Finding the median requires 2n comparisons

1. Overview. A long-standing problem in the analysis of algorithms is to determine the number of comparisons needed to find the t-th largest element in a totally ordered universe of size n. This number has been christened Vt(r) in the literature. By symmetry, we may always assume that 1 < [n/21. Of particuiar interest is the asymptotic behavior of V*(n) when n goes to infinity either with f bed or with 1 = an for a fixed constant a in the range 0 < a 5 l/2. The case 1 = [n/21, of course, gives the complexity of finding the median of n elements. The problem has an illustrious history. Knuth [lo] describes an investigation of Vz((n) made by Dodgson (Lewis Carroll) in 1883 that event.ually inspired its exact determination,