By Dr Antonio Gulli
A suite of Graph Programming Interview Questions Solved in C++
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Additional resources for A Collection of Graph Programming Interview Questions Solved in C++
Solution A DFS or a BFS visit can be performed by assigning colors to the graph in such a way that the children have opposite colors from their parents. If two directly connected nodes have same color, the graph is not bipartite. v] == colour[n]) return false; } } return true; } Complexity Time complexity is , space complexity is . 11 Given a connected graph, compute the minimum spanning tree (MST) Let’s start with some definitions. An undirected graph is said to be connected, if every pair of vertices in the graph is connected.
By using the notation defined in the above solution, this condition is represented by a transition from a grey node to a grey node. Code This implementation is left as an exercise. Complexity The complexity here is the same as DFS. 7 Given two nodes in an undirected graph, find the path connecting them Solution A simple solution is to visit the graph with DFS order starting from one of the two nodes and stopping the visit as soon as the other node is found. During this process the visited nodes are stored into a stack.
NumNodes(); ++id) if (articulationPoints[id]) std::cout << "articulation point id=" << id << std::endl; } Complexity Time complexity is . An example of articulation point is in the picture below 17 Find the shortest path in a graph with non-negative edge weight Solution Given a graph with non-negative edge weight, we can apply Dijkstra’s algorithm for finding the single-source shortest path tree. Edger Dijkstra was born in the Netherlands and he invented the algorithm in 1959. For a given source node , the algorithm looks for the path with lowest cost between and every other node.