ds-algo-study

<!DOCTYPE html> <html lang="en"> <head> <meta charset="UTF-8" /> <meta name="viewport" content="width=device-width, initial-scale=1.0" /> <meta name="description" content="A description of the page and its contents" /> <link rel="stylesheet" href="styles.css" /> <title>Page Title</title> <link rel="stylesheet" href="./../../../assets/style.css" /> <link rel="stylesheet" href="./../../../assets/prism.css" /> <script async src="./../../../assets/prism.js"></script> </head> <body> <h1 id="example-graph">Example Graph</h1> <h3 id="visual-aid">Visual Aid</h3> <hr /> <h2 id="picture-alt"><img src="https://s3-us-west-1.amazonaws.com/appacademy-open-assets/data_structures_algorithms/graphs/images/graphs.png" alt="picture alt" /></h2> <hr /> <h3 id="example-code">Example Code</h3> <hr /> <div id=">pre data-role=" codeBlock" data-info="js" class="language-javascript"><code><a title="1">class GraphNode {</a> <a title="2"> constructor(val) {</a> <a title="3"> this.val = val;</a> <a title="4"> this.neighbors = [];</a> <a title="5"> }</a> <a id=-6" title="6">}</a> <a title="7"></a> <a title="8">let a = new GraphNode("a");</a> <a title="9">let b = new GraphNode("b");</a> <a id=-10" title="10">let c = new GraphNode("c");</a> <a title="11">let d = new GraphNode("d");</a> <a id=-12" title="12">let e = new GraphNode("e");</a> <a id=-13" title="13">let f = new GraphNode("f");</a> <a id=-14" title="14">a.neighbors = [b, c, e];</a> <a id=-15" title="15">c.neighbors = [b, d];</a> <a id=-16" title="16">e.neighbors = [a];</a> <a id=-17" title="17">f.neighbors = [e];</a></code></pre></div> <hr /> <hr /> <h1 id="basics">Basics</h1> <ul> <li>A graph is any collection of nodes and edges. <ul> <li>Much more relaxed in structure than a tree.</li> </ul></li> <li>It doesn't have to have a root node (so not every node can be accessed from a single node)</li> <li>It could have cycles (a group of nodes whose paths begin and end at the same node)</li> <li>Any number of edges may leave a node</li> </ul> <hr /> <h1 id="ways-to-reference-a-graph-data-structure">Ways To Reference a Graph Data Structure</h1> <h2 id="visual-reference">Visual Reference</h2> <hr /> <h2 id="picture-alt-1"><img src="https://s3-us-west-1.amazonaws.com/appacademy-open-assets/data_structures_algorithms/graphs/images/adj_matrix_graph.png" alt="picture alt" /></h2> <hr /> <h2 id="adjacency-matrix">Adjacency Matrix</h2> <hr /> The row index will corespond to the source of an edge and the column index will correspond to the edges destination. <ul> <li>When the edges have a direction, <code>matrix[i][j]</code> may not be the same as <code>matrix[j][i]</code></li> <li>It is common to say that a node is adjacent to itself so matrix[x][x] is true for any node</li> <li>Will be O(n^2) space complexity</li> </ul> <hr /> <h3 id="a-2d-array-as-the-method-of-storing-the-location-of-nodes">A 2D Array as the method of storing the location of Nodes</h3> let matrix = [ <table> <thead> <tr > <th></th> <th>A</th> <th>B</th> <th>C</th> <th>D</th> <th>E</th> <th>F</th> </tr> </thead> <tbody> <tr> <td>A</td> <td>[True,</td> <td>True,</td> <td>True,</td> <td>False,</td> <td>True,</td> <td>False]</td> </tr> <tr> <td>B</td> <td>[False,</td> <td>True,</td> <td>False,</td> <td>False,</td> <td>False,</td> <td>False]</td> </tr> <tr> <td>C</td> <td>[False,</td> <td>True,</td> <td>True,</td> <td>True,</td> <td>False,</td> <td>False]</td> </tr> <tr> <td>D</td> <td>[False,</td> <td>False,</td> <td>False,</td> <td>True,</td> <td>False,</td> <td>False]</td> </tr> <tr> <td>E</td> <td>[True,</td> <td>False,</td> <td>False,</td> <td>False,</td> <td>True,</td> <td>False]</td> </tr> <tr> <td>F</td> <td>[False,</td> <td>False,</td> <td>False,</td> <td>False,</td> <td>True,</td> <td>True]</td> </tr> </tbody> </table> ]; <hr /> <h2 id="adjacency-list">Adjacency List</h2> <hr /> Seeks to solve the shortcomings of the matrix implementation. It uses an object where keys represent node labels and values associated with that key are the adjacent nodes. <hr /> <div id=">pre data-role=" codeBlock" data-info="js" class="language-javascript"><code><a title="1">let graph = {</a> <a id=-2" title="2"> a: ["b", "c", "e"],</a> <a id=-3" title="3"> b: [],</a> <a id=-4" title="4"> c: ["b", "d"],</a> <a id=-5" title="5"> d: [],</a> <a id=-6" title="6"> e: ["a"],</a> <a id=-7" title="7"> f: ["e"],</a> <a id=-8" title="8">};</a></code></pre></div> <hr /> <h1 id="graph-traversal">Graph Traversal</h1> <h2 id="depth-first">Depth First</h2> <hr /> <h3 id="with-a-node-class">With a Node Class</h3> <hr /> <h4 id="node-class-example">Node Class Example</h4> <ul> <li>There may not always be a suitable root-like starting point. But in this example all the nodes can be traversed to in some way from the "f" node</li> </ul> <div id=">pre data-role=" codeBlock" data-info="js" class="language-javascript"><code><a title="1">class GraphNode {</a> <a title="2"> constructor(val) {</a> <a title="3"> this.val = val;</a> <a id=-4" title="4"> this.neighbors = [];</a> <a id=-5" title="5"> }</a> <a id=-6" title="6">}</a> <a id=-7" title="7"></a> <a id=-8" title="8">let a = new GraphNode("a");</a> <a id=-9" title="9">let b = new GraphNode("b");</a> <a id=-10" title="10">let c = new GraphNode("c");</a> <a id=-11" title="11">let d = new GraphNode("d");</a> <a id=-12" title="12">let e = new GraphNode("e");</a> <a id=-13" title="13">let f = new GraphNode("f");</a> <a id=-14" title="14">a.neighbors = [e, c, b];</a> <a id=-15" title="15">c.neighbors = [b, d];</a> <a id=-16" title="16">e.neighbors = [a];</a> <a id=-17" title="17">f.neighbors = [e];</a></code></pre></div> <hr /> <hr /> <h4 id="recursive-traversal">Recursive Traversal</h4> <div id=">pre data-role=" codeBlock" data-info="js" class="language-javascript"><code><a title="1">function depthFirstRecur(node, visited = new Set()) {</a> <a id=-2" title="2"> if (visited.has(node.val)) return;</a> <a id=-3" title="3"></a> <a id=-4" title="4"> console.log(node.val);</a> <a id=-5" title="5"> visited.add(node.val);</a> <a id=-6" title="6"></a> <a id=-7" title="7"> node.neighbors.forEach((neighbor) => {</a> <a id=-8" title="8"> depthFirstRecur(neighbor, visited);</a> <a id=-9" title="9"> });</a> <a id=-10" title="10">}</a> <a id=-11" title="11"></a> <a id=-12" title="12">depthFirstRecur(f); // starting with f as it is a node that can reach all other nodes</a></code></pre></div> <h4 id="iterative-traversal">Iterative Traversal</h4> <div> <pre