时间复杂度

https://en.wikipedia.org/wiki/Time_complexity#Table_of_common_time_complexities

 

Table of common time complexities

Further information: Computational complexity of mathematical operations

The following table summarizes some classes of commonly encountered time complexities. In the table, poly(x) = x^O(1), i.e., polynomial in x.

Name	Complexity class	Running time (T(n))	Examples of running times	Example algorithms
constant time		O(1)	10	Determining if an integer (represented in binary) is even or odd
inverse Ackermann time		O(α(n))		Amortized time per operation using a disjoint set
iterated logarithmic time		O(log* n)		Distributed coloring of cycles
log-logarithmic		O(log log n)		Amortized time per operation using a bounded priority queue[2]
logarithmic time	DLOGTIME	O(log n)	log n, log(n2)	Binary search
polylogarithmic time		poly(log n)	(log n)2
fractional power		O(nc) where 0 < c < 1	n1/2, n2/3	Searching in a kd-tree
linear time		O(n)	n	Finding the smallest or largest item in an unsorted array
"n log star n" time		O(n log* n)		Seidel's polygon triangulation algorithm.
quasilinear time		O(n log n)	n log n, log n!	Fastest possible comparison sort; Fast Fourier transform.
quadratic time		O(n2)	n2	Bubble sort; Insertion sort; Direct convolution
cubic time		O(n3)	n3	Naive multiplication of two n×n matrices. Calculating partial correlation.
polynomial time	P	2O(log n) = poly(n)	n, n log n, n10	Karmarkar's algorithm for linear programming; AKS primality test
quasi-polynomial time	QP	2poly(log n)	nlog log n, nlog n	Best-known O(log2 n)-approximation algorithm for the directed Steiner tree problem.
sub-exponential time (first definition)	SUBEXP	O(2nε) for all ε > 0	O(2log nlog log n)	Assuming complexity theoretic conjectures, BPP is contained in SUBEXP.[3]
sub-exponential time (second definition)		2o(n)	2n1/3	Best-known algorithm for integer factorization and graph isomorphism
exponential time (with linear exponent)	E	2O(n)	1.1n, 10n	Solving the traveling salesman problem using dynamic programming
exponential time	EXPTIME	2poly(n)	2n, 2n2	Solving matrix chain multiplication via brute-force search
factorial time		O(n!)	n!	Solving the traveling salesman problem via brute-force search
double exponential time	2-EXPTIME	22poly(n)	22n	Deciding the truth of a given statement in Presburger arithmetic