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This is a Medium difficulty Coding & Algorithms question, commonly asked during Onsite rounds at Other.

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This question is commonly asked for Data Scientist candidates at Other during technical interviews.

Prove reservoir sampling correctness

Last updated: Mar 29, 2026

Quick Overview

This question evaluates randomized and streaming algorithm skills, including mastery of reservoir sampling, induction-based correctness proofs, probability reasoning, and complexity analysis for sampling under strict memory constraints.

Other

Oct 13, 2025, 9:49 PM

Data Scientist

Onsite

Coding & Algorithms

Design an algorithm to sample k items uniformly at random from a stream of unknown and potentially massive length N, using O(k) memory and one pass. (a) Write the algorithm for k=1 and generalize to k>1. (b) Prove by induction that after processing i items, each seen item has probability k/i to be in the reservoir. (c) Discuss time and memory complexity, and outline how you would adapt it for weighted sampling.

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