MIT 算法导论 （二）Math Notation

O:

f(n) = O(g(n)) ,  means that there are some suitable constants,such that 0 <= f(n) <= c·g(n). Consider as less than or equal to.

Ex:

f(n) = n^{3 +} O(n²) , means that f(n) is basically n³ but there are these lower order terms that are O(n²).

n² + O(n) = O(n²)

 

Ω：

f(n) = Ω(g(n)) , means that f(n) is at least some constant times g(n).  0 <= cg(n) <= f(n). Consider as greater than or equal to.

Ex:

√n = Ω(log n) , means root n is at least log n for suffciently large n.

 

θ:

θ(g(n)) = O(g(n)) ∩ Ω（g(n)） . Consider as equal to.

 

o,ω:

o is the strict version of O and ω is the strict version of Ω.  Consider as > and <.