package algo.graph;
import ds.graph.Edge;
import ds.graph.WeightedGraph;
import java.util.*;
/**
* Created by sherxon on 3/31/17.
*/
/**
* This is Prim's greedy Minimum Spanning Tree algorithm which can be used in connected weighted graphs.
* Algorithms starts building MST by randomly choosing one vertex. Then, we add least weighted edge from already
* selected vertices and add its adjacent vertex to tree if it is not already in the tree.
* Running time is O(V^2). It can be done O(E+ V logV) by using Fibonacci heap.
*/
public class PrimsMST {
private WeightedGraph graph;
public PrimsMST(WeightedGraph graph) {
this.graph = graph;
}
public List<Edge> getMST() {
List<Edge> list = new ArrayList<>();
Integer start = getRandomVertex();
if (start == null) return list;
Set<Integer> mst = new HashSet<>();
PriorityQueue<Edge> q = new PriorityQueue<>();
mst.add(start);
q.addAll(graph.getEdges(start));
while (!q.isEmpty()) {
Edge minEdge = q.remove(); // get min weighted edge
Integer vertex = minEdge.getTo();
if (mst.contains(vertex)) continue; // if it is already in the MST tree, ignore it
q.addAll(graph.getEdges(vertex));
list.add(minEdge);
mst.add(vertex); // add this vertex to mst
}
return list;
}
/**
* we can start any from any random vertex
* */
private Integer getRandomVertex() {
if (graph.getVertices().size() > 0)
return graph.getVertices().iterator().next();
return null;
}
}