quartz/content/notes/big-o.md

title	tags
big-o	cosc201

big-o

Big O means f(n) = O(g(n)) if there is some constant A > 0 such that for all sufficiently large n, f(n) ≤ A × g(n).

• Big O provides upper bounds only. (usually on worst case runtimes)
  • sometimes cost will be much less
    • does not take special cases into account
    • upper bound
• O says that g(n) provides an upper bound for f(n)
  • "Insertion sort is $O(n^2)$" -> the maximum number of basic operations in never more than some constanct times n^2
• if f(n) =O(g(n)) then the opposite is also true
• usually f(n) is complex but g(n) is very simple