Largest Rectangle in a Histogram
Last updated: September 2, 2026
Quick Overview
The question asks the candidate to find the largest rectangle that can be formed in a histogram, represented by an array of integers where each integer represents the height of the bars.
Airwallex
September 2, 20261
0
13 solved
The question asks the candidate to find the largest rectangle that can be formed in a histogram, represented by an array of integers where each integer represents the height of the bars.
This question is commonly asked in technical screens for software engineering roles, particularly to assess a candidate's problem-solving and algorithmic skills. The interviewer is evaluating the candidate's ability to understand and implement an efficient algorithm, as well as their proficiency in coding and debugging under time constraints.
What the Interviewer Expects
- Explain the problem clearly and identify edge cases.
- Outline a clear approach to solving the problem, ideally using a stack-based method.
- Provide a working implementation in Python with proper handling of edge cases.
- Discuss the time and space complexity of the solution.
- Be prepared to optimize the solution if time permits.
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 explain how you would handle very large input sizes?
- What would you change in your approach if the histogram was dynamic and updated frequently?
- How would you modify your solution to find the largest rectangle in a binary matrix instead?
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Practice DSA ProblemsSample Answer
Approach
To find the largest rectangle in a histogram, we can use a stack-based approach. The idea is to maintain a stack to keep track of the indices of the histogram bars. As we iterate through the heights, ...
Algorithm
- Initialize a stack to keep track of indices and a variable to store the maximum area.
- Iterate through each bar in the histogram:
- While the current bar is less than the bar at the index stor...
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