Detecting cyclic pairs

Question

Assume a std::set< std::pair<char, char> >, can somebody suggest an algorithm or approach to check whether there are cyclic pairs?

e.g.

std::set< std::pair<char, char> > cyclic = { {'A', 'B'}, {'B', 'C'}, {'C', 'A'} };
std::set< std::pair<char, char> > not_cyclic = { {'A', 'B'}, {'B', 'C'}, {'C', 'C'} };

isCyclic(cyclic);     // true
isCyclic(not_cyclic); // false

I don't want to use any extern library (c++ library is allowed), since the function bool isCyclic(const std::set< std::pair<char, char> >& set); will only be used once and it should be overkill to #include a big library like boost just for that one function...

Any ideas how to tackle this problem?

What you have is an adjacency list. Use it to build a tree using DFS, and look for a back edge. http://en.wikipedia.org/wiki/Depth-first_search — IdeaHat, Nov 18 '13 at 18:09
@Beta The first one is still the cyclic one that I'm looking for and the second is not. — user2804578, Nov 18 '13 at 18:31

score 0 · Answer 1 · edited May 23 '17 at 12:28

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What you have here is a graph, characters being its vertices and pairs in the set - the edges. You can detect whether there is a cycle easily using any search for instance BFS or DFS. Also have a look at this question. Don't mind that it deals with undirected case as the algorithm is the same.

edited May 23 '17 at 12:28

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answered Nov 18 '13 at 18:09

Ivaylo Strandjev

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Detecting cyclic pairs

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