# Algorithms

## Big-O Algorithm Computational Complexity

### Big-O Domination

- O(2
^{n}) dominates O(n^{2}) - O(n
^{2}) dominates O(n log(n)) - O(n
^{2}) and O(n^{2}+ n) don't dominate each other - O(n
^{4}) dominates O(n^{3}+ n^{2}) - O(log
_{2}n) and O(log_{10}n) don't dominate each other - O(3
^{n}) dominates O(2^{n}) - O(2
^{2n}) dominates O(2^{n})

limit dominated/dominating as n->infinity = 0

If the Big-O complexity of an algorithm dominates another then the limit of the dominated algorithm divided by the dominating algorithm will approach zero as n approaches infinity.

Example: 2^{n} dominates n^{2}

limit n^2 / 2^n as n->infinity = 0

http://www.cs.dartmouth.edu/~dwagn/research/ordernotation.html