By Dr Antonio Gulli

ISBN-10: 1497484464

ISBN-13: 9781497484467

A suite of Graph Programming Interview Questions Solved in C++

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This edge is added to the tree and the previous step is repeated until all vertices are in the tree. priority << std::endl; } } } std::cout << "MST" << std::endl; for (MatrixGraph::NodeID i = 1; i < numNodes; ++i) { std::cout << parent[i] << '-' << i << " weight=" << g(parent[i], i) << std::endl; } } \ This particular implementation uses an adjacency matrix and therefore its complexity is . However it is possible to get by using adjacent lists and a Fibonacci heap in which a Find-minimum is amortized time[2] adjacency matrix for dense or sparse graph binary heap and adjacency lists for sparse graph binary heap and adjacency lists for dense graph Fibonacci heap and adjacency list 12 Space complexity evaluation is here left as an exercise.

A collection of Graph Programming Interview Questions Solved in C++ Antonio Gulli Copyright © 2015 Antonio Gulli All rights reserved. ISBN: ISBN-13: “Graph” is the second of a series of 25 Chapters devoted to algorithms, problem solving and C++ programming. DEDICATION To my father Elio and my mother Maria. For your priceless help during all my life ACKNOWLEDGMENTS Thanks to Gaetano Mendola for code reviewing Table of Contents 1 Implementing a direct graph Solution Code 2 Choosing matrices or adjacency lists Solution 3 Implementing a BFS visit Solution Code Complexity 4 Erdős number 5 Implementing a DFS visit Solution Code Complexity 6 How to detect a cycle in a graph Solution Code Complexity 7 Given two nodes in an undirected graph, find the path connecting them Solution Code Complexity 8 Solving mazes Solution 9 Given a direct acyclic graph, implement a topological sort Solution Code Complexity 10 Detecting a bipartite graph Solution Code Complexity 11 Given a connected graph, compute the minimum spanning tree (MST) Solution Code \ 12 13 Find the strongly connected components in a direct graph Solution Code Complexity 14 Covering DFS Trees 15 Find an Hamiltonian cycle Solution Code 16 Find the articulation points in a graph Solution Code Complexity 17 Find the shortest path in a graph with non-negative edge weight Solution Code Complexity 18 Find MST(Minimum Spanning Tree) using Kruskal Algorithm Solution Complexity 19 Find the longest path in a DAG Solution Code Complexity 20 Find MST (Minimum Spanning Tree) using Prim Algorithm Solution Complexity 21 Find all pairs shortest paths using the Floyd-Warshall Algorithm Solution Complexity 22 Find all the single source shortest paths using Bellman Ford Algorithm Solution Complexity 23 Independent set of intervals Solution Complexity 24 Dominant set of intervals Solution Complexity 25 Weighted dominant set of intervals Solution 26 Weighted shortest paths with cost associated to the nodes Solution 27 Find the flow network using Ford–Fulkerson’Algorithm Solution Complexity 28 Assignment matching problem Solution 29 Find an Eulerian circuit Solution Code Complexity 30 Scheduling Solution Complexity 1 Implementing a direct graph A graph data structure involves a finite set of nodes or vertices and a set of ordered pairs called edges or arcs connecting two nodes.

U ← EXTRACT-MIN(Q) for each vertex v in Adj[u] if (w(u,v) + d[u] < d[v]) d[v] ← w(u,v) + d[u] p[v] ← u if (color[v] == WHITE) color[v] ← GRAY INSERT(Q, v) else if (color[v] == GRAY) DECREASE-KEY(Q, v) color[u] ← BLACK return (d, p) For this exercise[7] we start using boost::BGL a powerful framework for graph creation and processing[8]. A graph can have weights and names labels associated to the edges and those are stored in a boost::property. In addition a graph can be represented either with a boost::adjacency_list or with a boost:adjacenty_matrix.

### A Collection of Graph Programming Interview Questions Solved in C++ by Dr Antonio Gulli

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