Merge 7dfa081 into a2d30b0

algorithms/graph/prim.js

@@ -0,0 +1,55 @@
+'use strict';
+
+var PriorityQueue = require('../../data_structures/priority_queue'),
+    Graph = require('../../data_structures/graph');
+
+
+/**
+ * Prim's minimum spanning tree (forest) algorithm.
+ * Complexity: O(E * log(V)).
+ *
+ * @param {Graph} graph - Undirected graph.
+ * @return {Graph} Minimum spanning tree or forest
+ *   (depending on whether input graph is connected itself).
+ */
+var prim = function (graph) {
+  if (graph.directed) {
+    throw new Error('Can\'t build MST of a directed graph.');
+  }
+
+  var mst = new Graph(false);
+  var parent = Object.create(null);
+
+  var q = new PriorityQueue();
+  graph.vertices.forEach(function (vertex) {
+    q.insert(vertex, Infinity);
+  });
+
+  /* jshint loopfunc: true */
+  while (!q.isEmpty()) {
+    var top = q.extract(true);
+    var vertex = top.item,
+        weight = top.priority;
+
+    if (parent[vertex]) {
+      mst.addEdge(parent[vertex], vertex, weight);
+    }
+    else {
+      mst.addVertex(vertex);
+    }
+
+    // Relax.
+    graph.neighbors(vertex).forEach(function (neighbor) {
+      var weight = graph.edge(vertex, neighbor);
+      if (weight < q.priority(neighbor)) {
+        q.changePriority(neighbor, weight);
+        parent[neighbor] = vertex;
+      }
+    });
+  }
+
+  return mst;
+};
+
+
+module.exports = prim;

data_structures/priority_queue.js

@@ -33,9 +33,13 @@ PriorityQueue.prototype.insert = function (item, priority) {
   MinHeap.prototype.insert.call(this, o);
 };
 
-PriorityQueue.prototype.extract = function () {
+PriorityQueue.prototype.extract = function (withPriority) {
   var min = MinHeap.prototype.extract.call(this);
-  return min && min.item;
+  return withPriority ? min : min && min.item;
+};
+
+PriorityQueue.prototype.priority = function (item) {
+  return this._items[item].priority;
 };
 
 PriorityQueue.prototype.changePriority = function (item, priority) {

main.js

@@ -11,6 +11,7 @@ var lib = {
     kruskal: require('./algorithms/graph/kruskal'),
     breadthFirstSearch: require('./algorithms/graph/breadth_first_search'),
     bfsShortestPath: require('./algorithms/graph/bfs_shortest_path'),
+    prim: require('./algorithms/graph/prim'),
   },
   Math: {
     fibonacci: require('./algorithms/math/fibonacci'),

test/algorithms/graph/minimum_spanning_tree.js

@@ -1,6 +1,7 @@
 'use strict';
 
 var kruskal = require('../../../algorithms/graph/kruskal'),
+    prim = require('../../../algorithms/graph/prim'),
     Graph = require('../../../data_structures/graph'),
     depthFirstSearch = require('../../../algorithms/graph/depth_first_search'),
     assert = require('assert');
@@ -179,4 +180,5 @@ var testMstAlgorithm = function (mst) {
 
 describe('Minimum Spanning Tree', function () {
   describe('#Kruskal\'s Algorithm', testMstAlgorithm.bind(null, kruskal));
+  describe('#Prim\'s Algorithm', testMstAlgorithm.bind(null, prim));
 });