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z%@)Iws*R}Env-5>Q(D!LoGoN^f>ulAMB>Fk3f2S)o)4=4FD7!M*Z6b>9+E|2Q7X?8 z8$GzY7r9^CI*p)RJ$kth6uD}D`z$)G7ECQJJ61>ry9y zJLS>JH{VU}Br#b`JEKj-O`CB0&yjAEw9FvBbN63U*@i5fI&lSR^-^7{$VRD7nykgG z$}|gE4rYB1n$3K(+0DwuEj=uU2dee0vp3f_?)8=Iougd#Miy_aR-?x{^?OJ4-K>Kd z7I;fsgU$%oV;Di*f3ckcFyt_;C| znSpC_edlntInE_Zvm3u*vWXq!APcaGn1T@m`_mTg+>OupHV|yg-MeDBr}=CM#*8PX zxYnaa3W9l3xSQ7pBa{cKqqU4V6F@XB-hwZqmKKpnRnREY=7Uzjl%tA#dD5RA9)%J| z6}EMc5ZUbZb|za==dZFm0jd*I4o_NW3OBHr+`q>NQu)8E9Ik^4O(h{eiYOIb? zE5r7t_n8+;Shk>gGWfyc@zWq+ApG$jbHqTO)DuSp8e>^Ix!A2iK0Zg7hrQ{CtObB^Vq3vPyPl z7~kfQfeLcIxXH8-m@Os~1+}_IzbxKbd_CYk39s>h9J(=D0a``ORG;E_^?|$A~7UAn)`}@&>G6<*LGS) zNG`QWY`aA0%>7DPu75!lKUw1Iw?$`GEK|!%Kb7Z!4aj@(rR#E680P--CBE}gv-h6m zdI0=S#u68^BYo?-2 11 -  1->4->3 5 -  1->4->5 8(since 1->4 has capacity of 13) -A(2)=5+6=11 -Details: 2->1->4->3 5 -  2->1->4->5 6 +**题意** +![](https://dsideal.obs.cn-north-1.myhuaweicloud.com/HuangHai/BlogImages/202401161333814.png) -A(3)=5 -Details: 3->4->5 5 +![](https://dsideal.obs.cn-north-1.myhuaweicloud.com/HuangHai/BlogImages/202401161333206.png) -A(4)=11+5+10=26 -Details: 4->1->2 11 -  4->3 5 -  4->5 10 -A(5)=10 -Details: 5->4->1->2 10 -``` **思路分析** 这是一道 **不定根** 的树形$DP$问题,这类题目的特点是,给定一个树形结构,需要以每个结点为根进行一系列统计。我们一般通过两次扫描来求解此类问题: @@ -858,10 +839,16 @@ Details: 5->4->1->2 10 - 1.第一次扫描,任选一个点为根,在 **有根树** 上执行一次树形$DP$。 - 2.第二次扫描,从刚才选出的根出发,对整棵树执行一次$DFS$,在每次递归前进行 **自上而下** 的推导,计算出 **换根** 之后的解。 -首先,我们选择结点$1$,然后树形$DP$一下: -1、求出$f$数组($f[i]$表示以$1$这根的树,以$i$为根的子树中流量的最大值)。 -2、设$g[u]$表示以$u$为源点,流向整个水系的最大流量,则显然$g[1]=f[1]$。假设$g[u]$已经求出,考虑其子结点$v$,则$f[v]$包含两部分: +**本题思路** +![](https://dsideal.obs.cn-north-1.myhuaweicloud.com/HuangHai/BlogImages/202401161324729.png) + +![](https://dsideal.obs.cn-north-1.myhuaweicloud.com/HuangHai/BlogImages/202401161325661.png) + +首先,选择$1$号结点,然后树形$dfs$: +- 1、求出$f$数组($f[i]$表示以$1$这根的树,以$i$为根的子树中流量的最大值)。 +- 2、设$g[u]$表示以$u$为源点,流向整个水系的最大流量,则显然$g[1]=f[1]$。 +假设$g[u]$已经求出,考虑其子结点$v$,则$g[v]$包含两部分: - 1.从$v$流向以$v$为根的子树的流量,已经计算出来。 - 2.从$v$沿着到父节点$u$的河道,进而流向水系中其他部分的流量。