62 lines
2.0 KiB
Java
62 lines
2.0 KiB
Java
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package com.jwetherell.algorithms.graph;
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import java.util.ArrayList;
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import java.util.HashSet;
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import java.util.List;
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import java.util.PriorityQueue;
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import java.util.Queue;
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import java.util.Set;
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import com.jwetherell.algorithms.data_structures.Graph;
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/**
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* Prim's minimum spanning tree. Only works on undirected graphs. It finds a
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* subset of the edges that forms a tree that includes every vertex, where the
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* total weight of all the edges in the tree is minimized.
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*
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* https://en.wikipedia.org/wiki/Prim%27s_algorithm
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*
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* @author Justin Wetherell <phishman3579@gmail.com>
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*/
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public class Prim {
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private Prim() { }
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public static Graph.CostPathPair<Integer> getMinimumSpanningTree(Graph<Integer> graph, Graph.Vertex<Integer> start) {
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if (graph == null)
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throw (new NullPointerException("Graph must be non-NULL."));
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// Prim's algorithm only works on undirected graphs
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if (graph.getType() == Graph.TYPE.DIRECTED)
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throw (new IllegalArgumentException("Undirected graphs only."));
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int cost = 0;
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final Set<Graph.Vertex<Integer>> unvisited = new HashSet<Graph.Vertex<Integer>>();
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unvisited.addAll(graph.getVertices());
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unvisited.remove(start); // O(1)
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final List<Graph.Edge<Integer>> path = new ArrayList<Graph.Edge<Integer>>();
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final Queue<Graph.Edge<Integer>> edgesAvailable = new PriorityQueue<Graph.Edge<Integer>>();
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Graph.Vertex<Integer> vertex = start;
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while (!unvisited.isEmpty()) {
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// Add all edges to unvisited vertices
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for (Graph.Edge<Integer> e : vertex.getEdges()) {
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if (unvisited.contains(e.getToVertex()))
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edgesAvailable.add(e);
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}
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// Remove the lowest cost edge
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final Graph.Edge<Integer> e = edgesAvailable.remove();
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cost += e.getCost();
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path.add(e); // O(1)
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vertex = e.getToVertex();
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unvisited.remove(vertex); // O(1)
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}
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return (new Graph.CostPathPair<Integer>(cost, path));
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}
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}
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