IIT Bombay 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 (Depth-First Search) Program 1Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay

IIT Bombay Depth-First Search Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay2 Function 1: getVertices Gets the vertices of the graph and stores it in an array. Called by function DFS Function 2: DFS Traverses the graph in DFS fashion List ‘s’ Used to store adjacent nodes, from the current node We use the list construct of STL, as a stack Use ‘push_back’ to push the nodes in the list Use ‘pop_back’ to pop the nodes out of the list

IIT Bombay Demonstration Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay3 A B E C D StepsList ‘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 1 Visited: A

IIT Bombay Demonstration Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay4 A B E C D StepsList ‘s’ Pop C from the list C is not visited, so, visit it Push back the outgoing nodes of C in the list B, C B B, D 1 2 Visited: A, C

IIT Bombay Demonstration Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay5 A B E C D StepsList ‘s’ Pop D from the list D is not visited, so, visit it Push back the outgoing nodes of D in the list B, D B B, E Visited: A, C, D

IIT Bombay Demonstration Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay6 A B E C D StepsList ‘s’ Pop E from the list E is not visited, so, visit it There are no outgoing edges of E, so continue to examine the ‘back’ element in the list B, E B Visited: A, C, D, E

IIT Bombay Demonstration Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay7 A B E C D StepsList ‘s’ Pop B from the list B is not visited, so, visit it Push back the outgoing nodes of B in the list BDBD Visited: A, C, D, E, B

IIT Bombay Demonstration Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay8 A B E C D StepsList ‘s’ D is already visited, so pop it out All nodes traversed successfully, as list is empty D Visited: A, C, D, E, B

IIT Bombay Another DFS Example Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay9 A B E C D G F Nodes visited in DFS order A, D, G, F, E, C, B

IIT Bombay Program Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay10 template class graph{ vector > vectorList; int size; public: void createGraphNodes(int a, T*); bool addEdge(T, T); bool removeEdge(T, T); void getVertices(T c[]); void DFS(T a); void printOutgoing(); void printIncoming(); }; //End of class template void graph ::createGraphNodes(int a, T vertex[]){ size = a; vectorList.resize(a); int arrayIndex = 0; for(typename vector >::iterator vectorIterator = vectorList.begin(); vectorIterator != vectorList.end(); vectorIterator++, arrayIndex++){ (*vectorIterator).push_back(vertex[arrayIndex]); } } //End of function

IIT Bombay Program Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay11 template void graph ::getVertices(T c[]){ int index = 0; for(typename vector >::iterator vectorIterator = vectorList.begin(); vectorIterator != vectorList.end(); vectorIterator++, index++){ typename list ::iterator listIterator = (*vectorIterator).begin(); c[index] = (*listIterator); } } // End of function

IIT Bombay Program Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay12 template void graph ::DFS(T a){ T *c = new T[size]; getVertices(c); bool visited[size]; for(int i = 0; i < size; i++) visited[i] = false; list s; s.push_back(a); while(s.size() > 0){ T node = s.back(); s.pop_back(); 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

IIT Bombay Program Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay13 //Code to perform operations if the node is not visited visited[positionOfNode] = true; //Visit it cout << "Visiting: " << node << endl; for(typename vector >::iterator vectorIterator = vectorList.begin(); vectorIterator != vectorList.end(); vectorIterator++){ typename list ::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

IIT Bombay Program Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay14 int main(){ char vertex[] = {'A','B','C','D','E'}; graph 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 DFS" << endl; g.DFS('A'); return 0; } //End of main

IIT Bombay Thank you Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay15