Help on Hooligan problem

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Автор alurquiza, история, 9 лет назад, По-английски

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

maxflow, flow, acm-icpc

alurquiza
9 лет назад
6

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Saat

9 лет назад, скрыть # |

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, ..., x_n - 1. Now, between x_i and x_j (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 x_i with capacity equal to the number of matches the i^th team still has to play, and a node E, in such a way that there is an edge from each x_i to this node with capacity equal to P - p_i, where p_i are the points that the i^th 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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alurquiza

9 лет назад, скрыть # ^ |

Do you consider whether the team wins, loses or draw?

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Saat

9 лет назад, скрыть # ^ |

← Rev. 2 →

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 x_i. 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 x_i to x_j means that team i lose to team j. If no transfer occurs, then i and j drew their game.