[j]. The key pattern here is the ...
Approach
- Data Structure: Use a balanced binary search tree (BST) or a Fenwick Tree (Binary Indexed Tree) to keep track of the elements seen so far. This allows us to efficiently count how many elements ...
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