Optimize inversion for O(n) time
Last updated: April 9, 2026
Quick Overview
Given an array of integers, write a function to count the number of inversions in the array, where an inversion is defined as a pair of indices (i, j) such that i < j and arr[i] > arr[j]. Your solution should run in O(n) time and output the total count of inversions.
Apple
April 9, 2026503
4
2,456 solved
Given an array of integers, write a function to count the number of inversions in the array, where an inversion is defined as a pair of indices (i, j) such that i < j and arr[i] > arr[j]. Your solution should run in O(n) time and output the total count of inversions.
This coding problem is frequently asked during Technical Screen at Apple. The interviewer is testing your ability to translate a problem into clean, working code while discussing time and space complexity. Apple expects candidates to write production-quality code, not just solve the puzzle.
What the Interviewer Expects
- Identify the correct data structure and algorithm for the problem
- Write clean, bug-free code with proper variable naming
- Analyze time and space complexity correctly
- Handle basic edge cases (empty input, single element)
- Communicate your thought process while coding
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
- What happens if the input contains duplicates?
- How would you parallelize this solution?
- Can you solve this iteratively instead of recursively (or vice versa)?
- Can you solve this in a single pass?
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Practice DSA ProblemsSample Answer
Problem Analysis
To solve the problem of counting inversions in an array efficiently, we need to analyze the properties of inversions. An inversion is defined for a pair of indices (i, j) such that i < j and arr[i] > ...
Approach
Given the constraints of the problem, we will use a modified merge sort approach which allows for counting inversions in O(n log n) time. The algorithm works by recursively dividing the array into hal...
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