Palo·Software Engineer·Technical Phone Screen·Intermediate

Intermediate

Jul 2026

Summary

Interviewed for a software engineer role at Palo and got a classic histogram problem. Nothing too surprising but the constraints were large enough that a naive O(n^2) solution would've timed out, so they clearly wanted the stack-based approach.

Questions Asked (1)

Given an array of non-negative integers representing bar heights in a histogram (each bar has width 1), find the largest rectangular area you can form using one or more consecutive bars. The rectangle's height is limited by the shortest bar in the chosen range.

Algorithms & Data Structures

Author's notes

I knew this problem but still fumbled the stack logic under pressure.

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AI HintsAI Generated

Suggested Approach

Start by clarifying the problem and edge cases, then propose a brute-force solution to establish a baseline. Explain the optimal monotonic stack approach that computes the largest rectangle in O(n) time, and walk through a small example to demonstrate correctness.

Pro tip: Mention that the monotonic stack approach can be implemented in a single pass by maintaining a stack of indices with increasing heights, and that adding a sentinel bar of height 0 at the end simplifies the code by ensuring all bars are popped.

1. Clarify and Confirm

Restate the problem in your own words and ask clarifying questions about input constraints, expected output, and edge cases (e.g., empty array, all zeros).

2. Discuss Brute Force

Outline a naive O(n^2) solution: for each bar, expand left and right to find the maximum width where it is the minimum height, and compute the area.

3. Introduce Optimal Approach

Explain the monotonic stack technique: maintain a stack of indices with increasing heights, and when a lower bar is encountered, pop and calculate areas to find the maximum.

4. Walk Through Example

Trace the algorithm on a small example (e.g., heights = [2,1,5,6,2,3]) to show how the stack evolves and how the maximum area is computed.

5. Analyze Complexity and Edge Cases

State that the optimal solution runs in O(n) time and O(n) space, and discuss handling edge cases like empty input or single bar.

Key Points to Mention

Monotonic stack maintains indices of bars in increasing order of height.
When a shorter bar is encountered, pop from stack and compute area using the popped bar's height and the width determined by the current index and the new stack top.
Adding a sentinel bar of height 0 at the end ensures all bars are processed.
Time complexity: O(n) because each bar is pushed and popped at most once.
Space complexity: O(n) for the stack.
Edge cases: empty array returns 0; all bars same height; strictly increasing/decreasing heights.

AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.