Binary Trees and Binary Search Trees Questions

Focuses on tree data structures, specifically binary trees and binary search trees. Candidates should understand node relationships, common traversals including in order, pre order, post order, and level order, and be able to implement traversals both recursively and iteratively. Cover binary search tree properties and operations including search, insertion, deletion, validation of binary search tree property, and finding the lowest common ancestor. Include problems on tree paths, height and balance calculations, serialization and deserialization, checking and restoring balance at a high level, and use cases in system design. Emphasize complexity analysis, recursion versus iterative solutions using stacks or queues, and handling edge cases such as duplicate keys and degenerate trees.

MediumTechnical

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During a rollout, a new binary-tree serialization format was deployed but older nodes cannot read it, causing partial failures and increasing error budget. As an SRE, describe step-by-step incident response to mitigate the outage, perform a safe rollback, and create a migration plan that supports both formats with minimal SLO impact. Include communication steps and rollback safety checks.

HardTechnical

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Design an on-disk representation for a very large BST (billions of nodes) that supports search and insert with minimal memory overhead. Compare using a simple BST versus using a B-tree or an LSM-tree for disk-backed storage. Discuss I/O patterns, caching, locality, compaction, and which structure an SRE would recommend for workloads with high read throughput and occasional writes.

HardTechnical

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Design preprocessing to answer many LCA queries quickly on a static tree using binary lifting (sparse table). Implement preprocessing in Python with O(n log n) time and O(n log n) memory and answer queries in O(log n). Then discuss how to adapt to dynamic trees where nodes are frequently inserted or deleted and what SRE trade-offs arise.

HardTechnical

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As an SRE you must choose between a BST-backed ordered index and a hash-based index for a new telemetry pipeline. Explain how you would evaluate trade-offs including latency, memory usage, support for range queries, write amplification, operational complexity, and recovery. Present a recommendation for a telemetry pipeline and describe how you would communicate that decision and measure success.

HardSystem Design

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Design a distributed indexing service that supports range queries and point lookups for millions of keys using tree-like data structures. Specify the API, data partitioning/sharding strategy (range vs hash), replication and failover behavior, consistency model, and where you would use self-balancing trees or B-trees within each shard. Discuss operational concerns for SRE like re-sharding, hot partitions, and backups.

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