Differences
This shows you the differences between two versions of the page.
| Both sides previous revision Previous revision Next revision | Previous revision | ||
|
aa:lab:notations [2016/11/02 18:09] dalex [Syntactic sugars] |
aa:lab:notations [2016/11/02 18:18] (current) dalex |
||
|---|---|---|---|
| Line 109: | Line 109: | ||
| Let $math[f(n) = \log(n)] and $math[g(n) = n]\\ | Let $math[f(n) = \log(n)] and $math[g(n) = n]\\ | ||
| We see that, for $math[c = 1, n_0 = 1 \Rightarrow 0 \le \log(n) \le n]\\ | We see that, for $math[c = 1, n_0 = 1 \Rightarrow 0 \le \log(n) \le n]\\ | ||
| - | for $math[c = 10, n_0 = 64 \Rightarrow 0 \le 10\l | + | for $math[c = 10, n_0 = 64 \Rightarrow 0 \le 10 \log(n) \le n]\\ |
| - | og(n) \le n]\\ | + | for $math[c = 100, n_0 = 1024 \Rightarrow 0 \le 100 \log(n) \le n]\\ |
| - | for $math[c = 100, n_0 = 1024 \Rightarrow 0 \le 100\log(n) \le n]\\ | + | |
| etc.\\ | etc.\\ | ||
| Thus, $math[g(n) \in \omega(f(n))] | Thus, $math[g(n) \in \omega(f(n))] | ||
| Line 153: | Line 152: | ||
| * $math[\log(n\cdot \log(n))\in\Theta(\log(n))] | * $math[\log(n\cdot \log(n))\in\Theta(\log(n))] | ||
| * $math[\sqrt{n}\in\omega(\log(n))] | * $math[\sqrt{n}\in\omega(\log(n))] | ||
| - | * $math[f(n) + g(n) \in O(n\cdot\log(n))$ for $f(n)\in\Theta(n)$ and $g(n)\in O(n\cdot\log n)] | + | * $math[f(n) + g(n) \in O(n\cdot\log(n))] for $math[f(n)\in\Theta(n)] and $math[g(n)\in O(n\cdot\log n)] |
| ===== Exercises (syntactic sugars) ===== | ===== Exercises (syntactic sugars) ===== | ||