NP-Completeness

Almost all algorithms considered so far run in worst-case polynomial time.

That is,

T(n) = O(n^k) for some constant k

n = input size

Size n
Complexity	10	20	30	40	50	60
n	.00001 s	.00002 s	.00003 s	.00004 s	.00005 s	.00006 s
n2	.0001 s	.0004 s	.0009 s	.0016 s	.0025 s	.0036 s
n3	.001 s	.008 s	.027 s	.064 s	.125 s	.216 s
n5	.1 s	3.2 s	24.3 s	1.7 min	5.2 min	13.0 min
2n	.001 s	1.0 s	17.9 min	12.7 days	35.7 years	366 centuries
3n	.059 s	58 min	6.5 years	3855 centuries	2x108 centuries	1.3 x 1013 centuries