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18 lines
630 B
Markdown
18 lines
630 B
Markdown
---
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title: "big-theta"
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tags:
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- cosc201
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---
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# big-theta
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>Big theta means $f(n) = \Theta(g(n))$ if there are constants 0 < B < A such that for all sufficiently large n, ==$B × g(n) ≤ f(n) ≤ A × g(n)$==
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- Upper and lower bound
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- $Θ$ says that $g(n)$ provides **upper** and **lower** bound for $f(n)$
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- "selection sort is $\Theta(n^2)$" -> the maximum number of operations will be bounded bothh above and below by some constant times $n^2$
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- $f(n) = \Theta(g(n))$ means that f and g have similar growth rates
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- if $f(n) = \Theta(g(n))$ then the opposite is also true
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- usually $f(n)$ is complex but $g(n)$ is very simple
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