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dijkstra
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‎README.md‎

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@@ -72,6 +72,62 @@ console.log(g.V); // display 13, which is the number of vertices in g
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console.log(g.adj(0)); // display the adjacency list which are vertices directed from vertex 0
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```
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### Create undirected weighted graph
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The sample code below shows show to create undirected weighted graph:
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```javascript
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var jsgraphs = require('js-graph-algorithms');
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var g = new jsgraphs.WeightedGraph(8);
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g.addEdge(new jsgraphs.Edge(0, 7, 0.16));
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g.addEdge(new jsgraphs.Edge(2, 3, 0.17));
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g.addEdge(new jsgraphs.Edge(1, 7, 0.19));
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g.addEdge(new jsgraphs.Edge(0, 2, 0.26));
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g.addEdge(new jsgraphs.Edge(5, 7, 0.28));
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g.addEdge(new jsgraphs.Edge(1, 3, 0.29));
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g.addEdge(new jsgraphs.Edge(1, 5, 0.32));
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g.addEdge(new jsgraphs.Edge(2, 7, 0.34));
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g.addEdge(new jsgraphs.Edge(4, 5, 0.35));
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g.addEdge(new jsgraphs.Edge(1, 2, 0.36));
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g.addEdge(new jsgraphs.Edge(4, 7, 0.37));
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g.addEdge(new jsgraphs.Edge(0, 4, 0.38));
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g.addEdge(new jsgraphs.Edge(6, 2, 0.4));
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g.addEdge(new jsgraphs.Edge(3, 6, 0.52));
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g.addEdge(new jsgraphs.Edge(6, 0, 0.58));
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g.addEdge(new jsgraphs.Edge(6, 4, 0.93));
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console.log(g.V); // display 13, which is the number of vertices in g
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console.log(g.adj(0)); // display the adjacency list which are undirected edges connected to vertex 0
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```
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### Create directed weighted graph
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The sample code below shows show to create directed weighted graph:
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```javascript
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var jsgraphs = require('js-graph-algorithms');
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var g = new jsgraphs.WeightedDiGraph(8);
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g.addEdge(new jsgraphs.Edge(0, 7, 0.16));
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g.addEdge(new jsgraphs.Edge(2, 3, 0.17));
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g.addEdge(new jsgraphs.Edge(1, 7, 0.19));
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g.addEdge(new jsgraphs.Edge(0, 2, 0.26));
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g.addEdge(new jsgraphs.Edge(5, 7, 0.28));
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g.addEdge(new jsgraphs.Edge(1, 3, 0.29));
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g.addEdge(new jsgraphs.Edge(1, 5, 0.32));
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g.addEdge(new jsgraphs.Edge(2, 7, 0.34));
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g.addEdge(new jsgraphs.Edge(4, 5, 0.35));
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g.addEdge(new jsgraphs.Edge(1, 2, 0.36));
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g.addEdge(new jsgraphs.Edge(4, 7, 0.37));
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g.addEdge(new jsgraphs.Edge(0, 4, 0.38));
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g.addEdge(new jsgraphs.Edge(6, 2, 0.4));
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g.addEdge(new jsgraphs.Edge(3, 6, 0.52));
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g.addEdge(new jsgraphs.Edge(6, 0, 0.58));
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g.addEdge(new jsgraphs.Edge(6, 4, 0.93));
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console.log(g.V); // display 13, which is the number of vertices in g
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console.log(g.adj(0)); // display the adjacency list which are directed edges from vertex 0
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```
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### Depth First Search
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The sample code below show how to perform depth first search of an undirected graph
@@ -264,4 +320,39 @@ for(var i=0; i < mst.length; ++i) {
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var w = e.other(v);
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console.log('(' + v + ', ' + w + '): ' + e.weight);
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}
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```
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### Use Eager Prim algorithm to find the minimum spanning tree of a weighted graph
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The sample code below show how to obtain the minimum spanning tree from a weighted graph using Eager Prim algorithm:
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```javascript
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var jsgraphs = require('js-graph-algorithms');
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var g = new jsgraphs.WeightedGraph(8);
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g.addEdge(new jsgraphs.Edge(0, 7, 0.16));
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g.addEdge(new jsgraphs.Edge(2, 3, 0.17));
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g.addEdge(new jsgraphs.Edge(1, 7, 0.19));
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g.addEdge(new jsgraphs.Edge(0, 2, 0.26));
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g.addEdge(new jsgraphs.Edge(5, 7, 0.28));
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g.addEdge(new jsgraphs.Edge(1, 3, 0.29));
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g.addEdge(new jsgraphs.Edge(1, 5, 0.32));
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g.addEdge(new jsgraphs.Edge(2, 7, 0.34));
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g.addEdge(new jsgraphs.Edge(4, 5, 0.35));
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g.addEdge(new jsgraphs.Edge(1, 2, 0.36));
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g.addEdge(new jsgraphs.Edge(4, 7, 0.37));
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g.addEdge(new jsgraphs.Edge(0, 4, 0.38));
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g.addEdge(new jsgraphs.Edge(6, 2, 0.4));
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g.addEdge(new jsgraphs.Edge(3, 6, 0.52));
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g.addEdge(new jsgraphs.Edge(6, 0, 0.58));
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g.addEdge(new jsgraphs.Edge(6, 4, 0.93));
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var prim = new jsgraphs.EagerPrimMST(g);
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var mst = prim.mst;
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for(var i=0; i < mst.length; ++i) {
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var e = mst[i];
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var v = e.either();
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var w = e.other(v);
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console.log('(' + v + ', ' + w + '): ' + e.weight);
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}
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```

