From 92a084895f595bef4351654a32353a57686fadea Mon Sep 17 00:00:00 2001
From: Adithya Anilkumar <adithyaanilkumar1@gmail.com>
Date: Sat, 30 Oct 2021 19:29:30 +0530
Subject: [PATCH] added kruskal

---
 Javascript/graph/kruskal.js | 62 +++++++++++++++++++++++++++++++++++++
 1 file changed, 62 insertions(+)
 create mode 100644 Javascript/graph/kruskal.js

diff --git a/Javascript/graph/kruskal.js b/Javascript/graph/kruskal.js
new file mode 100644
index 0000000..296616a
--- /dev/null
+++ b/Javascript/graph/kruskal.js
@@ -0,0 +1,62 @@
+import Graph from '../../../data-structures/graph/Graph';
+import QuickSort from '../../sorting/quick-sort/QuickSort';
+import DisjointSet from '../../../data-structures/disjoint-set/DisjointSet';
+
+/**
+ * @param {Graph} graph
+ * @return {Graph}
+ */
+export default function kruskal(graph) {
+  // It should fire error if graph is directed since the algorithm works only
+  // for undirected graphs.
+  if (graph.isDirected) {
+    throw new Error('Kruskal\'s algorithms works only for undirected graphs');
+  }
+
+  // Init new graph that will contain minimum spanning tree of original graph.
+  const minimumSpanningTree = new Graph();
+
+  // Sort all graph edges in increasing order.
+  const sortingCallbacks = {
+    /**
+     * @param {GraphEdge} graphEdgeA
+     * @param {GraphEdge} graphEdgeB
+     */
+    compareCallback: (graphEdgeA, graphEdgeB) => {
+      if (graphEdgeA.weight === graphEdgeB.weight) {
+        return 1;
+      }
+
+      return graphEdgeA.weight <= graphEdgeB.weight ? -1 : 1;
+    },
+  };
+  const sortedEdges = new QuickSort(sortingCallbacks).sort(graph.getAllEdges());
+
+  // Create disjoint sets for all graph vertices.
+  const keyCallback = (graphVertex) => graphVertex.getKey();
+  const disjointSet = new DisjointSet(keyCallback);
+
+  graph.getAllVertices().forEach((graphVertex) => {
+    disjointSet.makeSet(graphVertex);
+  });
+
+  // Go through all edges started from the minimum one and try to add them
+  // to minimum spanning tree. The criteria of adding the edge would be whether
+  // it is forms the cycle or not (if it connects two vertices from one disjoint
+  // set or not).
+  for (let edgeIndex = 0; edgeIndex < sortedEdges.length; edgeIndex += 1) {
+    /** @var {GraphEdge} currentEdge */
+    const currentEdge = sortedEdges[edgeIndex];
+
+    // Check if edge forms the cycle. If it does then skip it.
+    if (!disjointSet.inSameSet(currentEdge.startVertex, currentEdge.endVertex)) {
+      // Unite two subsets into one.
+      disjointSet.union(currentEdge.startVertex, currentEdge.endVertex);
+
+      // Add this edge to spanning tree.
+      minimumSpanningTree.addEdge(currentEdge);
+    }
+  }
+
+  return minimumSpanningTree;
+}