Optimize inversion for without recursion
Last updated: January 22, 2026
Quick Overview
Given an array of integers, optimize the process of counting the number of inversions in the array without using recursion. An inversion is defined as a pair of indices (i, j) such that i < j and array[i] > array[j]. Your solution should return the total count of such inversions in O(n log n) time complexity.
Waymo
January 22, 202643
14
1,398 solved
Given an array of integers, optimize the process of counting the number of inversions in the array without using recursion. An inversion is defined as a pair of indices (i, j) such that i < j and array[i] > array[j]. Your solution should return the total count of such inversions in O(n log n) time complexity.
This coding problem is frequently asked during Onsite at Waymo. The interviewer is testing your ability to translate a problem into clean, working code while discussing time and space complexity. Waymo 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
- Can you solve this iteratively instead of recursively (or vice versa)?
- What if the input doesn't fit in memory?
- Can you optimize the space complexity of your solution?
- How would your solution change if the input was sorted?
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Problem Analysis
To solve the problem of counting inversions in an array efficiently, we can utilize the Merge Sort algorithm, which employs a divide-and-conquer strategy. This approach is suitable here becaus...
Approach
- Divide: Split the array into two halves until each half contains a single element.
- Conquer: While merging two sorted halves, for each element in the left half, count how many elements i...
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