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

Senior

May 2026

Summary

Google SWE coding round with a range-assignment array problem. The efficiency angle was the real point of the question, not just getting a working solution.

Questions Asked (1)

You're given an integer array and a list of range-assignment queries, each specifying a start index, end index, and value to assign across that range. Queries are applied in order, so later ones overwrite earlier ones on overlapping positions. Return the final array. The naive O(n * q) solution is too slow. What's a more efficient approach?

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

My first instinct was just to simulate it, which is obviously wrong at scale.

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AI HintsAI Generated

Suggested Approach

First clarify the problem constraints and confirm that queries are applied in order with later ones overwriting earlier ones. Then propose an efficient solution such as processing queries in reverse order using a disjoint-set union (DSU) to skip already assigned positions, achieving near O(n + q) time. Explain the algorithm, analyze its complexity, and discuss trade-offs compared to other approaches like segment trees with lazy propagation.

Pro tip: Mention that processing queries in reverse ensures each position is assigned exactly once, and use a DSU to efficiently find the next unassigned index. This demonstrates strong algorithmic insight and practical optimization.

1. Understand the problem and constraints

Restate the problem to ensure clarity: given an array and range-assignment queries applied in order, return the final array. Ask about input sizes to determine the required efficiency.

2. Identify the inefficiency of the naive approach

Explain that the naive O(n * q) solution is too slow for large inputs, and that we need a method that avoids redundant assignments.

3. Propose an efficient algorithm

Describe processing queries in reverse order and using a disjoint-set union (DSU) to track unassigned positions, skipping already assigned indices. This ensures each position is written at most once.

4. Analyze complexity and correctness

Show that the time complexity is nearly O(n + q) with DSU path compression, and argue correctness: later queries overwrite earlier ones, so processing in reverse assigns the final value first.

5. Discuss alternatives and trade-offs

Mention other possible approaches like segment trees with lazy propagation (O(q log n)) or difference arrays (not directly applicable due to overwrites), and compare their trade-offs in terms of implementation complexity and performance.

Key Points to Mention

Reverse processing of queries ensures that the last assignment to a position is applied first, avoiding overwrites.
Disjoint-set union (DSU) with path compression efficiently finds the next unassigned index, skipping already filled positions.
Time complexity: O((n + q) α(n)) where α is the inverse Ackermann function, effectively linear.
Space complexity: O(n) for the array and DSU parent pointers.
Correctness: each position is assigned exactly once, with the value from the latest query that covers it.
Alternative approaches: segment tree with lazy propagation (O(q log n)) or interval merging, but DSU is simpler and faster for this specific problem.

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