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Up: CSE 2320: Algorithms and Previous: Asymptotic Notation in Equations

Summary



o notation
f(n) = o(g(n)), g(n) is an upper bound of f(n) that is not asymptotically tight



$\omega$ notation
f(n) = $\omega(g(n))$, g(n) is a lower bound of f(n) that is not asymptotically tight
Example: f(n) = 3n3 + 4
  • f(n) = $\Theta(n^3)$
  • f(n) = O(n3) = O(n4) = ...
  • f(n) = $\Omega(n^3)$ = $\Omega(n^2)$ = $\Omega(n)$ = $\Omega(1)$
  • f(n) = o(n4) = o(n5) = ...
  • f(n) = $\omega(n^2)$ = $\omega(n)$ = $\omega(1)$



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