mirror of
https://github.com/Steffo99/appunti-magistrali.git
synced 2024-11-25 19:44:18 +00:00
29 lines
585 B
Markdown
29 lines
585 B
Markdown
|
---
|
||
|
|
aliases:
|
||
|
|
- small-o
|
||
|
|
---
|
||
|
|
[[notazione asintotica]] per il [[limite inferiore]].
|
||
|
|
|
||
|
|
$$
|
||
|
|
\def \varAsym {{\color{royalblue} g(n)}}
|
||
|
|
\def \varFunc {{\color{orangered} f(n)}}
|
||
|
|
\def \varMore {{\color{palegreen} c_{more}}}
|
||
|
|
\def \varBeginning {{\color{turquoise} n_0}}
|
||
|
|
\Huge
|
||
|
|
o(\varAsym)
|
||
|
|
$$
|
||
|
|
In linguaggio formale, $\varFunc$ è in $O(\varAsym)$ se:
|
||
|
|
$$
|
||
|
|
o(\varAsym)
|
||
|
|
\Longleftrightarrow
|
||
|
|
\begin{cases}
|
||
|
|
\forall & \varMore > 0\\
|
||
|
|
\\
|
||
|
|
: & \begin{cases}
|
||
|
|
\exists & \varBeginning > 0\\
|
||
|
|
\forall & n \geq \varBeginning\\
|
||
|
|
: & 0 \leq \varFunc \leq (\varMore \cdot \varAsym)
|
||
|
|
\end{cases}
|
||
|
|
\end{cases}
|
||
|
|
$$
|