[PTA] ADS-2016 Assignment 6 2-4

        Which one of the following is the lowest upper bound of $T(n)$ for the following recursion T(n)=2T(√​n​​​)+logn?(4分)

       

        设 m = logn, 则2^m = n.

        T(2^m) = 2T(2^(m/2))) + m

        设 G(m) = T(2^m)，则原式转化为G(m) = 2G(m/2) + m

        根据主定理，a = 2, b = 2, k = 1, p = 0. a = b^k，满足条件2，所以算法复杂度为O（mlogm）

        又因为 m = logn,所以算法复杂度为O（logn loglogn )

附：主定理