Prim MST Algorithm
The Prim's Minimum Spanning Tree (MST) Algorithm is a greedy algorithm that is used to find the minimum spanning tree of a connected, undirected graph with weighted edges. The primary purpose of the minimum spanning tree is to connect all the vertices in the graph in such a way that the total weight of the edges is minimized. Prim's algorithm was developed by Czech mathematician Vojtěch Jarník in 1930 and later rediscovered and popularized by American computer scientist Robert C. Prim in 1957.
The Prim's MST algorithm starts with an arbitrary vertex in the graph, and then it grows the tree by iteratively choosing the smallest weighted edge that connects a vertex in the tree to a vertex not in the tree. The algorithm maintains a priority queue or a set data structure to store the candidate edges and selects the minimum weight edge from this set. The process is repeated until all the vertices are included in the tree, thus forming a minimum spanning tree. One of the advantages of Prim's algorithm is its simplicity and ease of implementation using adjacency lists or adjacency matrices, making it a popular choice for solving real-world network design problems.
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package com.algorithmexamples.graphs.undirected.weighted
import com.algorithmexamples.datastructures.IndexedPriorityQueue
import com.algorithmexamples.datastructures.Queue
class PrimMST(G: UWGraph): MST {
var weight: Double = 0.0
var edges: Queue<UWGraph.Edge> = Queue()
/**
* distTo[v] = distance of shortest s->v path
*/
private val distTo: DoubleArray = DoubleArray(G.V) { Double.POSITIVE_INFINITY }
/**
* edgeTo[v] = last edge on shortest s->v path
*/
private val edgeTo: Array<UWGraph.Edge?> = arrayOfNulls(G.V)
/**
* priority queue of vertices
*/
private val pq: IndexedPriorityQueue<Double> = IndexedPriorityQueue(G.V)
private val visited = Array(G.V) { false }
init {
for (s in G.vertices()) {
if (!visited[s]) {
distTo[s] = 0.0
pq.insert(s, 0.0)
while (!pq.isEmpty()) {
val v = pq.poll().first
visited[v] = true
for (e in G.adjacentEdges(v)) {
scan(e, v)
}
}
}
}
for (v in edgeTo.indices) {
val e = edgeTo[v]
if (e != null) {
edges.add(e)
weight += e.weight
}
}
}
private fun scan(e: UWGraph.Edge, v: Int) {
val w = e.other(v)
if (!visited[w]) { // v-w is obsolete edge
if (e.weight < distTo[w]) {
distTo[w] = e.weight
edgeTo[w] = e
if (pq.contains(w)) {
pq.decreaseKey(w, distTo[w])
} else {
pq.insert(w, distTo[w])
}
}
}
}
override fun edges(): Iterable<UWGraph.Edge> {
return edges
}
override fun weight(): Double {
return weight
}
}
