Lecture 08 Ticket

Complete before the beginning of class on Monday, 09/19.

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\[\def\compare{ {\mathrm{compare}} } \def\swap{ {\mathrm{swap}} } \def\sort{ {\mathrm{sort}} } \def\true{ {\mathrm{true}} } \def\false{ {\mathrm{false}} } \def\split{ {\mathrm{split}} } \def\val{ {\mathrm{val}} }\]

Give an argument that every (correct) sorting algorithm requires \(\Omega(n)\) elementary operations (e.g., \(\compare\) and \(\swap\)) to sort arrays of size \(n\). Your argument doesn’t need to be mathematically formal–an intuitive explanation is sufficient.

Hint. What can you say about an algorithm that uses \(\ll n\) operations on an array of size \(n\)?