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33 lines
726 B
Markdown
33 lines
726 B
Markdown
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---
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aliases:
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- big-Theta
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- notazione theta-grande
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- big-Θ
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- tight bound
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---
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[[notazione asintotica]] per il [[limite bilaterale]].
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$$
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\def \varAsym {{\color{royalblue} g(n)}}
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\def \varFunc {{\color{orangered} f(n)}}
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\def \varLess {{\color{lightcoral} c_{less}}}
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\def \varMore {{\color{palegreen} c_{more}}}
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\def \varBeginning {{\color{turquoise} n_0}}
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\Huge
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\Theta(\varAsym)
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$$
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In linguaggio formale, $\varFunc$ è in $\Theta(\varAsym)$ se:
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$$
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\Theta(\varAsym)
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\Longleftrightarrow
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\begin{cases}
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\exists & \varLess > 0\\
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\exists & \varMore > 0\\
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\exists & \varBeginning > 0\\
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\\
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\forall & n \geq \varBeginning\\
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: & 0 \leq (\varLess \cdot \varAsym) \leq \varFunc \leq (\varMore \cdot \varAsym)
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\end{cases}
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$$
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