Borůvka's algorithm is a greedy algorithm for finding a minimal spanning tree in a graph, or a minimal spanning forest in the case of a graph that is not connected. The algorithm was rediscovered by Choquet in 1938; again by Florek, Łukasiewicz, Perkal, Steinhaus, and Zubrzycki in 1951; and again by Georges Sollin in 1965.

COMING SOON!

```
/*
* Copyright (c) 2017 Kotlin Algorithm Club
*
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* of this software and associated documentation files (the "Software"), to deal
* in the Software without restriction, including without limitation the rights
* to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
* copies of the Software, and to permit persons to whom the Software is
* furnished to do so, subject to the following conditions:
*
* The above copyright notice and this permission notice shall be included in all
* copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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* SOFTWARE.
*/
package com.algorithmexamples.graphs.undirected.weighted
import com.algorithmexamples.datastructures.DisjointSet
import com.algorithmexamples.datastructures.Queue
class BoruvkaMST(G: UWGraph): MST {
var weight: Double = 0.0
var edges: Queue<UWGraph.Edge> = Queue()
init {
val uf = DisjointSet(G.V)
// repeat at most log V times or until we have V-1 edges
var t = 1
while (t < G.V && edges.size < G.V - 1) {
// foreach tree in forest, find closest edge
// if edge weights are equal, ties are broken in favor of first edge in G.edges()
val closest = arrayOfNulls<UWGraph.Edge>(G.V)
for (e in G.edges()) {
val v = e.v
val w = e.w
val i = uf.find(v)
val j = uf.find(w)
if (i == j) continue // same tree
if (closest[i] == null || e < closest[i]!!) closest[i] = e
if (closest[j] == null || e < closest[j]!!) closest[j] = e
}
// add newly discovered edges to MST
for (i in 0 until G.V) {
val e = closest[i]
if (e != null) {
val v = e.v
val w = e.w
// don't add the same edge twice
if (!uf.connected(v, w)) {
edges.add(e)
weight += e.weight
uf.union(v, w)
}
}
}
t += t
}
}
override fun edges(): Iterable<UWGraph.Edge> {
return edges
}
override fun weight(): Double {
return weight
}
}
```