Luo Gu $ P4249 \ [WC2007] $ Rock Paper Scissors network flow

Positive Solutions: Network Flow

Report problem solving:

Portal $ QwQ $

In fact, there is an effect that said subject n-$ $ nodes have to complete graph, and the edge portion has been given the direction, the direction of all edges required to determine that the number of three-membered ring with a $ max $. Defined herein three-membered ring said three sides are the same direction, that is counterclockwise along with $ QwQ $

This problem usually three-membered ring words is to consider the degree of point? If consideration must have non-three-membered ring into a 2-point degree in consideration of this point enumeration, it has $ as = \ binom {n} {3} - \ sum \ binom {in_i} {2} = \ frac {n (n-1) (n-2)} {6} - \ sum \ frac {in_i ^ 2-in_i} {2} = \ frac {n (n-1) (n-2)} {6} + \ frac {n (n-1)} {2} - \ sum \ frac {in_i ^ 2} {2} $, so it is to minimize this, $ \ sum \ frac {in_i ^ 2} {2} $

This time to use the incremental cost of $ QwQ $, because never before had this position Amway look so probably will not harbor at Port ,,, great detail because I was lazy $ bushi $

For just one edge, if the cost is a function of traffic on, and satisfies a monotonically increasing slope, can be considered split side, the first sides to $ X $ $ f_ {x} -f_ {x-1} $, then Europe Keke spicy $ QwQ $

So here the same thing, by the front have $ f (x) = x ^ 2 $ Obviously increments, so as said earlier demolition side like $ QwQ $

Eau concluded at how to build Figure $ QwQ $? Consider building a row of dots represent non-directional edge, to build a row of dots represent all points, so he $ S $ to edge even flow of 1 fee for the side 0, side to endpoint even flow of 0 1 cost side, points to the $ T $ edge even as the idea

Then finish hot?

$ Written $

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Origin www.cnblogs.com/lqsukida/p/11286284.html