复杂度定义 The Definition of Complexity

时间:2021-02-20 08:53:18

The upper bound   Big-O:

Definition: f(n) is in O(g(n)) if there are constants c0 and N0 such that f(n) < c0*g(n) for all n>N0. We are only interested in large n, n>N0.

(Heuristics)计算方法:删掉低阶变量(包括零阶),只保留最高阶变量,变量前的系数变为1。如15n2 + 33n + 17 is in O(n2),当然15n2 + 33n + 17 is in O(n3)也是对的,但我们通常只关心cloest bound。

Dominance Relation: n! >>2n >> n2 >> n3 >> nlogn >> n >> logn >> 1

在Dominance Relation中忽略log的底,可以通过换底公式换成相同的底,且因为系数忽略,所以底不重要。

(Arithmetic)计算方法:

复杂度定义 The Definition of Complexity

(截自Comp20003, University of Melbourne)

The lower bound    Big-Omega(Ω):

Definition: f(n) is Ω(g(n)) if g(n) is O(f(n))。

The tight bound / the growth rate   Big-Omega(Ω):

Definition: f(n) is θ(g(n)) is f(n) is O(g(n)) and f(n) is Ω(g(n))