http://notes.mehvix.com/docs/cs-170/Recent content in CS170 on notes.mehvix.comHugoen-ushttp://notes.mehvix.com/cs-170/mt1/Mon, 01 Jan 0001 00:00:00 +0000http://notes.mehvix.com/cs-170/mt1/<blockquote class="book-hint warning"> I never finished these. Consider checking out <a href="https://smartspot2.github.io/assets/pdf/CS170_Lecture_Notes.pdf">Alec Li&rsquo;s notes</a> and <a href="https://jshen13.github.io/notes/fa20/cs170_sg.pdf">Jeffrey Shen&rsquo;s final cheatsheet</a>. </blockquote> <link rel="stylesheet" href="http://notes.mehvix.com/katex/katex.min.css" /> <script defer src="http://notes.mehvix.com/katex/katex.min.js"></script> <script defer src="http://notes.mehvix.com/katex/auto-render.min.js" onload="renderMathInElement(document.body);"></script><span> \(\) </span> <h1 id="asymptotic-bound"> Asymptotic Bound <a class="anchor" href="#asymptotic-bound">#</a> </h1> <div class="book-columns flex flex-wrap"> <div class="flex-even markdown-inner" style="flex-grow: 1;"> <!-- mathjax fix --> <table> <thead> <tr> <th>Notation</th> <th>Meaning</th> <th>Definition</th> </tr> </thead> <tbody> <tr> <td>$$\mathcal O(\cdot)$$</td> <td>$$\le$$</td> <td>$$\lim_{n \to \infty} \dfrac{f(n)}{g(n)} &lt; \infty$$</td> </tr> <tr> <td>$$\Theta (\cdot)$$</td> <td>$$=$$</td> <td>$$\lim_{n \to \infty} \dfrac{f(n)}{g(n)} = c$$</td> </tr> <tr> <td>$$\Omega(\cdot)$$</td> <td>$$\ge$$</td> <td>$$\lim_{n \to \infty} \dfrac{f(n)}{g(n)}&gt; 0$$</td> </tr> </tbody> </table> </div> <div class="flex-even markdown-inner" style="flex-grow: 1;"> <!-- mathjax fix --> <p>$$\begin{aligned} c &amp;&lt; \log^\star n \\ &amp;&lt; \log n \\ &amp;&lt; n^{1/3}\\ &amp;&lt; n^{1/2} = \sqrt n\\ &amp;&lt; 2^{\log{n}} = n\\ &amp;&lt; n \log (n) = \log(n!) \\ &amp;&lt; n^3\\ &amp;&lt; 2^{\sqrt{n}}\\ &amp;&lt; 2^n\\ &amp;&lt; 3^n\\ &amp;&lt; n! \end{aligned}$$</p>