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Google·Software Engineer·Technical Phone Screen·Intermediate

IntermediatePrefer not to say
Apr 2026

Summary

Google SWE interview with a tree problem that had more layers to it than I expected. The core question wasn't too bad but the follow-up about broken tree conditions is where things got interesting.

Questions Asked (1)

Q1

Given a trinary tree where the left child is less than the root, the middle child equals the root, and the right child is greater than the root, write a function to find the mode (most frequently occurring value). Also handle edge cases like an empty tree or a tree with no duplicates, and handle the case where the tree violates its own structural rules.

Algorithms & Data StructuresTechnical Trade-offs
Author's notes

The mode part clicked pretty fast.

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AI HintsAI Generated

Suggested Approach

Clarify the problem and edge cases first, then propose an in-order traversal that tracks the current value and its count, updating the mode when a higher count is found. Discuss how to detect and handle structural violations, and analyze time and space complexity.

Pro tip: Mention that the trinary tree's structure allows in-order traversal to visit equal values consecutively, enabling O(1) extra space for mode tracking beyond recursion. Also, proactively discuss how to detect violations by checking the BST property during traversal.

1. Clarify Requirements and Edge Cases

Ask clarifying questions about the tree structure, what constitutes a violation, and expected behavior for edge cases like empty tree or no duplicates. Confirm that the mode is the value with the highest frequency, and if multiple, any or all?

2. Choose Traversal Strategy

Explain that an in-order traversal (left, middle, right) visits nodes in non-decreasing order, so equal values are consecutive. This allows tracking the current value's frequency and updating the mode efficiently.

3. Design Algorithm with State Tracking

Maintain variables for current value, current count, max count, and mode value(s). During traversal, compare node value with previous; if equal, increment count; else reset count to 1. Update mode when count exceeds max count.

4. Handle Structural Violations

During traversal, verify that left child < root, middle child == root, right child > root. If violated, either throw an error, log a warning, or attempt to correct? Discuss trade-offs and choose a reasonable approach.

5. Analyze Complexity and Test

State time complexity O(n) and space complexity O(h) for recursion stack. Walk through examples including empty tree, single node, no duplicates, and a tree with violations to ensure correctness.

Key Points to Mention

  • In-order traversal of trinary tree yields sorted order, enabling consecutive duplicate detection.
  • Edge cases: empty tree returns null or throws exception; no duplicates returns any node value (all frequency 1).
  • Structural violation handling: detect during traversal by comparing child values with parent; decide on error handling strategy.
  • Time complexity O(n) and space complexity O(h) for recursive solution; iterative with explicit stack also possible.
  • Mode definition: if multiple values have same max frequency, return any or all; clarify with interviewer.
  • Trade-offs: recursive vs iterative, handling violations by throwing exception vs attempting to fix tree.

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