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Original file line number Diff line number Diff line change
Expand Up @@ -227,7 +227,7 @@ $$
**Littel-o($o(·)$)**的定義如下:

$$
o(g(n))=\{\,f(n):對於所有正整數\:c,存在正整數\:n_0\,,使得對於所有n\geq n_0,\, 0\leq f(n) \leq cg(n)\:\}
o(g(n))=\{\,f(n):對於所有正整數\:c,存在正整數\:n_0\,,使得對於所有n\geq n_0,\, 0\leq f(n) < cg(n)\:\}
$$

怎麼說**Littel-o($o(·)$)**比較「不緊」呢?因為定義中是「對於所有正整數$c$」,因此$f(n)=o(g(n))$務必要求$g(n)$的「成長率」遠遠大於$f(n)$,等同於滿足以下極限關係式:
Expand Down Expand Up @@ -255,7 +255,7 @@ $$
**Littel-omega($\omega(·)$)**的定義如下:

$$
\omega(g(n))=\{\,f(n):對於所有正整數\:c,存在正整數\:n_0\,,使得對於所有n\geq n_0,\, 0\leq cg(n) \leq f(n)\:\}
\omega(g(n))=\{\,f(n):對於所有正整數\:c,存在正整數\:n_0\,,使得對於所有n\geq n_0,\, 0\leq cg(n) < f(n)\:\}
$$

同理,$f(n)=\omega(g(n))$要求$g(n)$的「成長率」遠遠小於$f(n)$,等同於滿足以下極限關係式:
Expand Down