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Add Prim.
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@ -69,7 +69,7 @@
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* [Dijkstra Algorithm](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/dijkstra) - finding shortest path to all graph vertices
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* [Bellman-Ford Algorithm](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/bellman-ford) - finding shortest path to all graph vertices
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* [Detect Cycle](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/detect-cycle) - for both directed and undirected graphs (DFS and Disjoint Set based versions)
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* [Prim’s Algorithm](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/prim) - finding Minimum Spanning Tree (MST)
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* [Prim’s Algorithm](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/prim) - finding Minimum Spanning Tree (MST) for weighted undirected graph
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* Kruskal’s Algorithm - finding Minimum Spanning Tree (MST)
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* Topological Sorting
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* Eulerian path, Eulerian circuit
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@ -44,3 +44,4 @@ are two possibilities of minimum spanning tree of the given graph.
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- [Minimum Spanning Tree on Wikipedia](https://en.wikipedia.org/wiki/Minimum_spanning_tree)
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- [Prim's Algorithm on Wikipedia](https://en.wikipedia.org/wiki/Prim%27s_algorithm)
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- [Prim's Algorithm on YouTube by Tushar Roy](https://www.youtube.com/watch?v=oP2-8ysT3QQ)
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- [Prim's Algorithm on YouTube by Michael Sambol](https://www.youtube.com/watch?v=cplfcGZmX7I)
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91
src/algorithms/graph/prim/__test__/prim.test.js
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src/algorithms/graph/prim/__test__/prim.test.js
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import GraphVertex from '../../../../data-structures/graph/GraphVertex';
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import GraphEdge from '../../../../data-structures/graph/GraphEdge';
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import Graph from '../../../../data-structures/graph/Graph';
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import prim from '../prim';
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describe('prim', () => {
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it('should fire an error for directed graph', () => {
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function applyPrimToDirectedGraph() {
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const graph = new Graph(true);
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prim(graph);
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}
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expect(applyPrimToDirectedGraph).toThrowError();
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});
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it('should find minimum spanning tree', () => {
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const vertexA = new GraphVertex('A');
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const vertexB = new GraphVertex('B');
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const vertexC = new GraphVertex('C');
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const vertexD = new GraphVertex('D');
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const vertexE = new GraphVertex('E');
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const vertexF = new GraphVertex('F');
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const vertexG = new GraphVertex('G');
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const edgeAB = new GraphEdge(vertexA, vertexB, 2);
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const edgeAD = new GraphEdge(vertexA, vertexD, 3);
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const edgeAC = new GraphEdge(vertexA, vertexC, 3);
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const edgeBC = new GraphEdge(vertexB, vertexC, 4);
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const edgeBE = new GraphEdge(vertexB, vertexE, 3);
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const edgeDF = new GraphEdge(vertexD, vertexF, 7);
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const edgeEC = new GraphEdge(vertexE, vertexC, 1);
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const edgeEF = new GraphEdge(vertexE, vertexF, 8);
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const edgeFG = new GraphEdge(vertexF, vertexG, 9);
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const edgeFC = new GraphEdge(vertexF, vertexC, 6);
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const graph = new Graph();
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graph
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.addEdge(edgeAB)
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.addEdge(edgeAD)
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.addEdge(edgeAC)
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.addEdge(edgeBC)
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.addEdge(edgeBE)
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.addEdge(edgeDF)
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.addEdge(edgeEC)
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.addEdge(edgeEF)
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.addEdge(edgeFC)
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.addEdge(edgeFG);
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expect(graph.getWeight()).toEqual(46);
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const minimumSpanningTree = prim(graph);
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expect(minimumSpanningTree.getWeight()).toBe(24);
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expect(minimumSpanningTree.getAllVertices().length).toBe(graph.getAllVertices().length);
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expect(minimumSpanningTree.getAllEdges().length).toBe(graph.getAllVertices().length - 1);
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expect(minimumSpanningTree.toString()).toBe('A,B,D,C,E,F,G');
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});
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it('should find minimum spanning tree for simple graph', () => {
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const vertexA = new GraphVertex('A');
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const vertexB = new GraphVertex('B');
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const vertexC = new GraphVertex('C');
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const vertexD = new GraphVertex('D');
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const edgeAB = new GraphEdge(vertexA, vertexB, 1);
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const edgeAD = new GraphEdge(vertexA, vertexD, 3);
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const edgeBC = new GraphEdge(vertexB, vertexC, 1);
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const edgeBD = new GraphEdge(vertexB, vertexD, 3);
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const edgeCD = new GraphEdge(vertexC, vertexD, 1);
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const graph = new Graph();
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graph
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.addEdge(edgeAB)
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.addEdge(edgeAD)
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.addEdge(edgeBC)
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.addEdge(edgeBD)
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.addEdge(edgeCD);
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expect(graph.getWeight()).toEqual(9);
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const minimumSpanningTree = prim(graph);
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expect(minimumSpanningTree.getWeight()).toBe(3);
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expect(minimumSpanningTree.getAllVertices().length).toBe(graph.getAllVertices().length);
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expect(minimumSpanningTree.getAllEdges().length).toBe(graph.getAllVertices().length - 1);
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expect(minimumSpanningTree.toString()).toBe('A,B,C,D');
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});
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});
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73
src/algorithms/graph/prim/prim.js
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73
src/algorithms/graph/prim/prim.js
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@ -0,0 +1,73 @@
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import Graph from '../../../data-structures/graph/Graph';
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import PriorityQueue from '../../../data-structures/priority-queue/PriorityQueue';
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/**
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* @param {Graph} graph
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* @return {Graph}
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*/
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export default function prim(graph) {
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// It should fire error if graph is directed since the algorithm works only
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// for undirected graphs.
