CF 219D Choosing capital for Treeland tree DP Good question

A country, there are N cities, numbered 1~n, there are n-1 to the edge

If we don't consider the direction of the edges, these n cities just form a tree.

Now the king is going to choose one of these n cities as the capital.

Request: From the capital can be reached in any city of this country (side is a direction)

So a city as the capital, there may be a number of sides need to change direction

Now ask, choose which cities as the capital, need to change the direction of the least side.

Output minimum number of edges that need to change direction

The output can be used as the capital's number

Tree-shaped DP

First assume the City 1 as the capital

Make tree (i) a subtree that is rooted in I

Dp[i] Indicates the number of edges that need to be changed if I is the capital of the tree (i)

First time DFS, find the DP array

Ans[i] Indicates the number of sides to change (note the difference between the meaning of the DP array) If I is the capital of the whole tree.

Obvious: ans[1]=dp[1]

Obviously there are:

In a directed tree, if the capital is U, now we want to make U's son node v the capital, only need to change the direction of 1 sides

Suppose node U is the parent node of Node V, e= (u,v), Ans[u] Known

If the direction of E is pointing to V, then: ans[v]=ans[u]+1

otherwise: ans[v]=ans[u]-1

So the second time Dfs, recursion out the ANS array

Next, find Min=min (Ans[i]) and output min

Outputs all of the I that make the ans[i]==min

1#include <cstdio>2#include <cstring>3 4 using namespacestd;5 6 Const intmaxn=200000+5;7 8 structEdge9 {Ten     intTo,next; One     BOOLFlag; A }; -Edge edge[maxn<<1]; - intHEAD[MAXN]; the inttot; - intANS[MAXN]; - intDP[MAXN]; - intPRINT[MAXN]; +  - voidInit () + { Amemset (head,-1,sizeofhead); attot=0; -Memset (DP,0,sizeofDP); - } -  - voidAddedge (intUintVBOOLflag) - { inedge[tot].to=v; -edge[tot].flag=Flag; toedge[tot].next=Head[u]; +head[u]=tot++; - } the  * voidDfs0 (int,int ); $ voidDFS1 (int,int );Panax Notoginseng  - intMain () the { +     intN; A init (); the     BOOLCnt=true; +scanf"%d",&n); -      for(intI=1; i<n;i++) $     { $         intu,v; -scanf"%d%d",&u,&v); - Addedge (u,v,cnt); theAddedge (v,u,!CNT); -     }WuyiDfs0 (1,-1); theans[1]=dp[1]; -DFS1 (1,-1); Wu  -     intmin=ans[1]; About      for(intI=2; i<=n;i++) $     { -         if(ans[i]<min) -min=Ans[i]; -     } Atot=1; +      for(intI=1; i<=n;i++) the     { -         if(ans[i]==min) $         { theprint[tot++]=i; the         } the     } the  -printf"%d\n", min); in      for(intI=1; i<tot-1; i++) the     { theprintf"%d", Print[i]); About     } theprintf"%d\n", print[tot-1]); the  the     return 0; + } -  the voidDfs0 (intUintpre)Bayi { the      for(intI=head[u];~i;i=edge[i].next) the     { -         intv=edge[i].to; -         BOOLflag=Edge[i].flag; the         if(v==pre) the             Continue; the Dfs0 (v,u); the         if(flag) -dp[u]+=Dp[v]; the         Else thedp[u]+= (dp[v]+1); the     }94     return ; the } the  the voidDFS1 (intUintpre)98 { About      for(intI=head[u];~i;i=edge[i].next) -     {101         intv=edge[i].to;102         intflag=Edge[i].flag;103         if(v==pre)104             Continue; the         if(flag)106ans[v]=ans[u]+1;107         Else108ans[v]=ans[u]-1;109 DFS1 (v,u); the     }111     return ; the}

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CF 219D Choosing capital for Treeland tree DP Good question