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29 lines
897 B
Markdown
29 lines
897 B
Markdown
---
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title: "asymptotic-notation"
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aliases: Big O, Big Theta, Algorithm Analysis
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tags:
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- cosc201
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---
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Asymptotic notations are used in computer science to classify algorithms based how its space and time requirements grow as the input grows.
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# big O notation
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Big O defines a bound for the *upper* bound of the running time (or space) of a algorithm. However, it is possible that the actual running time is much less as it does not take into account special cases ^fb2c3f
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## 1 Formal definition
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$f(n) = O(g(n))$ if there is some constant $A$ such that $f(n) < A \times g(n)$
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# big theta notation
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Big theta defines an *upper and a lower* bound for a the running time (or space) of an algorithm.
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## 2 Formal definition
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$f(n) = \theta(g(n))$ if there are some constants $A$ and $B$ where $0 < B < A$ such that for all sufficiently large $n$, $B \times g(n) \geq f(n) \leq A \times g(n)$
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