It is a greedy algorithm in graph theory as it finds a minimal spanning tree for a connected weighted graph adding increase price arcs at each step. If the graph is not connected, then it finds a minimal spanning forest (a minimal spanning tree for each connected component).

Make a forest F (a set of trees), where each vertex in the graph is a separate tree: -make a set S containing all the edges in the graph -while S is nonempty and F is not yet spanning -remove an edge with minimal weight from Sif the removed edge connects two different trees then add it to the forest F, combine two trees into a individual treeAt the termination of the algorithm, the forest forms a minimal spanning forest of the graph.

```
/*
* Copyright (c) 2017 Kotlin Algorithm Club
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*
* The above copyright notice and this permission notice shall be included in all
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* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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* SOFTWARE.
*/
package com.algorithmexamples.graphs.undirected.weighted
import com.algorithmexamples.datastructures.DisjointSet
import com.algorithmexamples.datastructures.PriorityQueue
import com.algorithmexamples.datastructures.Queue
/**
* Kruskal's algorithm will grow a solution from the cheapest edge by adding the next cheapest edge,
* provided that it doesn't create a cycle.
*/
class KruskalMST(G: UWGraph): MST {
var weight: Double = 0.0
var edges: Queue<UWGraph.Edge> = Queue()
/**
* Compute a minimum spanning tree (or forest) of an edge-weighted graph.
* @param G the edge-weighted graph
*/
init {
val pq = PriorityQueue<UWGraph.Edge>(G.V, compareBy({ it.weight }))
for (v in G.vertices()) {
for (e in G.adjacentEdges(v)) {
pq.add(e)
}
}
val set = DisjointSet(G.V)
while (!pq.isEmpty()) {
val edge = pq.poll()
if (!set.connected(edge.v, edge.w)) {
edges.add(edge)
set.union(edge.v, edge.w)
weight += edge.weight
}
}
}
override fun edges(): Iterable<UWGraph.Edge> {
return edges
}
override fun weight(): Double {
return weight
}
}
```