大O记法-BigO notation

what is big O notation?

The way that describe the relationship between the runing time and the size of problem.

1- Method of calculating time complexity of algorithm.

1)hypothesis(假设法)

class solution{
	int i = 0;
	while(i <= n){
		i = i * 2;
	}
}
assuming that the executing time is t
t = 1, i = 2
t = 2, i = 4
t = n, i = 2^t
when 2 ^ t > n then the loop is stopped.
so ㏒n = t
t = logn

2- Big O notation

(1)Constant Time: O(1)

(2)Logarithmic Time: O(log(n))

(3)Linear Time: O(n)

(4)Linearithmic Time: O(nlog(n))

(5)Quadric Time: O(n^2)

(6)Cubic Time: O(n^3)

(7)Exponential Time: O(2^n)

(3)Factorial Time: O(n!)