$ Bzoj2560 $ string of beads inclusion and exclusion + $ dp $

Positive Solutions: + $ dp $ Inclusion and Exclusion

Report problem solving:

Portal $ QwQ $

$ Umm $ Although the subject of a very concise but still a bit difficult to understand abstract ,,, me a little, say there are $ n $ points, there are $ a_ {i between point and point $ i $ $ j $, j } $ strips can be connected to the free edge, asked how many kinds of programs can be connected into a connected graph

Obviously consider the inclusion-exclusion chant? Set $ ​​f_i $ state $ i $ express a point of view of China Unicom together into a legitimate program, $ g_i $ express state $ i $ the point even casual side of all programs

Apparently $ g_i $ pretreatment can start out? Equals $ \ prod_ {u, v \ in i} a_ {u, v} $. Then $ f_i $ equals $ g_i $ subtracting the number of illegal. Illegal number obviously consider enumerated subset $ {i} '$, equals $ \ sum f _ {{i}'} \ cdot g_ {i- {i} '} $.

But this is obviously still have a pot, that is not a legitimate program will be enumerated Unicom block times it contains. In order to ensure that do not leak, it is only a block size pieces Unicom designated point of comparison it is common practice to enumerate the largest / Unicom block size minimum point, Imperial $ {i} '$ contains the maximum / minimum point

Then finished $ QwQ $

$over$