Algorithms · Divide-and-conquer algorithms
Using only comparisons, return both minimum and maximum among n≥1 distinct keys
Problem
Using only comparisons, return both minimum and maximum among \(n\ge1\) distinct keys. 1. Give the pairwise algorithm for odd and even \(n\). 2. Prove exactly \(\lceil3n/2\rceil-2\) comparisons. 3. Prove a matching worst-case lower bound, including odd \(n\). 4. Trace \([9,2,7,1,6,3,8]\).
Hint
** One within-pair comparison assigns separate minimum and maximum candidates.
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