Kruskal's algorithm in Javascript

Kruskal's algorithm is a greedy algorithm that works as follows −

1. It Creates a set of all edges in the graph.

2. While the above set is not empty and not all vertices are covered,

  • It removes the minimum weight edge from this set
  • It checks if this edge is forming a cycle or just connecting 2 trees. If it forms a cycle, we discard this edge, else we add it to our tree.

3. When the above processing is complete, we have a minimum spanning tree.

In order to implement this algorithm, we need 2 more data structures.

First, we need a priority queue that we can use to keep the edges in a sorted order and get our required edge on each iteration.

Next, we need a disjoint set data structure. A disjoint-set data structure (also called a union-find data structure or merge–find set) is a data structure that tracks a set of elements partitioned into a number of disjoint (non-overlapping) subsets. Whenever we add a new node to a tree, we will check if they are already connected. If yes, then we have a cycle. If no, we will make a union of both vertices of the edge. This will add them to the same subset.

Let us look at the implementation of UnionFind or DisjointSet data structure &minsu;


class UnionFind {
   constructor(elements) {
      // Number of disconnected components
      this.count = elements.length;

      // Keep Track of connected components
      this.parent = {};

      // Initialize the data structure such that all
      // elements have themselves as parents
      elements.forEach(e => (this.parent[e] = e));

   union(a, b) {
      let rootA = this.find(a);
      let rootB = this.find(b);

      // Roots are same so these are already connected.
      if (rootA === rootB) return;

      // Always make the element with smaller root the parent.
      if (rootA < rootB) {
         if (this.parent[b] != b) this.union(this.parent[b], a);
         this.parent[b] = this.parent[a];
      } else {
         if (this.parent[a] != a) this.union(this.parent[a], b);
         this.parent[a] = this.parent[b];

   // Returns final parent of a node
   find(a) {
      while (this.parent[a] !== a) {
         a = this.parent[a];
      return a;

   // Checks connectivity of the 2 nodes
   connected(a, b) {
      return this.find(a) === this.find(b);

You can test this using −


let uf = new UnionFind(["A", "B", "C", "D", "E"]);
uf.union("A", "B"); uf.union("A", "C");
uf.union("C", "D");

console.log(uf.connected("B", "E"));
console.log(uf.connected("B", "D"));


This will give the output −


Now let us look at the implementation of Kruskal's algorithm using this data structure −


kruskalsMST() {
   // Initialize graph that'll contain the MST
   const MST = new Graph();
   this.nodes.forEach(node => MST.addNode(node));
   if (this.nodes.length === 0) {
      return MST;

   // Create a Priority Queue
   edgeQueue = new PriorityQueue(this.nodes.length * this.nodes.length);

   // Add all edges to the Queue:
   for (let node in this.edges) {
      this.edges[node].forEach(edge => {
         edgeQueue.enqueue([node, edge.node], edge.weight);

   let uf = new UnionFind(this.nodes);

   // Loop until either we explore all nodes or queue is empty
   while (!edgeQueue.isEmpty()) {
      // Get the edge data using destructuring
      let nextEdge = edgeQueue.dequeue();
      let nodes =;
      let weight = nextEdge.priority;

      if (!uf.connected(nodes[0], nodes[1])) {
         MST.addEdge(nodes[0], nodes[1], weight);
         uf.union(nodes[0], nodes[1]);
   return MST;

You can test this using −


let g = new Graph();

g.addEdge("A", "C", 100);
g.addEdge("A", "B", 3);
g.addEdge("A", "D", 4);
g.addEdge("C", "D", 3);
g.addEdge("D", "E", 8);
g.addEdge("E", "F", 10);
g.addEdge("B", "G", 9);
g.addEdge("E", "G", 50);



This will give the output −

A->B, D
B->A, G
D->C, A, E
E->D, F
Samual Sam
Samual Sam

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