org.jgrapht.alg.EulerianCircuit Maven / Gradle / Ivy

Go to download
Show more of this group Show more artifacts with this name
Show all versions of jgrapht-core Show documentation
There is a newer version: 1.5.2
/*
 * (C) Copyright 2008-2016, by Andrew Newell and Contributors.
 *
 * JGraphT : a free Java graph-theory library
 *
 * This program and the accompanying materials are dual-licensed under
 * either
 *
 * (a) the terms of the GNU Lesser General Public License version 2.1
 * as published by the Free Software Foundation, or (at your option) any
 * later version.
 *
 * or (per the licensee's choosing)
 *
 * (b) the terms of the Eclipse Public License v1.0 as published by
 * the Eclipse Foundation.
 */
package org.jgrapht.alg;

import java.util.*;

import org.jgrapht.*;
import org.jgrapht.graph.*;

/**
 * This algorithm will check whether a graph is Eulerian (hence it contains an
 * Eulerian circuit). Also, if a
 * graph is Eulerian, the caller can obtain a list of vertices making up the Eulerian circuit. An
 * Eulerian circuit is a circuit which traverses each edge exactly once.
 *
 * @author Andrew Newell
 * @since Dec 21, 2008
 */
public abstract class EulerianCircuit
{
    /**
     * This method will check whether the graph passed in is Eulerian or not.
     *
     * @param g The graph to be checked
     * @param  the graph vertex type
     * @param  the graph edge type
     *
     * @return true for Eulerian and false for non-Eulerian
     */
    public static  boolean isEulerian(UndirectedGraph g)
    {
        // If the graph is not connected, then no Eulerian circuit exists
        if (!(new ConnectivityInspector<>(g)).isGraphConnected()) {
            return false;
        }

        // A graph is Eulerian if and only if all vertices have even degree
        // So, this code will check for that
        for (V v : g.vertexSet()) {
            if ((g.degreeOf(v) % 2) == 1) {
                return false;
            }
        }
        return true;
    }

    /**
     * This method will return a list of vertices which represents the Eulerian circuit of the
     * graph.
     *
     * @param g The graph to find an Eulerian circuit
     * @param  the graph vertex type
     * @param  the graph edge type
     *
     * @return null if no Eulerian circuit exists, or a list of vertices representing the Eulerian
     *         circuit if one does exist
     */
    public static  List getEulerianCircuitVertices(UndirectedGraph g)
    {
        // If the graph is not Eulerian then just return a null since no
        // Eulerian circuit exists
        if (!isEulerian(g)) {
            return null;
        }

        // The circuit will be represented by a linked list
        List path = new LinkedList<>();
        UndirectedGraph sg = new UndirectedSubgraph<>(g, null, null);
        path.add(sg.vertexSet().iterator().next());

        // Algorithm for finding an Eulerian circuit Basically this will find an
        // arbitrary circuit, then it will find another arbitrary circuit until
        // every edge has been traversed
        while (sg.edgeSet().size() > 0) {
            V v = null;

            // Find a vertex which has an edge that hasn't been traversed yet,
            // and keep its index position in the circuit list
            int index = 0;
            for (Iterator iter = path.iterator(); iter.hasNext(); index++) {
                v = iter.next();
                if (sg.degreeOf(v) > 0) {
                    break;
                }
            }

            // Finds an arbitrary circuit of the current vertex and
            // appends this into the circuit list
            while (sg.degreeOf(v) > 0) {
                for (V temp : sg.vertexSet()) {
                    if (sg.containsEdge(v, temp)) {
                        path.add(index, temp);
                        sg.removeEdge(v, temp);
                        v = temp;
                        break;
                    }
                }
            }
        }
        return path;
    }
}

// End EulerianCircuit.java