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
Source
Northeastern Europe 2005, Northern Subregion
题目大意：给定一颗有n个节点的树，求出这棵树的所有重心，并按编号从大到小输出。
先给出树的重心的定义：一棵树的重心是指删除这个节点之后使树分成几个部分，使得这几个部分中节点个数的最大值最小。
其实求法非常简单
用son[i]表示节点i的子节点有多少个。
blance表示以节点i为父亲的子树中节点个数的最大值。
那么删除节点i之后形成的几个部分中节点个数的最大值为
max(blance,n-son[i]-1);
然后我们dfs一遍就好了。
注意用vector会超时。需要使用next数组。。
代码：
#include<iostream>
#include<cstdio>
#include<cstring>
#include<vector>
#include<algorithm>
using namespace std;
const int N=50010;
const int inf=2100000000LL;
struct use{
int st,en;
}b[1000001];
int son[N],n,ans[N],minn,next[5000001]={0},point[100001]={0},tot;
bool f[N];
void add(int x,int y)
{
tot++;next[tot]=point[x];point[x]=tot;
b[tot].st=x;b[tot].en=y;
}
void dfs(int x)
{
int i,j,u,balance=0;
son[x]=0;
f[x]=false;
for(i=point[x];i;i=next[i]){
u=b[i].en;
if(!f[u]) continue;
dfs(u);
son[x]+=son[u]+1;
balance=max(balance,son[u]+1);
}
balance=max(balance,n-son[x]-1);
if(balance<minn){
minn=balance;
ans[0]=1;
ans[1]=x;
}
else if(balance==minn){
ans[0]+=1;
ans[ans[0]]=x;
}
}
int main()
{
int i,j,x,y;
scanf("%d",&n);
minn=inf;
memset(f,1,sizeof(f));
for(i=1;i<n;++i){
scanf("%d%d",&x,&y);
add(x,y);
add(y,x);
}
dfs(1);
sort(ans+1,ans+ans[0]+1);
for(i=1;i<=ans[0];++i)
printf("%d ",ans[i]);
printf("\n");
}