data-role="codeBlock" data-info="js" class="language-javascript"> ><code><a title="1">function depthFirstIter(node) {</a> <a id=-2" title="2"> let visited = new Set();</a> <a id=-3" title="3"> let stack = [node];</a> <a id=-4" title="4"></a> <a id=-5" title="5"> while (stack.length) {</a> <a id=-6" title="6"> let node = stack.pop();</a> <a id=-7" title="7"></a> <a id=-8" title="8"> if (visited.has(node.val)) continue;</a> <a id=-9" title="9"></a> <a id=-10" title="10"> console.log(node.val);</a> <a id=-11" title="11"> visited.add(node.val);</a> <a id=-12" title="12"></a> <a id=-13" title="13"> stack.push(...node.neighbors);</a> <a id=-14" title="14"> }</a> <a id=-15" title="15">}</a> <a id=-16" title="16"></a> <a id=-17" title="17">depthFirstIter(f);</a></code></pre></div> <hr /> <hr /> <h3 id="with-an-adjacency-list">With an Adjacency List</h3> <hr /> <h4 id="adjacency-list-example">Adjacency List Example</h4> Remember that the nodes are stored as strings in an array in an object. <div id=">pre data-role=" codeBlock" data-info="js" class="language-javascript"><code><a title="1">let graph = {</a> <a id=-2" title="2"> a: ["b", "c", "e"],</a> <a id=-3" title="3"> b: [],</a> <a id=-4" title="4"> c: ["b", "d"],</a> <a id=-5" title="5"> d: [],</a> <a id=-6" title="6"> e: ["a"],</a> <a id=-7" title="7"> f: ["e"],</a> <a id=-8" title="8">};</a></code></pre></div> <hr /> <hr /> <h4 id="recursive-example">Recursive Example</h4> <div id="cb7"> <pre data-role="codeBlock" data-info="js" class="language-javascript"> ><code><a title="1">function depthFirstRecur(node, graph, visited = new Set()) {</a> <a id="cb7-2" title="2"> if (visited.has(node)) return;</a> <a id="cb7-3" title="3"></a> <a id="cb7-4" title="4"> console.log(node);</a> <a id="cb7-5" title="5"> visited.add(node);</a> <a id="cb7-6" title="6"></a> <a id="cb7-7" title="7"> graph[node].forEach((neighbor) => {</a> <a id="cb7-8" title="8"> depthFirstRecur(neighbor, graph, visited);</a> <a id="cb7-9" title="9"> });</a> <a id="cb7-10" title="10">}</a> <a id="cb7-11" title="11"></a> <a id="cb7-12" title="12">depthFirstRecur("f", graph);</a></code></pre></div> <hr /> <h4 id="dynamic-recursive-example">Dynamic Recursive Example</h4> <div id="cb8"> <pre data-role="codeBlock" data-info="js" class="language-javascript"> ><code><a title="1">function depthFirst(graph) {</a> <a id="cb8-2" title="2"> let visited = new Set();</a> <a id="cb8-3" title="3"></a> <a id="cb8-4" title="4"> for (let node in graph) {</a> <a id="cb8-5" title="5"> _depthFirstRecur(node, graph, visited);</a> <a id="cb8-6" title="6"> }</a> <a id="cb8-7" title="7">}</a> <a id="cb8-8" title="8"></a> <a id="cb8-9" title="9">function _depthFirstRecur(node, graph, visited) {</a> <a id="cb8-10" title="10"> if (visited.has(node)) return;</a> <a id="cb8-11" title="11"></a> <a id="cb8-12" title="12"> console.log(node);</a> <a id="cb8-13" title="13"> visited.add(node);</a> <a id="cb8-14" title="14"></a> <a id="cb8-15" title="15"> graph[node].forEach((neighbor) => {</a> <a id="cb8-16" title="16"> _depthFirstRecur(neighbor, graph, visited);</a> <a id="cb8-17" title="17"> });</a> <a id="cb8-18" title="18">}</a> <a id="cb8-19" title="19"></a> <a id="cb8-20" title="20">depthFirst(graph);</a></code></pre></div>