<link>https://notes.bencuan.me/cs61b/abstract-data-types/graphs/</link><pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate><guid>https://notes.bencuan.me/cs61b/abstract-data-types/graphs/</guid><description><h2 id="introduction"> Introduction <a class="anchor" href="#introduction">#</a> </h2> <p>Graphs are simply a collection of <strong>vertices</strong> connected by <strong>edges.</strong> They’re very similar to trees, but are much more versatile and don’t require hierarchical relationships like trees do.</p> <p> <img src="https://notes.bencuan.me/cs61b/abstract-data-types/../img/assets/image%20%2855%29.png" width="auto" alt="A very simple graph." /></p> <p>For most purposes, we will be working with <strong>simple graphs</strong> that follow two rules:</p> <ul> <li>There are <strong>no loops</strong> (a connection of a node to itself).</li> <li>There are <strong>no parallel edges</strong> (two edges that connect the same two vertices).</li> </ul> <p> <img src="https://notes.bencuan.me/cs61b/abstract-data-types/../img/assets/image%20%2856%29.png" width="auto" alt="Don’t make these graphs pls. Keep life simple!" /></p></description></item><item><title>Hashing and Hash Tables</h1> <article> <p>Mon, 01 Jan 0001 00:00:00 +0000</p> <h2 id="introduction"> Introduction <a class="anchor" href="#introduction">#</a> </h2> <p>Graphs are simply a collection of <strong>vertices</strong> connected by <strong>edges.</strong> They’re very similar to trees, but are much more versatile and don’t require hierarchical relationships like trees do.</p> <p> </p> <p>For most purposes, we will be working with <strong>simple graphs</strong> that follow two rules:</p> <ul> <li>There are <strong>no loops</strong> (a connection of a node to itself).</li> <li>There are <strong>no parallel edges</strong> (two edges that connect the same two vertices).</li> </ul> <p> </p> </article> <article> <h1>Hashing and Hash Tables</h1> <p>Mon, 01 Jan 0001 00:00:00 +0000</p> <h2 id="data-indexed-sets-introduction"> Data Indexed Sets: Introduction <a class="anchor" href="#data-indexed-sets-introduction">#</a> </h2> <p>So far, we’ve explored a whole bunch of ways we can store items, but they aren’t really optimized for general searching. What if we could get searching in $\Theta(1)$ time??? Wouldn’t that be nice!</p> <p>See also: [[cs186/04 Sorting and Hashing]] (external hashing for databases that don’t fit in memory), [[cs70/probability/hashing-and-the-union-bound]] (the probability of collisions and the birthday problem), and [[cs161/Cryptography]] (cryptographic hash functions used for integrity).</p> </article> <article> <h1>Union Find (Disjoint Sets)</h1> <p>Mon, 01 Jan 0001 00:00:00 +0000</p> <h1 id="union-find-disjoint-sets"> Union Find (Disjoint Sets) <a class="anchor" href="#union-find-disjoint-sets">#</a> </h1> <blockquote> <p>[!info] Content Note</p> <p>This is not a complete entry, because I feel like existing course materials already cover this in an extremely intuitive manner. See <a href="https://inst.eecs.berkeley.edu/~cs61b/sp20/materials/lab/lab14/index.html" rel="noopener">lab 14</a> for a guide on how to implement your own Union Find structure!</p> </blockquote> <p>The Union Find data structure is a way of representing a bunch of nodes that are connected to each other in subsets. It’s used in <a href="https://notes.bencuan.me/cs61b/algorithms/minimum-spanning-trees/kruskals-algorithm/" rel="noopener" class="internal-link" data-src="https://notes.bencuan.me/cs61b/algorithms/minimum-spanning-trees/kruskals-algorithm/">Kruskal’s Algorithm</a> among other things.</p> </article> <article> <p>Mon, 01 Jan 0001 00:00:00 +0000</p> <h2 id="what-is-it"> What is it? <a class="anchor" href="#what-is-it">#</a> </h2> <p>A <strong>Comparable</strong> is a <strong>generic type</strong> that allows standardized comparisons between objects.</p> <p>In other words, anything that has a <code>compareTo()</code> method can be a Comparable!</p> <p>Many Java libraries already use Comparable without you knowing! Some of the more well-known ones are <code>Collection</code> and <code>String</code>.</p> <h3 id="compareto-cant-return-anything-you-want"> CompareTo can’t return anything you want! <a class="anchor" href="#compareto-cant-return-anything-you-want">#</a> </h3> <p>There are some very specific properties CompareTo needs to have! Usually, we take them for granted but might forget about them when making our own.</p> </article> </main></body></html>