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

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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

Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay 3

• 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

Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay 4

0

1

2

…

n-1

List 1

List 2

List 3

…

List n

vectorListIndex

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Representation of Vector

Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay 5

0

1

2

…

n-1

Node 1, Destination nodes from Node 1

vectorList

Node 2, Destination nodes from Node 2

Node 3, Destination nodes from Node 3

…

Node n, Destination nodes from Node n

Index

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Program

Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay 6

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

Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay 7

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

Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay 8

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

Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay 9

• 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

Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay 10

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

Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay 11

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

Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay 12

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();

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

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Program

Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay 13

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

Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay 14

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

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

//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;

}}

}

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Program

Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay 16

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

Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay 17

• 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

Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay 18

• 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

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