By Dr Antonio Gulli
A set of Graph Programming Interview Questions Solved in C++
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Extra info for A Collection of Graph Programming Interview Questions Solved in C++
His direct co-authors have distance 1 from him, while their respective co-authors have distance 2. Recursively, whoever has a collaboration with authors at distance from Erdős will therefore be at distance (also denoted as Erdős (author)=K). The author of this book has Erdős (“Antonio Gulli”)=3 because he wrote a paper with “Fabrizio Sebastiani” who, in turn, wrote a paper with “Micheal Anthony Steel”, who is a direct co-author of Erdős. Erdős numbers can be computed with a slight variation of the BFS visit and this implementation is left as an exercise.
We can build an acyclic graph with nodes corresponding to the intervals such that there is an edge , if and only if . Then we assign the weight to each edge. It can be verified that the shortest path on defines the independent set of intervals. Complexity G is a DAG and can be built in and therefore the shortest path can be computed in . 24 Dominant set of intervals Given a set of n intervals in the real line, a dominant set is a subset X of intervals with minimum size, such that any interval which is not in X has non-empty intersection with the intervals in X.
29 Find an Eulerian circuit An Eulerian path is a visit in a graph which touches every edge exactly once. If such a walk exists, the graph is said semi-eulerian or traversable. These problems were first discussed by Leonhard Euler for solving the famous problem of Seven Bridges of Konigsberg . The city of Königsberg in Prussia was built on both sides of the Pregel river, and had two large islands which were connected to each other and the mainland by seven bridges The problem was to find a walk through the city that would cross each bridge once and only once.