1. Implementation of Graphs Identification of Classes. The Vertex Interface. The Edge Interface. Graph and Digraph Interfaces. Two concrete Implementations. –GraphAsMatrix. –GraphAsLists. Review Questions.

2. Identification of Classes A graph can be viewed as a container with two sections, one which holds vertices and one which holds edges. Thus, we can identify four kinds of objects: vertices, edges, directed graphs, and undirected graphs. Accordingly, we define four interfaces: Vertex, Edge, Graph, and Digraph.

3. The Vertex Interface Each vertex must be distinguishable from other vertices. Thus, each vertex should have a unique ID number. Also, some applications require vertex-weighted graphs. The following code defines the Vertex interface. 1 public interface Vertex 2 extends MyComparable 3 { 4 int getNumber (); 5 Object getWeight (); 6 Enumeration getIncidentEdges (); 7 Enumeration getEmanatingEdges (); 8 Enumeration getPredecessors (); 9 Enumeration getSuccessors (); 10 }

4. The Edge Interface An edge in a directed graph is an ordered pair of vertices; while in an undirected graph it is a set of two vertices. We use the same class for both--the context determines whether it is directed or undirected. The following code defines the Edge interface. 1 public interface Edge 2 extends MyComparable 3 { 4 Vertex getV0 (); 5 Vertex getV1 (); 6 Object getWeight (); 7 boolean isDirected (); 8 Vertex getMate (Vertex vertex); 9 }

5. The Graph Interface We define the Graph interface to represent undirected graphs and then use it to derive the Digraph interface. 1 public interface Graph extends Container { 2 int getNumberOfEdges (); 3 int getNumberOfVertices (); 4 boolean isDirected (); 5 void addVertex (int v); 6 void addVertex (int v, Object weight); 7 Vertex getVertex (int v); 8 void addEdge (int v, int w); 9 void addEdge (int v, int w, Object weight); 10 Edge getEdge (int v, int w); 11 boolean isEdge (int v, int w); 12 Enumeration getVertices (); 13 Enumeration getEdges (); 14 boolean isConnected (); 15 boolean isCyclic (); 16 void depthFirstTraversal(PrePostVisitor visitor,int start); 17 void breadthFirstTraversal (Visitor visitor, int start); 18 }

6. The Digraph Interface The following defines the Digraph interface as an extention of the Graph interface. 1 public interface Digraph 2 extends Graph 3 { 4 boolean isStronglyConnected (); 5 void topologicalOrderTraversal (Visitor visitor); 6 }

7. The AbstractGraph class The following introduces the AbstractGraph class. 1 public abstract class AbstractGraph extends 2 AbstractContainer implements Graph { 3 protected int numberOfVertices; 4 protected int numberOfEdges; 5 protected Vertex vertex[]; 6 public AbstractGraph(int size) { 7 vertex = new Vertex[size]; 8 } 9 public int getNumberOfVertices() { 10 return numberOfVertices; 11 } 12 public int getNumberOfEdges() { 13 return numberOfEdges; 14 } 15 public Vertex getVertex(int v) { 16 if (v>=0 && v<numberOfVertices) 17 return vertex[v]; 18 else 19 throw new NoSuchElementException(); 20 }

8. The AbstractGraph class- Cont'd 21 public Enumeration getVertices() { 22 return new Enumeration() { 23 protected int v; 24 public boolean hasMoreElements(){ 25 return v < numberOfVertices; 26 } 27 public Object nextElement() { 28 if(v >= numberOfVertices) 29 throw new NoSuchElementException(); 30 else 31 return vertex[v++]; 32 } 33 }; 34 } 35 public abstract Enumeration getIncidentEdges(int i); 36 public abstract Enumeration getEmanatingEdges(int i); 37 public abstract void addEdge(Edge edge); 38 public abstract Edge getEdge(int i, int j); 39 public abstract boolean isEdge(int i, int j); 40 public abstract Enumeration getEdges(); 41 //...

9. The GraphVertex class The GraphVertex is implemented as an inner class. 1 public abstract class AbstractGraph extends 2 AbstractContainer implements Graph { 3 protected final class GraphVertex extends AbstractObject 4 implements Vertex { 5 protected int number; 6 protected Object weight; 7 public GraphVertex(int i, Object obj) { 8 number = i; weight = obj; 9 } 10 public int getNumber() { 11 return number; 12 } 14 public Object getWeight() { 15 return weight; 16 } 17 public Enumeration getIncidentEdges() { 18 return AbstractGraph.this.getIncidentEdges(number); 19 } 20 //....

