# Big O

• Expresses computing time as the term in a function that increases most rapidly to the size of a problem
• How fast an algorithm is
• Rate of growth of operations
• How the running time will increase as the input increases
• Worst-case run time
• Can we do better?

## Common Run Times

• Fastest --> slowest
Big OName
$O(1)$constant/bounded time
$O(log ; n)$log time
$O(n)$linear time
$O(n ; log ; n)$$n ; log ; n$ time
$O(n^2)$quadratic/exponential time
$O(2^n)$exponential time
$O(n!)$factorial time