Optimize partitioning for O(n) time
Last updated: February 10, 2026
Quick Overview
Given an array of integers, partition the array into two subsets such that all elements in the first subset are less than or equal to a specified pivot value, and all elements in the second subset are greater than the pivot. Implement the partitioning in O(n) time complexity, where n is the number of elements in the array, and return the indices that separate the two subsets.
Palo Alto Networks
February 10, 20269
13
2,634 solved
Given an array of integers, partition the array into two subsets such that all elements in the first subset are less than or equal to a specified pivot value, and all elements in the second subset are greater than the pivot. Implement the partitioning in O(n) time complexity, where n is the number of elements in the array, and return the indices that separate the two subsets.
Palo Alto Networks uses this problem in the Onsite 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
- 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
- How would you modify your solution to handle streaming input?
- What if the input doesn't fit in memory?
- Can you solve this iteratively instead of recursively (or vice versa)?
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Practice DSA ProblemsSample Answer
Problem Analysis
The problem requires partitioning an array into two subsets based on a pivot value. This suggests a two-pointer technique, which is efficient for sorting and partitioning tasks. By using two pointers,...
Approach
- Initialize two pointers:
leftat the start of the array andrightat the end. - While
leftis less than or equal toright:- If the element at the
leftpointer is less than or equal t...
- If the element at the
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