499 lines
3.8 KiB
Markdown
499 lines
3.8 KiB
Markdown
TODO
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挖坑待填
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https://blog.csdn.net/yingxue_cat/article/details/133648992
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树上背包
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发现这个也不会。枯。希望现学来得及吧。
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P2014 [CTSC1997] 选课
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虽然以前写过，但似乎是没咋看懂式子稀里糊涂敲上去的(？
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啊啊啊以前好多这种稀里糊涂照着题解思路/老师代码贺上去的题，每当提起我都记得做过，每当考到就发现不会，深受其害/ll
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这题是个森林，则对每棵树的根节点向 0
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0
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连边，使之变成一棵树。
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设 fi,j,k
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<EFBFBD>
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<EFBFBD>
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,
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<EFBFBD>
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,
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<EFBFBD>
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表示子树 i
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<EFBFBD>
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的前 j
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<EFBFBD>
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个儿子，已经选了 k
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<EFBFBD>
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门课的最大值。注意：必须选点 i
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<EFBFBD>
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那么 fnow,tot,j=max(fnow,tot,j,fnow,tot−1,j−k+fv,mxtot,k)
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<EFBFBD>
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<EFBFBD>
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<EFBFBD>
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<EFBFBD>
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,
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<EFBFBD>
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<EFBFBD>
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<EFBFBD>
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,
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<EFBFBD>
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=
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max
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(
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<EFBFBD>
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<EFBFBD>
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<EFBFBD>
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<EFBFBD>
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,
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<EFBFBD>
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<EFBFBD>
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<EFBFBD>
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,
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<EFBFBD>
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,
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<EFBFBD>
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<EFBFBD>
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<EFBFBD>
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<EFBFBD>
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,
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<EFBFBD>
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<EFBFBD>
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<EFBFBD>
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−
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1
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,
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<EFBFBD>
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−
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<EFBFBD>
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+
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<EFBFBD>
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<EFBFBD>
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,
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<EFBFBD>
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<EFBFBD>
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<EFBFBD>
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<EFBFBD>
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<EFBFBD>
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,
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<EFBFBD>
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)
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。同样注意 k
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<EFBFBD>
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只能循环到 j−1
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<EFBFBD>
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−
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1
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。
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类似背包进行滚动数组优化。(似乎滚动了反而更好写(？)
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也不知道自己到底会没会/kk
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P4516 [JSOI2018] 潜入行动
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题面看起来还挺套路，但我不会，树形 dp 是真忘光了啊啊啊啊啊怎么办
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式子好长不想写...算了口胡一下吧。
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设 dp[u][j][0/1][0/1]
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<EFBFBD>
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<EFBFBD>
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[
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<EFBFBD>
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]
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[
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<EFBFBD>
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]
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[
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0
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/
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1
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]
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[
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0
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/
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1
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]
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表示子树 u
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<EFBFBD>
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里放了 j
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<EFBFBD>
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个，点 u
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<EFBFBD>
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放了/没放，是否已经被监听。
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于是滚动数组一下推出长下面这样的转移柿子↓
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↓
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⎧⎩⎨⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪dp[x][i+j][0][0]=∑dp[x][i][0][0]×dp[v][j][0][1]dp[x][i+j][1][0]=∑dp[x][i][1][0]×(dp[v][j][0][0]+dp[v][j][0][1])dp[x][i+j][0][1]=∑(dp[x][i][0][1]×(dp[v][j][0][1]+dp[v][j][1][1])+dp[x][i][0][0]×dp[v][j][1][1])dp[x][i+j][1][1]=∑(dp[x][i][1][0]×(dp[v][j][1][0]+dp[v][j][1][1])+dp[x][i][1][1]×(dp[v][j][0][0]+dp[v][j][0][1]+dp[v][j][1][0]+dp[v][j][1][1]))
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{
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<EFBFBD>
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<EFBFBD>
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[
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<EFBFBD>
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]
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[
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<EFBFBD>
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+
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<EFBFBD>
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]
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[
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0
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]
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[
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0
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]
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=
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∑
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<EFBFBD>
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<EFBFBD>
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[
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<EFBFBD>
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]
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[
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<EFBFBD>
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]
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[
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0
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]
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[
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0
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]
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×
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<EFBFBD>
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<EFBFBD>
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[
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<EFBFBD>
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]
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<EFBFBD>
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]
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[
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0
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]
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[
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1
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]
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<EFBFBD>
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<EFBFBD>
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<EFBFBD>
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]
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[
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<EFBFBD>
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+
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<EFBFBD>
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]
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1
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]
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0
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]
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=
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∑
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<EFBFBD>
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<EFBFBD>
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<EFBFBD>
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]
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<EFBFBD>
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]
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1
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]
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0
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]
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×
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(
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<EFBFBD>
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<EFBFBD>
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[
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<EFBFBD>
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]
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<EFBFBD>
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]
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0
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]
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]
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+
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<EFBFBD>
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<EFBFBD>
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<EFBFBD>
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]
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<EFBFBD>
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]
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[
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0
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]
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[
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1
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]
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)
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<EFBFBD>
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<EFBFBD>
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[
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<EFBFBD>
