quartz/content/notes/big-theta-notation.md

title	tags
big-theta-notation	cosc201

Big theta means f(n) = \Theta(g(n)) if there are constants 0 < B < A such that for all sufficiently large n, ==$B × g(n) ≤ f(n) ≤ A × g(n)$==

• Upper and lower bound
• Θ says that g(n) provides upper and lower bound for f(n)
  • "selection sort is $\Theta(n^2)$" -> the maximum number of operations will be bounded both above and below by some constant times n^2
• f(n) = \Theta(g(n)) means that f and g have similar growth rates
• if f(n) = \Theta(g(n)) then the opposite is also true
• usually f(n) is complex but g(n) is very simple