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: Graph Traversal (Breadth-First Search) Program
Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay

2. Breadth-First Search Function 1: getVertices
Gets the vertices of the graph and stores it in an array.
Called by function BFS
Function 2: BFS
Traverses the graph in BFS fashion
List ‘s’
Used to store outgoing nodes
We use the list construct of STL, as a queue
Use ‘push_back’ to push the nodes in the list
Use ‘pop_front’ to pop the nodes out of the list
Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay

3. Demonstration A B E C D Visited: A 1 Steps List ‘s’
Initial: Insert A in the list
Pop A from the list
A is not visited, so, visit it
Push back the outgoing nodes of A in the list A
B, C A B E C D 1
Visited: A
Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay

4. Demonstration A B E C D Visited: A, B 2 1 Steps List ‘s’
Pop B from the list
B is not visited, so, visit it
Push back the outgoing nodes of B in the list
B, C C
C, D A B E C D 1
Visited: A, B
Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay

5. Demonstration A B E C D Visited: A, B, C 2 1 3 Steps List ‘s’
Pop C from the list
C is not visited, so, visit it
Push back the outgoing nodes of C in the list
C, D D
D D A B E C D 1 3
Visited: A, B, C
Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay

6. Demonstration A B E C D Visited: A, B, C, D 2 1 4 3 Steps List ‘s’
Pop D from the list
D is not visited, so, visit it
Push back the outgoing nodes of D in the list
D, D D
D, E A B E C D 1 4 3
Visited: A, B, C, D
Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay

7. Demonstration A B E C D Visited: A, B, C, D 2 1 4 3 Steps List ‘s’
Pop D from the list
D is already visited
Now, examine the next node in the list
D, E E A B E C D 1 4 3
Visited: A, B, C, D
Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay

8. Demonstration A B E C D Visited: A, B, C, D, E 2 1 4 5 3 Steps
List ‘s’
Pop E from the list
E is not visited, so, visit it
All nodes traversed successfully, as list is empty E A B E C D 1 4 5 3
Visited: A, B, C, D, E
Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay

9. BFS Example Nodes visited in BFS order A, B, C, D, F, E, G B A D E C F
Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay

10. Program template<class T> class graph{ template<class T>
vector<list<T> > vectorList;
int size;
public:
void createGraphNodes(int a, T*);
bool addEdge(T, T);
bool removeEdge(T, T);
void getVertices(T c[]);
void BFS(T a);
void printOutgoing();
void printIncoming();
}; //End of class
template<class T>
void graph<T>::createGraphNodes(int a, T vertex[]){
size = a;
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

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

12. Program template<class T> void graph<T>::BFS(T a){
T *c = new T[size]; getVertices(c); bool visited[size];
for(int i = 0; i < size; i++) visited[i] = false;
list<T> s; s.push_back(a);
while(s.size() > 0){
T node = s.front();
s.pop_front();
int positionOfNode = find(c,c+size, node) - c;
if(visited[positionOfNode] == false){
//Code to perform operations if the node is not visited
} // End of if that determines whether the node is visited or not
} //End of while
} //End of function
Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay

13. Program //Code to perform operations if the node is not visited
visited[positionOfNode] = true; //Visit it
cout << "Visiting: " << node << endl;
for(typename vector<list<T> >::iterator vectorIterator = vectorList.begin();
vectorIterator != vectorList.end();
vectorIterator++){
typename list<T>::iterator listIterator = (*vectorIterator).begin();
if((*listIterator) == node){
listIterator++;
for( ; listIterator != (*vectorIterator).end(); listIterator++){
s.push_back((*listIterator)); //Push all outgoing edges of the node in the list }
break;
} // End of for
Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay

14. Program
int main(){
char vertex[] = {'A','B','C','D','E'}; graph<char> g;
g.createGraphNodes(sizeof(vertex)/sizeof(vertex[0]),vertex);
g.addEdge('A','B');
g.addEdge('A','C');
g.addEdge('B','D');
g.addEdge('C','D');
g.addEdge('D','E');
g.printOutgoing();
cout << endl;
cout << endl << "Printing BFS" << endl;
g.BFS('A');
return 0;
} //End of main
Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay

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