‎src/jsgraphs.js‎

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@@ -437,6 +437,19 @@ var jsgraphs = jsgraphs || {};
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jss.WeightedGraph = WeightedGraph;
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var WeightedDiGraph = function(V) {
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WeightedGraph.call(this, V);
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};
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WeightedDiGraph.prototype = Object.create(jss.WeightedGraph.prototype);
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WeightedDiGraph.prototype.addEdge = function(e) {
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var v = e.from();
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this.adjList[v].push(e);
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};
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jss.WeightedDiGraph = WeightedDiGraph;
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var DepthFirstSearch = function(G, s) {
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this.s = s;
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var V = G.V;
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};
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jss.EagerPrimMST = EagerPrimMST;
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var Dijkstra = function(G, s) {
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var V = G.V;
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this.s = s;
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this.marked = [];
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this.edgeTo = [];
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this.cost = [];
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this.pq = new jss.IndexMinPQ(V, function(cost1, cost2){
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return cost1, cost2;
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});
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for(var v =0; v < V; ++v){
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this.marked.push(false);
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this.edgeTo.push(null);
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this.cost.push(Number.MAX_VALUE);
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}
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this.cost[s] = 0;
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this.pq.insert(s, this.cost[s]);
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while(!this.pq.isEmpty()) {
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var v = this.pq.delMin();
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this.marked[v] = true;
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var adj_v = G.adj(v);
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for(var i = 0; i < adj_v.length; ++i) {
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var e = adj_v[i];
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this.relax(e);
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}
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}
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};
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Dijkstra.prototype.relax = function(e) {
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var v = e.from();
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var w = e.to();
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if(this.cost[w] > this.cost[v] + e.weight) {
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this.cost[w] = this.cost[v] + e.weight;
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this.edgeTo[w] = e;
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if(this.pq.containsIndex(w)){
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this.pq.decreaseKey(w, this.cost[w]);
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} else {
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this.pq.insert(w, this.cost[w]);
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}
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}
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};
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Dijkstra.prototype.hasPathTo = function(v) {
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return this.marked[v];
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};
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Dijkstra.prototype.pathTo = function(v) {
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var path = new jss.Stack();
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for(var x = v; x != this.s; x = this.edgeTo[x].from()) {
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path.push(this.edgeTo[x]);
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}
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return path.toArray();
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};
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Dijkstra.prototype.distanceTo = function(v) {
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return this.cost[v];
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};
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jss.Dijkstra = Dijkstra;
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})(jsgraphs);
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‎test/dijkstra-spec.js‎

