Slowest Computational Complexity (Big-O)

Question

Out of these algorithms, I know Alg1 is the fastest, since it is n squared. Next would be Alg4 since it is n cubed, and then Alg2 is probably the slowest since it is 2^n (which is supposed to have a very poor performance).

However Alg3 and Alg5 are something I have yet to come across in my reading in terms of speed. How do these two algorithms rank up to the other 3 in terms of which is faster and slower? Thanks for any help.

Edit: Now that I think about it, is Alg3 referring to O(n log n)? If the ln inside of it means 'log', then that would make it the fastest.

Answer 1

The ascending order would be: n·log(n) < n² < n³ < 2ⁿ < n! for n ≥ 10.

Also have a look at the Big-O Algorithm Complexity Cheat Sheet.