Optimize partitioning for O(n) time
Last updated: November 16, 2025
Quick Overview
Given an array of integers, optimize the partitioning process to rearrange the elements such that all values less than a given pivot are on the left, and all values greater than the pivot are on the right, achieving this in O(n) time complexity. The input consists of the array and the pivot value, and the output should be the rearranged array.
Goldman Sachs
November 16, 2025157
11
4,305 solved
Given an array of integers, optimize the partitioning process to rearrange the elements such that all values less than a given pivot are on the left, and all values greater than the pivot are on the right, achieving this in O(n) time complexity. The input consists of the array and the pivot value, and the output should be the rearranged array.
This coding problem is frequently asked during Onsite at Goldman Sachs. The interviewer is testing your ability to translate a problem into clean, working code while discussing time and space complexity. Goldman Sachs expects candidates to write production-quality code, not just solve the puzzle.
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
- How would you modify your solution to handle streaming input?
- Can you solve this in a single pass?
- What is the worst-case input for your solution?
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Problem Analysis
The problem requires us to partition an array around a given pivot such that all elements less than the pivot appear on the left side and all elements greater than the pivot appear on the right side. ...
Approach
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Initialize Pointers: Start with two pointers,
leftat the beginning (index 0) andrightat the end (index len(array) - 1) of the array. -
Partitioning Process:
- Increment `left...
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