Houjun Liu

big-o

Intuition:

  • \(O\): \(\leq\)
  • \(\theta\): \(=\)
  • \(\Omega\): \(\geq\)

Definitions:

  • \(f(n) = O(g(n)) \implies \exists n_{0}: \forall n > n_0, f(n) \leq c (g(n))\)
  • \(f(n) = \Omega(g(n)) \implies \exists n_{0}: \forall n > n_0, f(n) \geq c (g(n))\)
  • \(f(n) = \theta(g(n)) \implies \exists n_{0}: \forall n > n_0, f(n) \geq 1 (g(n)), f(n) \leq c (g(n))\)

Little ones:

  • \(o\): \(<\)
  • \(\omega\): \(>\)