Google·Software Engineer·Technical Phone Screen·Intermediate

Intermediate

May 2026

Summary

Google SWE interview with a tree problem that sounds straightforward until you realize the data structure is weirder than a standard BST. One question, but it had some teeth to it.

Questions Asked (1)

You're given a ternary tree where each node can have up to three children: a left child with a smaller value, a middle child with an equal value, and a right child with a larger value. Find the mode (most frequently occurring value) across all nodes in the tree.

Algorithms & Data Structures

Author's notes

My first instinct was to just do a traversal and count frequencies in a hashmap, which works, but then I realized the middle child structure is literally storing duplicates for you in the tree itself.

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AI HintsAI Generated

Suggested Approach

Clarify the problem and constraints, then discuss multiple approaches: a simple traversal with a hash map, and an optimized in-order traversal that exploits the BST-like property to count duplicates in O(1) space. Analyze time and space complexity, and handle edge cases like empty tree or multiple modes.

Pro tip: Mention that the tree's structure allows an in-order traversal to visit equal values consecutively, enabling mode-finding without a hash map, which is a space-efficient solution Google interviewers appreciate.

1. Clarify requirements and constraints

Ask about tree size, value range, whether multiple modes are possible, and if the tree is guaranteed to be a valid ternary search tree. Confirm the definition of mode and how to handle ties.

2. Discuss brute-force approach

Propose traversing the tree (any order) while using a hash map to count frequencies, then finding the maximum. Analyze time O(n) and space O(n).

3. Optimize using in-order traversal

Explain that an in-order traversal (left, middle, right) visits nodes in non-decreasing order, so equal values are consecutive. Track current value, count, and max count to find mode in O(n) time and O(1) space (excluding recursion stack).

4. Handle edge cases and multiple modes

Consider empty tree, single node, all unique values, and multiple modes. Decide whether to return all modes or any one, and adjust the algorithm accordingly.

5. Analyze complexity and trade-offs

Compare the hash map and in-order approaches, highlighting space efficiency. Mention that recursion stack adds O(h) space, which can be O(n) in worst case, but can be mitigated with iterative traversal.

Key Points to Mention

In-order traversal of a ternary search tree yields sorted order, grouping equal values.
Hash map approach is simple but uses O(n) extra space; in-order approach uses O(1) space (excluding recursion).
Time complexity is O(n) for both approaches, as each node is visited once.
Edge cases: empty tree, single node, multiple modes, and skewed tree affecting recursion depth.
Iterative in-order traversal can achieve true O(1) space by using parent pointers or Morris-like traversal.
Clarify with interviewer whether to return all modes or just one, and how to handle ties.

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