Hi, the South American ICPC regional phase took part yesterday. I wasn't able to solve the problem Link. Some contestants said to me that it's solved by max flow, do someone know another solution or have a clue on how to build the flow graph ? Thanks in advance.
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Maybe you find these useful:
TopCoder max flow tutorial with the example problem of rooks.
RookAttack
this is a solution (spanish) but I could be sure that you could read code: http://algorithmmx.blogspot.mx/2013/11/problema-attacking-rooks-regional.html
The idea is convert each '.' in a two nodes left and right, then for each pair of '.' that we can't take at the same time add a undirected edge from left to right. The result will be the (http://en.wikipedia.org/wiki/Maximal_independent_set) Maximal independent set / 2 that in a bipartite graph is (nodes — matching).
There was a problem from SWERC 2012 that the solution is very similar (Sentry Robots). I guess the judges were not expecting that many teams would solve this problem.
I was impressed by the number of teams solving this problem as well, at a first glance, I didn't imagined of a graph problem, I tried some kind of backtrack/dp which exceed the time limit loose. At least it was one of the problems with the clearest statement in the contest.
It is similar to SRM 594 Div1 Problem 2 too. http://community.topcoder.com/stat?c=problem_statement&pm=12808&rd=15706&rm=319061&cr=23011413
Yes, it's similar, but it seems like this one can be solved by brute forcing successive depth first search. But it's definitely unfeasible in the case of the problem I posted.