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if (graph.isDirected) {
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throw new Error('Prim\'s algorithms works only for undirected graphs');
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}
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// Init new graph that will contain minimum spanning tree of original graph.
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const minimumSpanningTree = new Graph();
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// This priority queue will contain all the edges that are starting from
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// visited nodes and they will be ranked by edge weight - so that on each step
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// we would always pick the edge with minimal edge weight.
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const edgesQueue = new PriorityQueue();
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// Set of vertices that has been already visited.
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const visitedVertices = {};
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// Vertex from which we will start graph traversal.
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const startVertex = graph.getAllVertices()[0];
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// Add start vertex to the set of visited ones.
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visitedVertices[startVertex.getKey()] = startVertex;
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// Add all edges of start vertex to the queue.
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startVertex.getEdges().forEach((graphEdge) => {
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edgesQueue.add(graphEdge, graphEdge.weight);
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});
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// Now let's explore all queued edges.
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while (!edgesQueue.isEmpty()) {
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// Fetch next queued edge with minimal weight.
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/** @var {GraphEdge} currentEdge */
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const currentMinEdge = edgesQueue.poll();
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// Find out the next unvisited minimal vertex to traverse.
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let nextMinVertex = null;
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if (!visitedVertices[currentMinEdge.startVertex.getKey()]) {
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nextMinVertex = currentMinEdge.startVertex;
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} else if (!visitedVertices[currentMinEdge.endVertex.getKey()]) {
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nextMinVertex = currentMinEdge.endVertex;
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}
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// If all vertices of current edge has been already visited then skip this round.
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if (nextMinVertex) {
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// Add current min edge to MST.
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minimumSpanningTree.addEdge(currentMinEdge);
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// Add vertex to the set of visited ones.
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visitedVertices[nextMinVertex.getKey()] = nextMinVertex;
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// Add all current vertex's edges to the queue.
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nextMinVertex.getEdges().forEach((graphEdge) => {
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// Add only vertices that link to unvisited nodes.
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if (
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!visitedVertices[graphEdge.startVertex.getKey()] ||
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!visitedVertices[graphEdge.endVertex.getKey()]
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) {
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edgesQueue.add(graphEdge, graphEdge.weight);
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}
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});
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}
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}
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return minimumSpanningTree;
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}
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@ -110,12 +110,18 @@ export default class Graph {
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return null;
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}
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/**
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* @return {number}
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*/
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getWeight() {
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return this.getAllEdges().reduce((weight, graphEdge) => {
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return weight + graphEdge.weight;
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}, 0);
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}
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/**
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* @return {string}
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*/
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toString() {
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return Object.keys(this.vertices).toString();
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}
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@ -19,4 +19,11 @@ export default class GraphEdge {
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return `${startVertexKey}_${endVertexKey}`;
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}
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/**
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* @return {string}
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*/
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toString() {
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return this.getKey();
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}
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}
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@ -1,6 +1,9 @@
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import LinkedList from '../linked-list/LinkedList';
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export default class GraphVertex {
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/**
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* @param {*} value
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*/
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constructor(value) {
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if (value === undefined) {
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throw new Error('Graph vertex must have a value');
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@ -37,6 +40,13 @@ export default class GraphVertex {
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return edges.map(neighborsConverter);
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}
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/**
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* @return {GraphEdge[]}
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*/
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getEdges() {
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return this.edges.toArray().map(linkedListNode => linkedListNode.value);
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}
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/**
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* @param {GraphEdge} requiredEdge
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* @returns {boolean}
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@ -8,6 +8,7 @@ describe('GraphEdge', () => {
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const edge = new GraphEdge(startVertex, endVertex);
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expect(edge.getKey()).toBe('A_B');
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expect(edge.toString()).toBe('A_B');
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expect(edge.startVertex).toEqual(startVertex);
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expect(edge.endVertex).toEqual(endVertex);
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expect(edge.weight).toEqual(0);
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expect(vertex.toString()).toBe('A');
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expect(vertex.getKey()).toBe('A');
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expect(vertex.edges.toString()).toBe('');
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expect(vertex.getEdges()).toEqual([]);
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});
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it('should add edges to vertex and check if it exists', () => {
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const vertexA = new GraphVertex('A');
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const vertexB = new GraphVertex('A');
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const vertexB = new GraphVertex('B');
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const edgeAB = new GraphEdge(vertexA, vertexB);
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vertexA.addEdge(edgeAB);
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expect(vertexA.hasEdge(edgeAB)).toBeTruthy();
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expect(vertexB.hasEdge(edgeAB)).toBeFalsy();
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expect(vertexA.getEdges().length).toBe(1);
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expect(vertexA.getEdges()[0].toString()).toBe('A_B');
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});
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it('should return vertex neighbors in case if current node is start one', () => {
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