LinkedIn·AI Engineer·Technical Phone Screen·Senior

Senior

May 2026

Summary

LinkedIn AI Engineer interview that was basically one meaty coding problem about building a priority queue from the ground up. No library shortcuts allowed, which made it more interesting than I expected.

Questions Asked (1)

Implement a priority queue from scratch without using any built-in heap libraries. Your implementation should support push, pop (returning and removing the highest-priority element), and peek, with O(log n) and O(1) complexity respectively. Back it with an array-based binary heap and implement sift-up and sift-down. Also discuss min-heap vs max-heap and how you'd handle custom comparators.

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

The 'no built-in heap' constraint is what made this non-trivial.

Create a free account to read the full note

AI HintsAI Generated

Suggested Approach

Start by clarifying requirements and edge cases, then outline the array-based binary heap structure and the sift-up/sift-down algorithms. Implement push, pop, and peek with the required complexities, and discuss min-heap vs max-heap and custom comparators. Finally, analyze trade-offs and potential optimizations.

Pro tip: Mention that using a dynamic array (like Python's list) with amortized O(1) append and O(1) index access is ideal for the heap, and that you can avoid swaps by using hole-based sift operations for efficiency.

1. Clarify Requirements and Edge Cases

Ask about expected operations, data types, and whether the heap should be min or max by default. Discuss handling empty heap, duplicate priorities, and custom comparators.

2. Design the Heap Structure

Explain that the heap is an array where for index i, children are at 2i+1 and 2i+2, and parent at (i-1)//2. Mention that this structure ensures the heap property and enables O(log n) operations.

3. Implement Core Operations

Describe push: append to array, then sift-up. Pop: replace root with last element, remove last, then sift-down. Peek: return root. Highlight O(log n) for push/pop and O(1) for peek.

4. Discuss Min-Heap vs Max-Heap and Comparators

Explain that min-heap has smallest at root, max-heap largest. For custom comparators, either invert the comparator for min-heap or use a wrapper class. Mention that Python's heapq is min-heap, so for max-heap you can negate keys.

5. Analyze Trade-offs and Optimizations

Discuss time/space complexity, stability, and alternatives like d-ary heaps. Mention that array-based heap is cache-friendly and that sift operations can be optimized with hole technique.

Key Points to Mention

Array-based binary heap representation with index calculations
Sift-up (bubble-up) and sift-down (bubble-down) algorithms with O(log n) complexity
Push: append then sift-up; Pop: swap root with last, remove last, then sift-down; Peek: O(1) access to root
Min-heap vs max-heap: default and how to switch (e.g., negate keys or invert comparator)
Custom comparators: using a comparator function or wrapper class, and implications for heap property
Edge cases: empty heap, single element, duplicate priorities, and dynamic resizing

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