10. The GraphEdge class The GraphEdge is also implemented as an inner class. 1 public abstract class AbstractGraph extends 2 AbstractContainer implements Graph { 3 protected final class GraphEdge extends AbstractObject 4 implements Edge { 5 protected int v0, v1; 6 protected Object weight; 7 public GraphEdge(int v, int w, Object obj) 8 v0 = v; v1 = w; weight = obj; 9 } 10 public Vertex getV0() { 11 return vertex[v0]; 12 } 13 public Vertex getMate(Vertex vertex1) { 14 if(vertex1.getNumber() == v0) 15 return vertex[v1]; 16 if(vertex1.getNumber() == v1) 17 return vertex[v0]; 18 else 19 throw new IllegalArgumentException("Bad Vertex"); 20 } 21...

11. Implementing GraphAsMatrix The following describes the concrete class, GraphAsMatrix. 1 public class GraphAsMatrix extends AbstractGraph { 2 protected Edge matrix[][]; 3 public GraphAsMatrix(int size) { 4 super(size); 5 matrix = new Edge[size][size]; 6 } 7 protected void addEdge(Edge edge) { 8 int i = edge.getV0().getNumber(); 9 int j = edge.getV1().getNumber(); 10 if(matrix[i][j] != null) 11 throw new IllegalArgumentException("duplicate edge); 12 if(i == j) { 13 throw new IllegalArgumentException("not simple"); 14 } 15 else { 16 matrix[i][j] = edge; 17 matrix[j][i] = edge; 18 super.numberOfEdges++; 19 } 20 }

12. Implementing GraphAsMatrix - Cont'd 21 public Enumeration getEdges() { 22 return new Enumeration() { 23 protected int v, w; 24 { 25 for(v = 0; v < numberOfVertices; v++) 26 for(w = v + 1; w < numberOfVertices; w++) 27 if(matrix[v][w] != null) break; 28 } 29 public boolean hasMoreElements() { 30 return v < numberOfVertices && w < numberOfVertices; 31 } 32 public Object nextElement() { 33 if(v >= numberOfVertices || w >= numberOfVertices) 34 throw new NoSuchElementException(); 35 Edge edge = matrix[v][w]; 36 for(w++; w < numberOfVertices; w++) 37 if(matrix[v][w] != null) return edge; 38 for(v++; v < numberOfVertices; v++) 39 for(w = v + 1; w < numberOfVertices; w++) 40 if(matrix[v][w] != null) return edge; 41 return edge; 42 }}; 43 } //..

13. Implementing GraphAsLists The following describes the concrete class, GraphAsLists. 1 public class GraphAsLists extends AbstractGraph { 2 protected LinkedList adjacencyList[]; 3 public GraphAsLists(int i) { 4 super(i); 5 adjacencyList = new LinkedList[i]; 6 for(int j = 0; j < i; j++) 7 adjacencyList[j] = new LinkedList(); 8 } 9 protected void addEdge(Edge edge) { 10 int i = edge.getV0().getNumber(); 11 adjacencyList[i].append(edge); 12 super.numberOfEdges++; 13 } 14 //…

14. Implementing GraphAsLists - Cont'd 15 protected Enumeration getEmanatingEdges(int i) { 16 final Vertex final_vertex = getVertex(i); 17 return new Enumeration() { 18 protected int v; 19 protected LinkedList.Element ptr; 20 { 21 v = final_vertex.getNumber(); 22 ptr = adjacencyList[v].getHead(); 23 } 24 public boolean hasMoreElements() { 25 return ptr != null; 26 } 27 public Object nextElement() { 28 if(ptr == null) { 29 throw new NoSuchElementException(); 30 } else { 31 Object obj = ptr.getDatum(); 32 ptr = ptr.getNext(); 33 return obj; 34} 35 }}; 36 }//…

15. Review Questions 1.Complete the implementation of the GraphVertex class by implementing the following methods: getEmanatingEdges(), getPredecessors(), getSuccessors(), toString() and compareTo(). 2.Complete the implementation of the GraphEdge class by implementing the following methods: getV1(), getWeight(), isDirected(), toString() and compareTo(). 3.Complete the implementation of the AbstractGraph class by implementing the following methods: the two addEdge methods, the three addVertex methods, isDirected(), getEnumeration(), accept(), purge() and toString(). 4.Complete the implementation of the GraphAsMatrix class by implementing the following methods: getEdge(int v, int w), isEdge(int v, int w), getEmanatingEdges(), getIncidentEdges(), purge() and compareTo(). 5.Complete the implementation of the GraphAsLists class by implementing the following methods: getEdge(int v, int w), isEdge(int v, int w), getEdges(), getIncidentEdges(), purge() and compareTo().