Google·Software Engineer·Onsite - Coding / Algorithms·Intermediate

Intermediate

Jul 2026

Summary

Google SWE coding round with a tree construction problem. The question was more involved than it looked at first glance, lots of edge cases hiding in the tie-breaking rules.

Questions Asked (1)

Given a list of symbols and their frequencies, build a Huffman tree and output a valid prefix-free binary code for each symbol. Tie-breaking must be deterministic: always merge the two lowest-frequency nodes first, and if frequencies are equal, use lexicographic order of the node's minimum symbol to decide which becomes the left child (edge 0). If there's only one symbol, output code 0.

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

I spent the first few minutes just staring at the tie-breaking rules.

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AI HintsAI Generated

Suggested Approach

Start by clarifying the deterministic tie-breaking rules and edge cases, then outline the Huffman algorithm using a min-heap with a custom comparator. Walk through a small example to demonstrate correctness, and finally discuss the code assignment and complexity.

Pro tip: Emphasize that deterministic tie-breaking ensures reproducible codes, which is crucial for testing and debugging in production systems. Mention that using a stable priority queue or sorting symbols initially can simplify implementation.

1. Clarify requirements and edge cases

Confirm the tie-breaking rules: merge two lowest-frequency nodes, and for equal frequencies, use lexicographic order of the minimum symbol in each node. Handle the single-symbol case by outputting '0'.

2. Design data structures

Use a min-heap (priority queue) where each node stores frequency, minimum symbol, and left/right children. The comparator should order by frequency, then by minimum symbol lexicographically.

3. Build the Huffman tree

Insert all symbol nodes into the heap. Repeatedly extract the two smallest nodes, create a new internal node with their combined frequency and minimum symbol (the smaller of the two), and insert it back. Continue until one node remains.

4. Generate prefix-free codes

Traverse the tree from root to leaves, assigning '0' for left edges and '1' for right edges. For a single symbol, assign '0'. Collect codes for each symbol.

5. Analyze complexity and trade-offs

Discuss time complexity O(n log n) due to heap operations, and space O(n). Mention that deterministic tie-breaking may affect code lengths but not optimality.

Key Points to Mention

Huffman coding produces optimal prefix-free codes for given frequencies.
Deterministic tie-breaking ensures consistent output, important for reproducibility.
Using a min-heap with a custom comparator efficiently selects the two smallest nodes.
The algorithm handles edge cases like a single symbol and empty input.
Time complexity is O(n log n) and space complexity is O(n).
Prefix-free property guarantees unambiguous decoding.

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