Package org.jgrapht.alg.cycle
Class HierholzerEulerianCycle<V,E>
- java.lang.Object
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- org.jgrapht.alg.cycle.HierholzerEulerianCycle<V,E>
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- Type Parameters:
V
- the graph vertex typeE
- the graph edge type
- All Implemented Interfaces:
EulerianCycleAlgorithm<V,E>
public class HierholzerEulerianCycle<V,E> extends java.lang.Object implements EulerianCycleAlgorithm<V,E>
An implementation of Hierholzer's algorithm for finding an Eulerian cycle in Eulerian graphs. The algorithm works with directed and undirected graphs which may contain loops and/or multiple (parallel) edges. The running time is linear, i.e. $O(|E|)$ where $|E|$ is the cardinality of the edge set of the graph.See the Wikipedia article for details and references about Eulerian cycles and a short description of Hierholzer's algorithm for the construction of an Eulerian cycle. The original presentation of the algorithm dates back to 1873 and the following paper: Carl Hierholzer: Über die Möglichkeit, einen Linienzug ohne Wiederholung und ohne Unterbrechung zu umfahren. Mathematische Annalen 6(1), 30–32, 1873.
- Author:
- Dimitrios Michail
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Nested Class Summary
Nested Classes Modifier and Type Class Description protected class
HierholzerEulerianCycle.EdgeNode
protected class
HierholzerEulerianCycle.VertexNode
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Field Summary
Fields Modifier and Type Field Description protected HierholzerEulerianCycle.EdgeNode
eulerianHead
protected Graph<V,E>
g
protected boolean
isDirected
protected V
startVertex
protected HierholzerEulerianCycle.VertexNode
verticesHead
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Constructor Summary
Constructors Constructor Description HierholzerEulerianCycle()
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Method Summary
All Methods Instance Methods Concrete Methods Modifier and Type Method Description protected void
addEdge(HierholzerEulerianCycle.VertexNode sNode, HierholzerEulerianCycle.VertexNode tNode, E e)
Add an edge to the index.protected GraphWalk<V,E>
buildWalk()
Build final walkprotected void
cleanup()
Release any memory held.protected Pair<HierholzerEulerianCycle.EdgeNode,HierholzerEulerianCycle.EdgeNode>
computePartialCycle()
Computes a partial cycle assuming that all vertices have an even degree.GraphPath<V,E>
getEulerianCycle(Graph<V,E> g)
Compute an Eulerian cycle of a graph.protected HierholzerEulerianCycle.VertexNode
getOppositeVertex(HierholzerEulerianCycle.VertexNode v, HierholzerEulerianCycle.EdgeNode e)
Compute the opposite end-point of an end-point of an edge.protected void
initialize(Graph<V,E> g)
Index the graph and create a double-linked list representation suitable for vertex and edge removals in constant time.boolean
isEulerian(Graph<V,E> graph)
Test whether a graph is Eulerian.protected void
moveToFront(HierholzerEulerianCycle.VertexNode vNode)
Move a vertex as first in the vertex list.protected void
unlink(HierholzerEulerianCycle.EdgeNode eNode)
Unlink an edge from the adjacency lists of its end-points.protected void
unlink(HierholzerEulerianCycle.VertexNode vNode)
Unlink a vertex from the vertex list.protected void
updateGraphAndInsertLocations(Pair<HierholzerEulerianCycle.EdgeNode,HierholzerEulerianCycle.EdgeNode> partialCycle, HierholzerEulerianCycle.VertexNode partialCycleSourceVertex)
Iterate over the partial cycle to remove vertices with zero degrees and compute new insert locations for vertices with non-zero degrees.
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Field Detail
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isDirected
protected boolean isDirected
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verticesHead
protected HierholzerEulerianCycle.VertexNode verticesHead
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eulerianHead
protected HierholzerEulerianCycle.EdgeNode eulerianHead
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startVertex
protected V startVertex
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Method Detail
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isEulerian
public boolean isEulerian(Graph<V,E> graph)
Test whether a graph is Eulerian. An Eulerian graph is a graph containing an Eulerian cycle.- Parameters:
graph
- the input graph- Returns:
- true if the graph is Eulerian, false otherwise
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getEulerianCycle
public GraphPath<V,E> getEulerianCycle(Graph<V,E> g)
Compute an Eulerian cycle of a graph.- Specified by:
getEulerianCycle
in interfaceEulerianCycleAlgorithm<V,E>
- Parameters:
g
- the input graph- Returns:
- an Eulerian cycle
- Throws:
java.lang.IllegalArgumentException
- in case the graph is not Eulerian
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initialize
protected void initialize(Graph<V,E> g)
Index the graph and create a double-linked list representation suitable for vertex and edge removals in constant time. Ignore any vertices with zero degrees.- Parameters:
g
- the graph to index
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cleanup
protected void cleanup()
Release any memory held.
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computePartialCycle
protected Pair<HierholzerEulerianCycle.EdgeNode,HierholzerEulerianCycle.EdgeNode> computePartialCycle()
Computes a partial cycle assuming that all vertices have an even degree. The partial cycle always begin from the first graph vertex in the vertex list.- Returns:
- the partial's cycle head and tail nodes as a pair
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updateGraphAndInsertLocations
protected void updateGraphAndInsertLocations(Pair<HierholzerEulerianCycle.EdgeNode,HierholzerEulerianCycle.EdgeNode> partialCycle, HierholzerEulerianCycle.VertexNode partialCycleSourceVertex)
Iterate over the partial cycle to remove vertices with zero degrees and compute new insert locations for vertices with non-zero degrees. It is important to move vertices with new insert locations to the front of the vertex list, in order to make sure that we always start partial cycles from already visited vertices.- Parameters:
partialCycle
- the partial cyclepartialCycleSourceVertex
- the source vertex of the first edge in the partial cycle
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addEdge
protected void addEdge(HierholzerEulerianCycle.VertexNode sNode, HierholzerEulerianCycle.VertexNode tNode, E e)
Add an edge to the index.- Parameters:
sNode
- source vertextNode
- target vertexe
- original (wrapped) edge
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unlink
protected void unlink(HierholzerEulerianCycle.VertexNode vNode)
Unlink a vertex from the vertex list.- Parameters:
vNode
- vertex to unlink
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moveToFront
protected void moveToFront(HierholzerEulerianCycle.VertexNode vNode)
Move a vertex as first in the vertex list.- Parameters:
vNode
- vertex to move to front
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unlink
protected void unlink(HierholzerEulerianCycle.EdgeNode eNode)
Unlink an edge from the adjacency lists of its end-points.- Parameters:
eNode
- edge to unlink
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getOppositeVertex
protected HierholzerEulerianCycle.VertexNode getOppositeVertex(HierholzerEulerianCycle.VertexNode v, HierholzerEulerianCycle.EdgeNode e)
Compute the opposite end-point of an end-point of an edge.- Parameters:
v
- vertex that is part of edgee
- edge used to find opposite vertex- Returns:
- opposite vertex in edge
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