graphs

Author: Prakharnagore

8. Data Structures/8.7 Graphs/graphs.js

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+/* A Graph consists of a finite set of vertices(or nodes) and a set of Edges that connect a pair of nodes.
+A Graph is a non-linear data structure consisting of nodes and edges. The nodes are sometimes also referred 
+to as vertices and the edges are lines or arcs that connect any two nodes in the graph
+ */
+
+/*
+ESSENTIAL GRAPH TERMS
+- Vertex - a node
+- Edge - connection between nodes
+- Weighted/Unweighted - values assigned to distances between vertices
+- Directed/Undirected - directions assigned to distanced between vertices
+*/
+
+// DIFFERENCES & BIG O
+// OPERATION ADJACENCY LIST ADJACENCY MATRIX
+// Add Vertex O(1) ​O(|V^2|)
+// Add Edge O(1) O(1)
+// Remove Vertex O(|V| + |E|) ​O(|V^2|)
+// Remove Edge O(|E|) O(1)
+// Query O(|V| + |E|) O(1)
+// Storage O(|V| + |E|) ​O(|V^2|)
+
+// Adjacency List
+// Takes up more space (in sparse graphs)
+// Slower to iterate over all edges
+// Faster to lookup specific edge
+// Can take up less space (in sparse graphs)
+// Faster to iterate over all edges
+// Can be slower to lookup specific edge
+
+// Adjacency Matrix
+// Takes up more space (in sparse graphs)
+// Slower to iterate over all edges
+// Faster to lookup specific edge
+
+// WE ARE BUILDING AN UNDIRECTED GRAPH
+class Graph {
+ constructor() {
+ this.adjacencyList = {};
+ }
+ addVertex(vertex) {
+ if (!this.adjacencyList[vertex]) this.adjacencyList[vertex] = [];
+ }
+ addEdge(vertex1, vertex2) {
+ this.adjacencyList[vertex1].push(vertex2);
+ this.adjacencyList[vertex2].push(vertex1);
+ }
+ removeEdge(vertex1, vertex2) {
+ this.adjacencyList[vertex1] = this.adjacencyList[vertex1].filter(
+ (v) => v != vertex2
+ );
+ this.adjacencyList[vertex2] = this.adjacencyList[vertex2].filter(
+ (v) => v != vertex1
+ );
+ }
+ remoVertex(vertex) {
+ while (this.adjacencyList[vertex].length) {
+ let adjacentVertex = this.adjacencyList[vertex].pop();
+ this.removeEdge(vertex, adjacentVertex);
+ }
+ delete this.adjacencyList[vertex];
+ }
+ depthFirstRecursive(start) {
+ let result = [];
+ let visited = [];
+ let adjacencyList = this.adjacencyList;
+ (function dfs(vertex) {
+ if (!vertex) return null;
+ visited[vertex] = true;
+ result.push(vertex);
+ adjacencyList[vertex].forEach((neighbour) => {
+ if (!visited[neighbour]) {
+ return dfs(neighbour);
+ }
+ });
+ })(start);
+ return result;
+ }
+ depthFirstIterative(start) {
+ const stack = [start];
+ const result = [];
+ const visited = {};
+ let currentVertex;
+ visited[start] = true;
+ while (stack.length) {
+ currentVertex = stack.pop();
+ result.push(currentVertex);
+ this.adjacencyList[currentVertex].forEach((neighbor) => {
+ if (!visited[neighbor]) {
+ visited[neighbor] = true;
+ stack.push(neighbor);
+ }
+ });
+ }
+ return result;
+ }
+ breadthFirst(start) {
+ let queue = [start];
+ let result = [];
+ let visited = {};
+ let currentVertex;
+ visited[start] = true;
+ while (queue.length) {
+ currentVertex = queue.shift();
+ result.push(currentVertex);
+ this.adjacencyList[currentVertex].forEach((neighbor) => {
+ if (!visited[neighbor]) {
+ visited[neighbor] = true;
+ queue.push(neighbor);
+ }
+ });
+ }
+ return result;
+ }
+}
+
+let g = new Graph();
+// g.addVertex("Tokyo");
+// g.addVertex("Dallas");
+// g.addEdge("Tokyo", "Dallas");
+// g.removeEdge("Tokyo", "Dallas");
+// g.remoVertex("Tokyo");
+
+g.addVertex("A");
+g.addVertex("B");
+g.addVertex("C");
+g.addVertex("D");
+g.addVertex("E");
+g.addVertex("F");
+
+g.addEdge("A", "B");
+g.addEdge("A", "C");
+g.addEdge("B", "D");
+g.addEdge("C", "E");
+g.addEdge("D", "E");
+g.addEdge("D", "F");
+g.addEdge("E", "F");
+
+// depthFirstRecursive
+// A
+// / \
+// B C
+// | |
+// D --- E
+// \ /
+// F
+
+console.log(g.depthFirstRecursive("A"));
+console.log(g.breadthFirst("A"));