A Collection of Graph Programming Interview Questions Solved by Dr Antonio Gulli

By Dr Antonio Gulli

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

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The dfs method implements a recursive solution which starts from the root node sid and it keeps a boolean vector of visited nodes and their colours. For each node the colour is ‘w’ (white) at the very beginning, ‘g’ (gray) when the node is visitedand ‘b’ (black) when all the adjacent nodes are also visited. In addition the time, when the node is visited, is stored in the vector timing. The dfsStack method implements an iterative solution where the root node is inserted in the stack. Then the top of the stack is removed and all the adjacent not yet visited nodes are put on the stack itself.

However if we have a DAG, we can easily compute the topological sort. Then for every node we update the distance of its adjacent nodes by using the distance of current vertex. numNodes(); ++id) if (distance[id] == std::numeric_limits::max()) std::cout << "id=" << id << " has infinity distance" << std::endl; else std::cout << "id=" << id << " has distance=" << distance[id] << std::endl; } Complexity Time complexity is . What is the space complexity? 20 Find MST (Minimum Spanning Tree) using Prim Algorithm Prim’s[11] algorithm finds a minimum spanning tree (MST) in an undirected graph with weighted edges.

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.

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