data structures and algorithms · session: basic operations on graphs (program) ajit a. diwan,...

IIT Bombay

Data Structures and AlgorithmsProf. Ajit A. Diwan

Prof. Ganesh RamakrishnanProf. Deepak B. Phatak

Department of Computer Science and EngineeringIIT Bombay

Session: Basic Operations on Graphs (Program)

1Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay

IIT Bombay

Data Structures and Functions

Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay 2

• 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

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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

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Representation of Vector


0

1

2

…

n-1

List 1

List 2

List 3

…

List n

vectorListIndex

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Representation of Vector


0

1

2

…

n-1

Node 1, Destination nodes from Node 1

vectorList



…

Node n, Destination nodes from Node n

Index

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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

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Example: Creating Graph Nodes


0

1

2

3

4

A

vectorList

B

C

D

E

Index

• Nodes A, B, C, D, and E are created• Its destination nodes are not known as of now

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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

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Example: Adding an Edge


• Add edge from C to A

0

1

2

3

4

A

vectorList

B

C

D

E

Index

0

1

2

3

4

A

vectorList

B

C, A

D

E

Index

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Program


template<class T>void graph<T>::addEdge(T source, T destination){

//Iterate through the ‘vectorList’ for adding an edgefor(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

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Example: Removing an Edge


0

1

2

3

4

A

vectorList

B

C, A

D

E

Index

• Remove edge from C to A

0

1

2

3

4

A

vectorList

B

C

D

E

Index

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Program


template<class T>void graph<T>::removeEdge(T source, T destination){

//Iterate through the ‘vectorList’ for removing an edgefor(typename vector<list<T> >::iterator vectorIterator = vectorList.begin();


typename list<T>::iterator listIterator = (*vectorIterator).begin();if ( (*listIterator) == source ) { //source node found

(*vectorIterator).remove(destination); //Edge removed}

} //End of for} //End of function

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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

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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

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Program


//Code to examine all nodes starting from A and display incoming edge(s)for(typename vector<list<T> >::iterator vectorIterator = vectorList.begin();


typename list<T>::iterator listIterator = (*vectorIterator).begin();listIterator++;for( ; listIterator != (*vectorIterator).end(); listIterator++){

if (*listIterator == *lIt) {cout << (*vectorIterator).front() << " ";break;

}}

}

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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');

cout << "\nOutgoing Edges\n";g.printOutgoing();cout << "\nIncoming Edges\n";g.printIncoming(); return 0;

} //End of main

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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

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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

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Thank you


data structures and algorithms · session: basic operations on graphs (program) ajit a. diwan,...

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