org.jgrapht.alg.EulerianCircuit Maven / Gradle / Ivy
/* ==========================================
* JGraphT : a free Java graph-theory library
* ==========================================
*
* Project Info: http://jgrapht.sourceforge.net/
* Project Creator: Barak Naveh (http://sourceforge.net/users/barak_naveh)
*
* (C) Copyright 2003-2008, by Barak Naveh and Contributors.
*
* 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.
*/
/* -------------------
* EulerianCircuit.java
* -------------------
* (C) Copyright 2008-2008, by Andrew Newell and Contributors.
*
* Original Author: Andrew Newell
* Contributor(s): -
*
* $Id$
*
* Changes
* -------
* 24-Dec-2008 : Initial revision (AN);
*
*/
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
*
* @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
Iterator iter = g.vertexSet().iterator();
while (iter.hasNext()) {
V v = iter.next();
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
*
* @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 (
Iterator iter = sg.vertexSet().iterator();
iter.hasNext();)
{
V temp = iter.next();
if (sg.containsEdge(v, temp)) {
path.add(index, temp);
sg.removeEdge(v, temp);
v = temp;
break;
}
}
}
}
return path;
}
}
// End EulerianCircuit.java