根据增长率排列渐近函数

Question

Arrange the following growth rates in the increasing order

O(n3),O(1),O(n2),O(nlogn),O(n2logn),Ω(n0.5),Ω(nlogn),Θ(n3),Θ(n0.5)

Answer 1

The Big Omega notation provides a lower bound to a function.

So Ω(n^0.5) < Ω(n log n)

The Big O notation provides an upper bound to a function.

So O(n^3) > O(n^2 log n) > O(n^2) > O(n log n) > O(1)

The Big Theta notation bounds a functions from above and below.

So Θ(n^3) > Θ(n^0.5)