算法导论 Exercise 4.2-2

The shortest path from the root to a leaf in the recursion tree is n → (1/3)n →
(1/3)2n → · · · → 1. Since (1/3)kn = 1 when k = log3 n, the height of the
part of the tree in which every node has two children is log3 n. Since the values at
each of these levels of the tree add up to n, the solution to the recurrence is at least
n log3 n = (n lg n).

O(lgn)标志一种对数级的增长速率，lgn的底数未必是2。