Pku3107 Godfather

Description
Last years Chicago was full of gangster fights and strange murders. The chief of the police got really tired of all these crimes, and decided to arrest the mafia leaders.
Unfortunately, the structure of Chicago mafia is rather complicated. There are n persons known to be related to mafia. The police have traced their activity for some time, and know that some of them are communicating with each other. Based on the data collected, the chief of the police suggests that the mafia hierarchy can be represented as a tree. The head of the mafia, Godfather, is the root of the tree, and if some person is represented by a node in the tree, its direct subordinates are represented by the children of that node. For the purpose of conspiracy the gangsters only communicate with their direct subordinates and their direct master.
Unfortunately, though the police know gangsters’ communications, they do not know who is a master in any pair of communicating persons. Thus they only have an undirected tree of communications, and do not know who Godfather is.
Based on the idea that Godfather wants to have the most possible control over mafia, the chief of the police has made a suggestion that Godfather is such a person that after deleting it from the communications tree the size of the largest remaining connected component is as small as possible. Help the police to find all potential Godfathers and they will arrest them.

Input
The first line of the input file contains n — the number of persons suspected to belong to mafia (2 ≤ n ≤ 50 000). Let them be numbered from 1 to n.
The following n − 1 lines contain two integer numbers each. The pair ai, bi means that the gangster ai has communicated with the gangster bi. It is guaranteed that the gangsters’ communications form a tree.

Output
Print the numbers of all persons that are suspected to be Godfather. The numbers must be printed in the increasing order, separated by spaces.

Sample Input
6
1 2
2 3
2 5
3 4
3 6

Sample Output
2 3

HINT
tree dp

题意简述
给一颗n个结点的树，节点编号为1~n，问删除一个节点之后，让剩下的分支中节点数量最多的尽量少，可能有多种方案，按编号顺序输出。

题解
三倍经验题（另外两道请戳这里和这里）
简单的tree dp
我用的是邻接表存树的结构

代码

#include <cstdio>#include <algorithm>const int maxn=50000;const int inf=2147483647;int n,i,x,y,tot,fl;int size[maxn+10],pre[maxn*2+10],now[maxn+10],son[maxn*2+10],z[maxn+10];int f[maxn+10][2],g[maxn+10][2];int maxlist[maxn+10],nummax,nowmax;int dfs(int u,int fa){    int maxx=-1;    size[u]=1;    int j=now[u];    while (j!=0)    {        if (son[j]==fa)        {            j=pre[j];            continue;        }        dfs(son[j],u);          size[u]+=size[son[j]];        if (size[son[j]]>maxx)        {            maxx=size[son[j]];        }        j=pre[j];    }    if (n-size[u]>maxx)    {        maxx=n-size[u];    }    if (maxx==nowmax)    {        nummax++;        maxlist[nummax]=u;    }    if (maxx<nowmax)    {        nowmax=maxx;        nummax=1;        maxlist[nummax]=u;    }    return size[u];}int main(){    nowmax=inf;    scanf("%d",&n);    for (i=1;i<=n-1;i++)    {        scanf("%d%d",&x,&y);        tot++;        pre[tot]=now[x];        now[x]=tot;        son[tot]=y;        tot++;        pre[tot]=now[y];        now[y]=tot;        son[tot]=x;    }    dfs(1,0);    std::sort(maxlist+1,maxlist+nummax+1);    for (i=1;i<nummax;i++)    {        printf("%d ",maxlist[i]);    }    printf("%d",maxlist[nummax]);    return 0;}