 问一道算法分析题
c,d两问如何搞呢 我做到 nk*c1+nlg(n/k)*c2=nlgn*c2 c1*k=c2*lgk 就把n给消掉了 后面不知该怎么推了 k应当是一个与n相关的量吧 原题如下： Problems 2-1: Insertion sort on small arrays in merge sort Although merge sort runs in Θ(n lg n) worst-case time and insertion sort runs in Θ(n) worst-
case time, the constant factors in insertion sort make it faster for small n. Thus, it makes sense
to use insertion sort within merge sort when subproblems become sufficiently small. Consider
a modification to merge sort in which n/k sublists of length k are sorted using insertion sort
and then merged using the standard merging mechanism, where k is a value to be determined. a. Show that the n/k sublists, each of length k, can be sorted by insertion sort in Θ(nk)
worst-case time.
b. Show that the sublists can be merged in Θ(n lg (n/k) worst-case time.
c. Given that the modified algorithm runs in Θ(nk + n lg (n/k)) worst-case time, what is
the largest asymptotic (Θnotation) value of k as a function of n for which the modified
algorithm has the same asymptotic running time as standard merge sort?
d. How should k be chosen in practice?
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2006/6/26 20:57:00
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