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var expect = require('chai').expect;
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var jsgraphs = require('../src/jsgraphs');
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describe('Dijkstra', function(){
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it('should get shortest path from Weigthed Directed Graph', function(){
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var g = new jsgraphs.WeightedDiGraph(8);
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g.addEdge(new jsgraphs.Edge(0, 1, 5.0));
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g.addEdge(new jsgraphs.Edge(0, 4, 9.0));
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g.addEdge(new jsgraphs.Edge(0, 7, 8.0));
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g.addEdge(new jsgraphs.Edge(1, 2, 12.0));
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g.addEdge(new jsgraphs.Edge(1, 3, 15.0));
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g.addEdge(new jsgraphs.Edge(1, 7, 4.0));
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g.addEdge(new jsgraphs.Edge(2, 3, 3.0));
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g.addEdge(new jsgraphs.Edge(2, 6, 11.0));
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g.addEdge(new jsgraphs.Edge(3, 6, 9.0));
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g.addEdge(new jsgraphs.Edge(4, 5, 5.0));
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g.addEdge(new jsgraphs.Edge(4, 6, 20.0));
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g.addEdge(new jsgraphs.Edge(4, 7, 5.0));
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g.addEdge(new jsgraphs.Edge(5, 2, 1.0));
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g.addEdge(new jsgraphs.Edge(5, 6, 13.0));
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g.addEdge(new jsgraphs.Edge(7, 5, 6.0));
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g.addEdge(new jsgraphs.Edge(7, 2, 7.0));
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expect(g.V).to.equal(8);
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var edgeCount = 0;
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for(var v = 0; v < g.V; ++v){
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var adj_v = g.adj(v);
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edgeCount += adj_v.length;
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}
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expect(edgeCount).to.equal(16);
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var dijkstra = new jsgraphs.Dijkstra(g, 0);
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for(var v = 1; v < g.V; ++v){
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if(dijkstra.hasPathTo(v)){
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var path = dijkstra.pathTo(v);
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console.log('=====path from 0 to ' + v + ' start==========');
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for(var i = 0; i < path.length; ++i) {
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var e = path[i];
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console.log(e.from() + ' => ' + e.to() + ': ' + e.weight);
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}
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console.log('=====path from 0 to ' + v + ' end==========');
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console.log('=====distance: ' + dijkstra.distanceTo(v) + '=========');
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}
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}
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});
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});

‎test/weighted-digraph-spec.js‎

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var expect = require('chai').expect;
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var jsgraphs = require('../src/jsgraphs');
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describe('Weigthed Directed Graph', function(){
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it('should be weighted and directed', function(){
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var g = new jsgraphs.WeightedDiGraph(8);
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g.addEdge(new jsgraphs.Edge(0, 1, 5.0));
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g.addEdge(new jsgraphs.Edge(0, 4, 9.0));
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g.addEdge(new jsgraphs.Edge(0, 7, 8.0));
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g.addEdge(new jsgraphs.Edge(1, 2, 12.0));
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g.addEdge(new jsgraphs.Edge(1, 3, 15.0));
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g.addEdge(new jsgraphs.Edge(1, 7, 4.0));
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g.addEdge(new jsgraphs.Edge(2, 3, 3.0));
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g.addEdge(new jsgraphs.Edge(2, 6, 11.0));
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g.addEdge(new jsgraphs.Edge(3, 6, 9.0));
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g.addEdge(new jsgraphs.Edge(4, 5, 5.0));
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g.addEdge(new jsgraphs.Edge(4, 6, 20.0));
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g.addEdge(new jsgraphs.Edge(4, 7, 5.0));
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g.addEdge(new jsgraphs.Edge(5, 2, 1.0));
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g.addEdge(new jsgraphs.Edge(5, 6, 13.0));
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g.addEdge(new jsgraphs.Edge(7, 5, 6.0));
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g.addEdge(new jsgraphs.Edge(7, 2, 7.0));
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expect(g.V).to.equal(8);
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var edgeCount = 0;
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for(var v = 0; v < g.V; ++v){
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var adj_v = g.adj(v);
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edgeCount += adj_v.length;
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}
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expect(edgeCount).to.equal(16);
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});
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});

‎test/weighted-graph-spec.js‎

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expect(found).to.equal(true);
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}
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var edgeCount = 0;
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for (var v = 0; v < g.V; ++v) {
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edgeCount+=g.adj(v).length;
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}
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expect(edgeCount).to.equal(32);
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});
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});
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