Pinterest·Machine Learning Engineer·Technical Phone Screen·Senior

Senior

Apr 2026

Summary

Pinterest ML Engineer interview with a warehouse packing problem that looks straightforward until you actually try to code it under pressure. One question, greedy approach, and a lot of second-guessing myself in the moment.

Questions Asked (1)

You have an array of box heights and an array of warehouse room heights (left to right). Boxes can only enter from the left, and a box can only reach room j if its height is at most the minimum height of all rooms from 0 to j. Each box takes exactly one room. What is the maximum number of boxes you can fit?

Algorithms & Data Structures

Author's notes

My first instinct was to sort both arrays and just greedily match, but the constraint that boxes push through all prior rooms tripped me up.

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AI HintsAI Generated

Suggested Approach

First, compute the prefix minimum array of room heights to determine the maximum allowable box height for each room. Then, sort the box heights and greedily assign the smallest possible box to each room from left to right, counting how many boxes can be placed. This greedy strategy maximizes the number of boxes because it preserves larger boxes for later rooms that might have higher constraints.

Pro tip: Clarify that each room can hold at most one box and boxes cannot be reused; this ensures the greedy assignment is valid. Mention that the algorithm runs in O(n log n + m log m) time due to sorting, which is optimal for this problem.

1. Understand the constraints

Restate the problem: boxes enter from the left, each room can hold at most one box, and a box can only be placed in room j if its height ≤ the minimum height of rooms 0..j. The goal is to maximize the number of boxes placed.

2. Compute prefix minimums

Create an array where each element represents the minimum room height from the start up to that index. This gives the maximum allowable box height for each room.

3. Sort boxes and rooms

Sort the box heights in ascending order. The prefix minimum array is already non-increasing, but we can process rooms in order without sorting them separately.

4. Greedy assignment

Iterate through the rooms from left to right. For each room, assign the smallest box that fits (i.e., height ≤ prefix minimum at that room). If no box fits, skip the room. Count the number of assignments.

5. Analyze complexity and correctness

Explain that sorting takes O(m log m) and the greedy pass takes O(n + m), where n is number of rooms and m is number of boxes. Argue correctness by exchange argument: assigning the smallest possible box never reduces the ability to place boxes in later rooms.

Key Points to Mention

Prefix minimum array to capture cumulative height constraints.
Greedy strategy: assign smallest fitting box to each room.
Sorting boxes to efficiently find the smallest fitting box.
Time complexity: O(n + m log m) where n is number of rooms and m is number of boxes.
Space complexity: O(n) for prefix minimum array (or O(1) extra if computed on the fly).
Proof of optimality via exchange argument or induction.

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