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TL;DR

Information-Theoretic Sorting Lower Bound: A canonical quantitative trading interview question at intermediate difficulty. Commonly asked at Jane Street, Citadel, Two Sigma.

By Valenke Exam Prep Team·Last updated 2026-06-01
intermediateComplexity & Lower Bounds

Information-Theoretic Sorting Lower Bound

Asked at: Jane Street, Citadel, Two Sigma

Problem
Prove that any comparison-based sorting algorithm must perform at least log2(n!)\lceil \log_2(n!) \rceil comparisons in the worst case to sort nn distinct elements. Use this to establish the Ω(nlogn)\Omega(n \log n) lower bound.

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