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chen0040chen0040
committedMay 26, 2017
kruskal
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Diff for: ‎README.md

+35
Original file line numberDiff line numberDiff line change
@@ -194,4 +194,39 @@ console.log(scc.componentCount()); // display 5
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for (var v = 0; v < graph.V; ++v) {
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console.log('id[' + v + ']: ' + scc.componentId(v));
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}
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```
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### Use Kruskal 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 Kruskal algorithm:
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```javascript
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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 kruskal = new jsgraphs.KruskalMST(g);
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var mst = kruskal.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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```

Diff for: ‎src/jsgraphs.js

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Original file line numberDiff line numberDiff line change
@@ -1,6 +1,17 @@
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var jsgraphs = jsgraphs || {};
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(function(jss){
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jss.less = function(a1, a2, compare) {
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return compare(a1, a2) < 0;
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};
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jss.exchange = function(a, i, j) {
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var temp = a[i];
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a[i] = a[j];
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a[j] = temp;
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};
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var StackNode = function (value) {
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this.value = value;
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this.next = null;
@@ -133,6 +144,102 @@ var jsgraphs = jsgraphs || {};
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jss.Queue = Queue;
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var MinPQ = function(compare) {
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this.s = [];
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this.N = 0;
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if(!compare) {
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compare = function(a1, a2) {
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return a1 - a2;
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};
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}
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this.compare = compare;
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};
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MinPQ.prototype.enqueue = function(item) {
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while(this.s.lengh <= this.N+1) {
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this.s.push(0);
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}
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this.s[++this.N] = item;
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this.swim(this.N);
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};
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MinPQ.prototype.swim = function(k) {
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while (k > 1){
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var parent = Math.floor(k / 2);
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if(jss.less(this.s[k], this.s[parent], this.compare)){
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jss.exchange(this.s, k, parent);
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k = parent;
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} else {
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break;
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}
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}
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};
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MinPQ.prototype.delMin = function() {
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if(this.N == 0) {
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return undefined;
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}
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var item = this.s[1];
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jss.exchange(this.s, 1, this.N--);
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this.sink(1);
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return item;
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};
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MinPQ.prototype.sink = function(k) {
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while(k * 2 <= this.N) {
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var child = 2 * k;
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if(child < this.N && jss.less(this.s[child+1], this.s[child], this.compare)){
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child++;
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}
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if(jss.less(this.s[child], this.s[k], this.compare)){
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jss.exchange(this.s, child, k);
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k = child;
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} else {
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break;
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}
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}
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};
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MinPQ.prototype.size = function(){
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return this.N;
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};
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MinPQ.prototype.isEmpty = function() {
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return this.N == 0;
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};
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jss.MinPQ = MinPQ;
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var QuickUnion = function(V) {
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this.id = [];
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for (var v = 0; v < V; ++v) {
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this.id.push(v);
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}
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};
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QuickUnion.prototype.union = function(v, w) {
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var q = this.root(v);
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var p = this.root(w);
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if(p != q) {
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this.id[p] = q;
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}
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};
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QuickUnion.prototype.root = function(q) {
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while(this.id[q] != q) {
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q = this.id[q];
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}
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return q;
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};
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QuickUnion.prototype.connected = function(v, w) {
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return this.root(v) == this.root(w);
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};
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jss.QuickUnion = QuickUnion;
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var Graph = function (V) {
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this.V = V;
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this.adjList = [];
@@ -433,6 +540,41 @@ var jsgraphs = jsgraphs || {};
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};
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jss.StronglyConnectedComponents = StronglyConnectedComponents;
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var KruskalMST = function(G) {
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var V = G.V;
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var pq = new jss.MinPQ(function(e1, e2){
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return e1.weight - e2.weight;
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});
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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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for (var i = 0; i < adj_v.length; ++i) {
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var e = adj_v[i];
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if(e.either() != v) {
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continue;
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}
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pq.enqueue(e);
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}
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}
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this.mst = [];
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var uf = new jss.QuickUnion(V);
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while (!pq.isEmpty() && this.mst.length < V-1) {
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var e = pq.delMin();
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var v = e.either();
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var w = e.other(v);
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if(!uf.connected(v, w)){
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uf.union(v, w);
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this.mst.push(e);
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}
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}
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};
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jss.KruskalMST = KruskalMST;
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})(jsgraphs);
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Diff for: ‎test/kruskal-spec.js

+34
Original file line numberDiff line numberDiff line change
@@ -0,0 +1,34 @@
1+
var expect = require('chai').expect;
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var jsgraphs = require('../src/jsgraphs');
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describe('Kruskal Minimum Spanning Tree', function(){
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it('should generate the minimum spanning tree', function(){
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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 kruskal = new jsgraphs.KruskalMST(g);
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var mst = kruskal.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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});
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});

Diff for: ‎test/min-pq-spec.js

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@@ -0,0 +1,26 @@
1+
var expect = require('chai').expect;
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var jsgraphs = require('../src/jsgraphs');
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describe('MinPQ', function(){
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it('should function as min priority queue', function(){
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var pq = new jsgraphs.MinPQ();
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pq.enqueue(10);
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pq.enqueue(9);
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pq.enqueue(7);
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pq.enqueue(8);
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pq.enqueue(3);
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pq.enqueue(4);
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pq.enqueue(5);
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pq.enqueue(2);
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pq.enqueue(1);
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pq.enqueue(6);
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expect(pq.isEmpty()).to.equal(false);
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for( var i = 1; i <= 10; ++i) {
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expect(pq.delMin()).to.equal(i);
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expect(pq.size()).to.equal(10 - i);
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}
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expect(pq.isEmpty()).to.equal(true);
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});
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});

Diff for: ‎test/quick-union-spec.js

+14
Original file line numberDiff line numberDiff line change
@@ -0,0 +1,14 @@
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var expect = require('chai').expect;
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var jsgraphs = require('../src/jsgraphs');
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describe('Quick Union', function(){
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it('should work as union find', function(){
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var uf = new jsgraphs.QuickUnion(10);
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expect(uf.connected(0, 3)).to.equal(false);
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uf.union(0, 3);
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expect(uf.connected(0, 3)).to.equal(true);
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uf.union(0, 7);
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expect(uf.connected(0, 7)).to.equal(true);
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expect(uf.connected(3, 7)).to.equal(true);
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});
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});

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