Asymptotic Analysis Basics</h1> <article> <h1>Asymptotic Analysis Basics</h1> <p>Mon, 01 Jan 0001 00:00:00 +0000</p> <blockquote> <p>[!info] Content Note</p> <p>This concept is a big reason why a strong math background is helpful for computer science, even when it’s not obvious that there are connections! Make sure you’re comfortable with Calculus concepts up to <a href="http://tutorial.math.lamar.edu/Classes/CalcII/PowerSeries.aspx" rel="noopener">power series</a>.</p> </blockquote> <h2 id="an-abstract-introduction-to-asymptotic-analysis"> An Abstract Introduction to Asymptotic Analysis <a class="anchor" href="#an-abstract-introduction-to-asymptotic-analysis">#</a> </h2> <p>The term <strong>asymptotics,</strong> or <strong>asymptotic analysis,</strong> refers to the idea of <strong>analyzing functions when their inputs get really big.</strong> This is like the <strong>asymptotes</strong> you might remember learning in math classes, where functions approach a value when they get very large inputs.</p> </article> <article> <p>Mon, 01 Jan 0001 00:00:00 +0000</p> <h1 id="amortization"> Amortization <a class="anchor" href="#amortization">#</a> </h1> <blockquote> <p>[!info] Content Note</p> <p>Please read <a href="https://notes.bencuan.me/cs61b/asymptotics/asymptotics/" rel="noopener" class="internal-link" data-src="https://notes.bencuan.me/cs61b/asymptotics/asymptotics/">Asymptotic Analysis Basics</a> first. If you don’t, none of this will make any sense!</p> </blockquote> <p><strong>Amortization</strong> means <strong>spreading out.</strong></p> <p>Sometimes, an operation takes different amounts of time for different values of $n$. Rather than having to report runtimes for each different case, we can instead average all of them out and report the <strong>amortized runtime.</strong></p> <p>This is especially good for functions where most actions have a low cost, but a few have a high cost. We’ll see an example of this further down the page!</p> </article> <article> <p>Mon, 01 Jan 0001 00:00:00 +0000</p> <h1 id="asymptotics-practice"> Asymptotics Practice <a class="anchor" href="#asymptotics-practice">#</a> </h1> <blockquote> <p>[!info] Content Note</p> <p>Make sure to review <a href="https://notes.bencuan.me/cs61b/asymptotics/asymptotics/" rel="noopener" class="internal-link" data-src="https://notes.bencuan.me/cs61b/asymptotics/asymptotics/">Asymptotic Analysis Basics</a> before proceeding with these problems.</p> </blockquote> <h2 id="introduction"> Introduction <a class="anchor" href="#introduction">#</a> </h2> <p>Asymptotics is a very intuition-based concept that often doesn’t have a set algorithm for computing. The best way to get good at analyzing programs is to practice!</p> <p>With that said, here are some problems of increasing difficulty for you to enjoy 😊</p> <blockquote> <p>[!hint] Read before you do the problems!</p> </article> </main></body></html>