Google·Software Engineer·Technical Phone Screen·Intermediate

IntermediatePrefer not to say

Apr 2026

Summary

Google SWE interview with a data structure design question that seems deceptively simple until you think about the efficiency constraint on findLargest.

Questions Asked (1)

Design a class with two operations: insert(num) to add a number, and findLargest(k) to return the (k+1)-th largest value using 0-based indexing. For example, after inserting 3, 3, and 2, findLargest(0) should return 3, findLargest(1) should return 3, and findLargest(2) should return 2. The findLargest operation should be as efficient as possible.

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

My first instinct was a sorted list and just index from the end.

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AI HintsAI Generated

Suggested Approach

Clarify the requirements and constraints, then propose a data structure that supports efficient insert and findLargest operations. Discuss trade-offs between different approaches, such as a balanced BST with subtree sizes versus a Fenwick tree over compressed values, and analyze time and space complexity.

Pro tip: Mention that duplicates must be handled correctly and that the (k+1)-th largest with 0-based indexing is equivalent to the k-th order statistic from the largest. Also, consider edge cases like k out of bounds and dynamic value ranges.

1. Clarify Requirements

Confirm that insert can be called multiple times with the same value, findLargest(k) returns the (k+1)-th largest (0-based), and discuss expected frequency of operations and value range.

2. Choose Data Structure

Select a data structure that maintains order statistics efficiently, such as a balanced BST (e.g., Red-Black Tree) with subtree sizes or a Fenwick tree over compressed values.

3. Design Operations

Detail how insert updates the structure and how findLargest(k) traverses or queries to find the k-th largest element, handling duplicates appropriately.

4. Analyze Complexity

State the time complexity for each operation (e.g., O(log n) for both) and space complexity, comparing with alternatives like sorting on demand.

5. Handle Edge Cases

Discuss handling of k out of bounds, empty structure, and potential need for dynamic resizing or coordinate compression.

Key Points to Mention

Order statistic tree (balanced BST with subtree sizes) for O(log n) insert and findLargest.
Fenwick tree (Binary Indexed Tree) with coordinate compression for efficient order statistics.
Handling duplicates: counts in nodes or multiple entries.
Time complexity: O(log n) per operation, space O(n).
Trade-offs: simplicity vs. performance, static vs. dynamic value range.
Edge cases: k >= total elements, empty structure, negative numbers.

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