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By Dr Antonio Gulli

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

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Visited[id]) { dfsUtil(g, id, visited); std::cout << "end component id=" << componentID++ << std::endl; } } } Complexity Time complexity is here 14 Covering DFS Trees Given a graph it is possible to define a path tree generated by a DFS visit. If G is not (strongly) connected then we need to restart the DFS from each node and the visit will generate a forest of trees, If the graph is direc,t the visit will respect the direction of the edges, while if the graph is not direct, the visit will produce a random orientation of each edge as a consequence of the direction of the visit.

Hpp Complexity Time complexity is where is the time needed for extracting nodes from and is the time needed for processing the adjacency list and update the queue. Note that if we use Fibonacci heap, then operations of insert and decreaseKey have cost amortized by deleteKey with cost . So complexity is by using Fibonacci 21 Find all pairs shortest paths using the Floyd-Warshall Algorithm Floyd & Warshall’s algorithm finds the shortest distance between every pair of vertices in the graph. The algorithm detects, if there are loops with negative weights, which will produce a degenerate negative infinite shortest path otherwise.

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.

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