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++
The interested reader should modify the code in order to verify the presence of cycles, if the graph is not a DAG (left as exercise). pop(); } } Complexity Time complexity is , space complexity is . 10 Detecting a bipartite graph A bipartite graph is a graph, in which its vertices can be divided into two disjoint sets U and . 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.
The process is repeated until the stack is empty. pop(); } std::cout << "End dfs" << std::endl << std::endl; } Complexity Space complexity is for the stack and , if the graph is represented using an adjacency list or if an adjacency matrix is adopted. Time complexity is , where may vary between and , depending on how sparse the graph is. 6 How to detect a cycle in a graph Solution A DFS visit can detect a cycle, if there is a back edge during the visit of the graph. By using the notation defined in the above solution, this condition is represented by a transition from a grey node to a grey node.
The lowpoint of can be computed after visiting all descendants of as the minimum of the depth of , the depth of all neighbors of (excluding the parent of in the DFS tree) and the lowpoint of all children of in the DFS tree. A non-root vertex is an articulation point, if and only if there is a child of such that This property can be tested, once the depth-first search is returned from every child of v. The root vertex must be handled separately: it is an articulation point, if and only if it has at least two children.
A Collection of Graph Programming Interview Questions Solved in C++ by Dr Antonio Gulli