add kruskal algorithm

Author: Gerhut

algorithm/category.json

@@ -13,7 +13,8 @@
   "mst": {
     "name": "Minimum Spanning Tree",
     "list": {
-      "prim": "Prim's Algorithm"
+      "prim": "Prim's Algorithm",
+      "kruskal": "Kruskal's Algorithm"
     }
   },
   "search": {

algorithm/mst/kruskal/desc.json

@@ -0,0 +1,14 @@
+{
+  "Kruskal's Algorithm": "Greedy algorithm that finds a minimum spanning tree for a weighted undirected graph.",
+  "Applications": [
+  ],
+  "Complexity": {
+    "time": "worst O(E log(E))"
+  },
+  "References": [
+    "<a href='https://en.wikipedia.org/wiki/Kruskal%27s_algorithm'>Wikipedia</a>"
+  ],
+  "files": {
+    "normal": "Finds minimum spanning tree of a given graph."
+  }
+}

algorithm/mst/kruskal/normal/code.js

@@ -0,0 +1,50 @@
+function kruskal () {
+  var vcount = G.length;
+
+  // Preprocess: sort edges by weight.
+  var edges = [];
+  for (var vi = 0; vi < vcount - 1; vi++) {
+    for (var vj = vi + 1; vj < vcount; vj++) {
+      edges.push({
+        0: vi,
+        1: vj,
+        weight: G[vi][vj]
+      });
+    }
+  }
+  edges.sort(function (ei, ej) { return ei.weight - ej.weight });
+
+  // Give each vertex a tree to decide if they are already in the same tree.
+  var t = [];
+  for (var i = 0; i < vcount; i++) {
+    t[i] = {};
+    t[i][i] = true;
+  }
+
+  var wsum = 0;
+  for (var n = 0; n < vcount - 1 && edges.length > 0;) {
+    var e = edges.shift(); // Get the edge of min weight
+    tracer._visit(e[0], e[1]);
+    if (t[e[0]] === t[e[1]]) {
+      // e[0] & e[1] already in the same tree, ignore
+      tracer._leave(e[0], e[1]);
+      continue;
+    }
+
+    // Choose the current edge.
+    wsum += e.weight;
+
+    // Merge tree of e[0] & e[1]
+    var tmerged = {};
+    for (i in t[e[0]]) tmerged[i] = true;
+    for (i in t[e[1]]) tmerged[i] = true;
+    for (i in tmerged) t[i] = tmerged;
+
+    n += 1;
+  }
+
+  tracer._print("The sum of all edges is: " + wsum);
+}
+
+tracer._pace(500);
+kruskal();

algorithm/mst/kruskal/normal/data.js

@@ -0,0 +1,10 @@
+var tracer = new WeightedUndirectedGraphTracer();
+/*var G = [ // G[i][j] indicates the weight of the path from the i-th node to the j-th node
+ [0, 3, 0, 1, 0],
+ [5, 0, 1, 2, 4],
+ [1, 0, 0, 2, 0],
+ [0, 2, 0, 0, 1],
+ [0, 1, 3, 0, 0]
+ ];*/
+var G = WeightedUndirectedGraph.random(5, 1, 1, 9);
+tracer._setData(G);