1. Data Structures and Algorithms
Prof. Ajit A. Diwan
Prof. Ganesh Ramakrishnan
Prof. Deepak B. Phatak
Department of Computer Science and Engineering
IIT Bombay
Session: Basic Operations on Graphs (Program)
Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay

2. Data Structures and Functions
Vector ‘vectorList’
Vector which is of type ‘list’
Function 1: ‘createGraphNodes’
Creates nodes of graph i.e. A, B, C, etc.
Function 2: ‘addEdge’
Adds an edge from one node to another node of the graph
Function 3: ‘removeEdge’
Removes an existing edge from one node to another node of the graph
Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay

3. Data Structures and Functions
Function 4: ‘printOutgoing’
Displays all outgoing edges for each node in the graph
Function 5: ‘printIncoming’
Displays all incoming edges for each node in the graph
Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay

4. Representation of Vector
Index
vectorList 1 2 …
n-1
List 1
List 2
List 3 …
List n
Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay

5. Representation of Vector
Index
vectorList 1 2 …
n-1
Node 1, Destination nodes from Node 1
Node 2, Destination nodes from Node 2
Node 3, Destination nodes from Node 3 …
Node n, Destination nodes from Node n
Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay

6. Program template<class T> class graph{
vector<list<T> > vectorList;
public:
void createGraphNodes(int a, T*);
void addEdge(T, T);
void removeEdge(T, T);
void printOutgoing();
void printIncoming();
}; //End of class
Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay

7. Example: Creating Graph Nodes
Nodes A, B, C, D, and E are created
Its destination nodes are not known as of now
Index
vectorList 1 2 3 4 A B C D E
Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay

8. Program template<class T>
void graph<T>::createGraphNodes(int a, T vertex[]){
vectorList.resize(a);
int arrayIndex = 0;
for(typename vector<list<T> >::iterator vectorIterator = vectorList.begin();
vectorIterator != vectorList.end();
vectorIterator++, arrayIndex++){
(*vectorIterator).push_back(vertex[arrayIndex]); }
} //End of function
Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay

9. Example: Adding an Edge
Add edge from C to A
Index
vectorList
Index
vectorList 1 2 3 4 1 2 3 4 A A B B C
C, A D D E E
Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay

10. Program template<class T>
void graph<T>::addEdge(T source, T destination){
//Iterate through the ‘vectorList’ for adding an edge
for(typename vector<list<T> >::iterator vectorIterator = vectorList.begin();
vectorIterator != vectorList.end();
vectorIterator++){
typename list<T>::iterator listIterator = (*vectorIterator).begin();
if ( (*listIterator) == source ) { //source node found
(*vectorIterator).push_back(destination); //Edge added }
} //End of for
} //End of function
Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay

11. Example: Removing an Edge
Remove edge from C to A
Index
vectorList
Index
vectorList 1 2 3 4 1 2 3 4 A A B B
C, A C D D E E
Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay

12. Program template<class T>
void graph<T>::removeEdge(T source, T destination){
//Iterate through the ‘vectorList’ for removing an edge
for(typename vector<list<T> >::iterator vectorIterator = vectorList.begin();
vectorIterator != vectorList.end();
vectorIterator++){
typename list<T>::iterator listIterator = (*vectorIterator).begin();
if ( (*listIterator) == source ) { //source node found
(*vectorIterator).remove(destination); //Edge removed }
} //End of for
} //End of function
Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay

13. Program template<class T> void graph<T>::printOutgoing(){
for(typename vector<list<T> >::iterator vectorIterator = vectorList.begin();
vectorIterator != vectorList.end();
vectorIterator++){
typename list<T>::iterator listIterator = (*vectorIterator).begin();
cout << (*listIterator) << ": ";
listIterator++;
for( ; listIterator != (*vectorIterator).end(); listIterator++){
cout << (*listIterator) << " "; }
cout << endl;
} //End of function
Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay

14. Program template<class T> void graph<T>::printIncoming(){
//Iterate for All Nodes (Incoming)
for(typename vector<list<T> >::iterator vIt = vectorList.begin(); vIt != vectorList.end(); vIt++){
typename list<T>::iterator lIt = (*vIt).begin();
cout << (*lIt) << ": ";
//Code to examine all nodes starting with A, and display incoming edge(s) for each
cout << endl; }
} //End of function
Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay

15. Program
//Code to examine all nodes starting from A and display incoming edge(s)
for(typename vector<list<T> >::iterator vectorIterator = vectorList.begin();
vectorIterator != vectorList.end();
vectorIterator++){
typename list<T>::iterator listIterator = (*vectorIterator).begin();
listIterator++;
for( ; listIterator != (*vectorIterator).end(); listIterator++){
if (*listIterator == *lIt) {
cout << (*vectorIterator).front() << " ";
break; }
Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay

16. Program int main(){ int size = 5;
char vertex[] = {'A','B','C','D','E'};
graph<char> g;
g.createGraphNodes(5,vertex);
cout << "\nCreating graph nodes\n\n";
g.addEdge('A','B');
g.addEdge('A','C');
g.addEdge('C','A');
g.addEdge('C','D');
g.addEdge('C','B');
g.addEdge('D','B');
cout << "\nOutgoing Edges\n";
g.printOutgoing();
cout << "\nIncoming Edges\n";
g.printIncoming();
cout << endl;
g.removeEdge('A','B');
g.removeEdge('C','D');
return 0;
} //End of main
Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay

17. Exercise
The program discussed implements a directed graph. Modify it to implement an undirected graph.
Write functions to:
Determine whether an edge exists from one node to another
Determine the ‘Outdegree’ of a node
Determine the ‘Indegree’ of a node
Remove an existing node from the graph
Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay

18. Problems in Real Life In real life, various errors can occur
Adding an edge which exists
Adding an edge where either the ‘Source’ node or ‘Destination’ node is not present in the graph
Removing an edge which is not present
Removing an edge where either the ‘Source’ node or ‘Destination’ node is not present in the graph
Adding a node to the graph, which exists
Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay

19. Thank you
Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay