A directed acyclic graph is given . At least how many directed edge we have to add to construct a cycle which contains all the vertices ? How to solve this ?
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Does it need to be simple cycle? Do you only need the number of extra edges? I know this problem might be similar to what you are asking, I think I remeber how I solved it but I don't remeber how to prove it.
https://icpcarchive.ecs.baylor.edu/index.php?option=com_onlinejudge&Itemid=8&page=show_problem&problem=2288