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]
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[
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<EFBFBD>
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+
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<EFBFBD>
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]
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0
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]
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[
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1
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]
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=
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∑
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(
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<EFBFBD>
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<EFBFBD>
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[
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<EFBFBD>
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]
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<EFBFBD>
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]
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0
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]
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1
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]
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×
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(
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<EFBFBD>
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<EFBFBD>
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[
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<EFBFBD>
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]
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<EFBFBD>
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]
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0
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]
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[
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1
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]
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+
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<EFBFBD>
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<EFBFBD>
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<EFBFBD>
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]
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<EFBFBD>
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]
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1
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]
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[
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1
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]
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)
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+
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<EFBFBD>
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<EFBFBD>
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[
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<EFBFBD>
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]
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<EFBFBD>
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]
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[
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0
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]
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[
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0
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]
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×
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<EFBFBD>
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<EFBFBD>
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<EFBFBD>
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]
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<EFBFBD>
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]
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[
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1
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]
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[
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1
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]
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)
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<EFBFBD>
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<EFBFBD>
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[
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<EFBFBD>
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]
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[
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<EFBFBD>
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+
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<EFBFBD>
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]
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[
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1
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]
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[
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1
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]
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=
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∑
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(
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<EFBFBD>
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<EFBFBD>
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[
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<EFBFBD>
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]
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[
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<EFBFBD>
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]
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[
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1
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]
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[
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0
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]
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×
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(
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<EFBFBD>
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<EFBFBD>
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[
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<EFBFBD>
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]
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[
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<EFBFBD>
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]
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[
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1
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]
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[
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0
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]
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+
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<EFBFBD>
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<EFBFBD>
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[
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<EFBFBD>
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]
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[
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<EFBFBD>
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]
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[
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1
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]
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[
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1
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]
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)
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+
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<EFBFBD>
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<EFBFBD>
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[
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<EFBFBD>
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]
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[
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<EFBFBD>
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]
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[
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1
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]
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[
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1
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]
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×
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(
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<EFBFBD>
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<EFBFBD>
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[
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<EFBFBD>
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]
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[
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<EFBFBD>
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]
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[
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0
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]
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[
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0
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]
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+
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<EFBFBD>
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<EFBFBD>
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[
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<EFBFBD>
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]
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[
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<EFBFBD>
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]
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[
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0
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]
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[
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1
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]
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+
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<EFBFBD>
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<EFBFBD>
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[
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<EFBFBD>
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]
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[
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<EFBFBD>
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]
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[
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1
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]
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[
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0
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]
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+
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<EFBFBD>
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<EFBFBD>
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[
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<EFBFBD>
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]
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[
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<EFBFBD>
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]
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[
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1
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]
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[
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1
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]
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)
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)
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卡 long long 空间，要强制类型转换。我不管，我胡了就是我写了！(确信
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不知道啥题
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OI wiki 为什么给我推黑题啊，不会/kk
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所以写到这吧awa
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|
||
树形 DP
|
||
范学长讲树上问题，顺路回来更新一波。
|
||
|
||
CF822F Madness
|
||
贪心题。胡了篇 lg 题解。
|
||
|
||
P2607 [ZJOI2008] 骑士
|
||
基环树上的 dp。第一次做这种题(？
|
||
对于每个基环树，dfs 找到环的那条边，对于这条边分别钦定 u
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<EFBFBD>
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不选/v
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<EFBFBD>
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不选，分别 dp 即可。
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转移显然。
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实现的时候写麻烦了，直接并查集判环就可以，不用 dfs。 |