From 2f90ba9cfb1434179d3e9cefe7d868111d3e0d4a Mon Sep 17 00:00:00 2001
From: Mauro Bringolf <mauro@webkinder.ch>
Date: Tue, 15 Aug 2017 14:37:35 +0200
Subject: [PATCH] Raw implementation and test case from wikipedia

---
 src/graphs/spanning-trees/kruskal.js       | 81 ++++++++++++++++++++++
 test/graphs/spanning-trees/kruskal.spec.js | 53 ++++++++++++++
 2 files changed, 134 insertions(+)
 create mode 100644 src/graphs/spanning-trees/kruskal.js
 create mode 100644 test/graphs/spanning-trees/kruskal.spec.js

diff --git a/src/graphs/spanning-trees/kruskal.js b/src/graphs/spanning-trees/kruskal.js
new file mode 100644
index 00000000..20e031d3
--- /dev/null
+++ b/src/graphs/spanning-trees/kruskal.js
@@ -0,0 +1,81 @@
+// Kruskal's algorithm for minimal spanning tree implemented with the UnionFind datastructure.
+
+(function(exports) {
+  'use strict';
+
+  var QuickUnion = require('../../sets/quickunion').QuickUnion;
+  var mergeSort = require('../../sorting/mergesort').mergeSort;
+  exports.Vertex = require('../../data-structures/vertex').Vertex;
+  exports.Edge = require('../../data-structures/edge').Edge;
+
+  exports.Graph = function (edges) {
+    this.edges = edges || [];
+  }
+
+  exports.Graph.prototype.kruskal = (function () {
+    var qunion;
+    var spanningTree;
+    var indexes;
+
+    /**
+     * Used for sorting the edges
+     *
+     * @private
+     * @param {Vertex} a First operand of the comparison.
+     * @param {Vertex} b Second operand of the comparison.
+     * @return {number} Number which which is equal, greater or
+     *  less then zero and indicates whether the first vertex is
+     *  "smaller" than the second.
+     */
+    function compareEdges(a, b) {
+      return a.distance - b.distance;
+    }
+
+    /**
+     * Initialize the algorithm.
+     *
+     * @private
+     */
+    function init() {
+      var edge;
+      var i = 0;
+
+      mergeSort(this.edges, compareEdges);
+      spanningTree = [];
+      indexes = {};
+
+      // Create links from vertices to QuickUnion elements
+      for (edge of this.edges) {
+        if (!(edge.from.id in indexes)) {
+          indexes[edge.from.id] = i;
+          i += 1;
+        }
+        if (!(edge.to.id in indexes)) {
+          indexes[edge.to.id] = i;
+          i += 1;
+        }
+      }
+
+      qunion = new QuickUnion(i);
+    }
+
+    return function () {
+      init.call(this);
+
+      var edge;
+
+      for (edge of this.edges) {
+        var from = indexes[edge.from.id];
+        var to = indexes[edge.to.id];
+        if (!qunion.connected(from, to)) {
+          qunion.union(from, to);
+          spanningTree.push(edge);
+        }
+      }
+
+      return new exports.Graph(spanningTree);
+    }
+
+  })();
+
+})(typeof window === 'undefined' ? module.exports : window);
diff --git a/test/graphs/spanning-trees/kruskal.spec.js b/test/graphs/spanning-trees/kruskal.spec.js
new file mode 100644
index 00000000..f3094b95
--- /dev/null
+++ b/test/graphs/spanning-trees/kruskal.spec.js
@@ -0,0 +1,53 @@
+var kruskal = require('../../../src/graphs/spanning-trees/kruskal');
+
+describe('Kruskal', function() {
+  'use strict';
+
+  it('should define a function', function () {
+    expect(kruskal).toBeDefined();
+    expect(typeof kruskal).toBe('object');
+    expect(typeof kruskal.Graph).toBe('function');
+    expect(typeof kruskal.Edge).toBe('function');
+    expect(typeof kruskal.Vertex).toBe('function');
+  });
+
+  it('should work with an empty graph', function() {
+    var graph = new kruskal.Graph([], 0);
+    var spanningTree = graph.kruskal();
+
+    expect(spanningTree.edges.length).toEqual(0);
+  });
+
+  it('should correctly compute general example', function() {
+    var nodes = [];
+    var edges = [];
+    var i;
+    for (i = 0; i < 7; i += 1) {
+      nodes[i] = new kruskal.Vertex(i);
+    }
+
+    edges.push(new kruskal.Edge(nodes[0], nodes[1], 7));
+    edges.push(new kruskal.Edge(nodes[1], nodes[2], 8));
+    edges.push(new kruskal.Edge(nodes[2], nodes[4], 5));
+    edges.push(new kruskal.Edge(nodes[4], nodes[6], 9));
+    edges.push(new kruskal.Edge(nodes[5], nodes[6], 11));
+    edges.push(new kruskal.Edge(nodes[3], nodes[5], 6));
+    edges.push(new kruskal.Edge(nodes[0], nodes[3], 5));
+    edges.push(new kruskal.Edge(nodes[1], nodes[4], 7));
+    edges.push(new kruskal.Edge(nodes[1], nodes[3], 9));
+    edges.push(new kruskal.Edge(nodes[3], nodes[4], 15));
+    edges.push(new kruskal.Edge(nodes[4], nodes[5], 8));
+
+    var graph = new kruskal.Graph(edges);
+    var spanningTree = graph.kruskal();
+
+    expect(spanningTree.edges.length).toEqual(6);
+
+    var sum = spanningTree.edges.reduce(function(acc, edge) {
+      return acc += edge.distance;
+    }, 0);
+
+    expect(sum).toEqual(39);
+
+  })
+});