Optimize inversion for O(n) time
Last updated: July 23, 2025
Quick Overview
Given an array of integers, implement a function to count the number of inversions in the array in O(n) time, where an inversion is defined as a pair of indices (i, j) such that i < j and arr[i] > arr[j]. Your function should return the count of these inversions as an integer.
Workday
July 23, 20255
10
1,340 solved
Given an array of integers, implement a function to count the number of inversions in the array in O(n) time, where an inversion is defined as a pair of indices (i, j) such that i < j and arr[i] > arr[j]. Your function should return the count of these inversions as an integer.
Coding interviews at Workday focus on problem-solving approach as much as the final solution. The interviewer wants to see you break down the problem, consider edge cases, and optimize iteratively. Communication throughout the process is key.
What the Interviewer Expects
- Quickly identify the optimal approach and its theoretical basis
- Handle complex algorithm design with multiple interacting components
- Write concise, elegant code under time pressure
- Prove correctness of your approach and discuss alternative solutions
- Optimize beyond the obvious: discuss constant factor improvements
- Address follow-up variations and explain how the solution generalizes
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 is the worst-case input for your solution?
- Can you optimize the space complexity of your solution?
- How would you test this solution thoroughly?
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Problem Analysis
To solve the problem of counting inversions in an array efficiently, we can leverage the concept of Merge Sort. The key here is that while merging two sorted halves of the array, we can count how ...
Approach
- Divide: Recursively split the array into two halves until each sub-array has one element.
- Conquer: While merging two halves, count the inversions.
- For any element
arr[i]in the le...
- For any element
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