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alurquiza's blog

Help on Hooligan problem
By alurquiza, history, 10 years ago, In English

How can I solve the problem Hooligan?, problem H of the ACM-ICPC Latin American Contest 2009. Could anyone help me? http://coj.uci.cu/24h/problem.xhtml?pid=1210

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10 years ago, hide # |
 
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First, we suppose greedily that our dream team wins all of its missing matches. After this, it should have P points. Then, build a graph with nodes x1, x2, ..., xn - 1. Now, between xi and xj (i ≠ j), put an edge in each direction with capacity equal to the number of games missing between teams i and j. Use a node B, which has an edge towards every xi with capacity equal to the number of matches the ith team still has to play, and a node E, in such a way that there is an edge from each xi to this node with capacity equal to P - pi, where pi are the points that the ith team already has. Your dream team can be a champion iff the maxflow from B to E equals the number of missing matches.

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    10 years ago, hide # ^ |
     
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    Do you consider whether the team wins, loses or draw?

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      10 years ago, hide # ^ |
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      Yes. I am considering that each team wins 1 point per every game that it has not played (This happens because every match distributes 2 points, so 1 per team). This amount of points is the flow from B to xi. After that, each team can "transfer" one point to other team, with the constraint that it cannot transfer more points than the matches that they can play between them. A point transfer from xi to xj means that team i lose to team j. If no transfer occurs, then i and j drew their game.

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10 years ago, hide # |
 
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This is a famous Max Flow problem, more info here

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