算法导论习题-1.2-2

题目

Suppose we are comparing implementations of insertion sort and merge sort on the same machine. For inputs of size n, insertion sort runs in 8n2 steps, while merge sort runs in 64nlgn steps. For which values of n does insertion sort beat merge sort?

解答

求解不等式: 8n2≤64nlgn，得n≤43.

注：可使用Excel来计算lgn，在单元格里输入公式即可。除此之外，Excel还是直观观察答案的好帮手。以求解上面的不等式为例，原始不等式化简后得: f(n)=n−8lgn≤0，可在Excel里将函数f(n)绘出，如下图所示：