Complexity Analysis
# Complexity Analysis
# Asymptotic Notations
Notations used to describe the order of growth of a given function
# Big-O $O(f(x))$
The limits when taking the 2 functions to infinity produces a constant C that $$\begin{align}\lim_{n\to \infty}\frac{f(n)}{g(n)}=C \\ C=0 \\ or\\ 0<C<\infty \end{align}$$
# Big-Omega $\Omega(f(x))$
The limits when taking the 2 functions to infinity produces a constant C that $$\begin{align}\lim_{n\to \infty}\frac{f(n)}{g(n)}=C \\ C=\infty \\ or\\ 0<C<\infty \end{align}$$
# Big-Theta $\theta(f(x))$
The limits when taking the 2 functions to infinity produces a constant C that $$\begin{align}\lim_{n\to \infty}\frac{f(n)}{g(n)}=C \\ 0<C<\infty \end{align}$$
# Properties
$$f(n)\in O(h(n)),g(n)\in O(h(n)) \implies f(n)+g(n)\in O(h(n))$$
# Example function comparisons
# Order of Common Functions
