sgu 134 Centroid 树的重心

      对于一棵树，定义点k，删掉点k后，产生的几个联通量中节点数最大值 最小时，k为树的重心。遍历一边，用两个数组,size[i]表示i和i的子树中的节点数之和，sonsize[i]表示节点最多的子树的节点数，（n-size[i]就是这个节点没有枚举到的那个分支的节点数），然后枚举各个节点就可以了。

      #include <iostream>
#include <cstdio>
#include <algorithm>
#include <memory.h>
#include <cmath>
#include <string>
#include <cstring>
#include <vector>
using namespace std;
typedef long long ll;
const int maxn=21000;
int n,m;
int ans,num;
int p,q,k;
vector<int> g[maxn];
int size[maxn],sonsize[maxn];
int dfs(int i,int fa)
{
size[i]=1;
for (int j=0; j<g[i].size(); j++)
{
if (fa!=g[i][j])
{
int v=g[i][j];
dfs(v,i);
size[i]+=size[v];
sonsize[i]=max(sonsize[i],size[v]);
}
}
}
int main()
{
// freopen("in.txt","r",stdin);
scanf("%d",&n);
for (int i=1; i<=n; i++) g[i].clear();
memset(size,0,sizeof size);
memset(sonsize,0,sizeof sonsize);

int x,y;
for (int i=1; i<n; i++)
{
scanf("%d%d",&x,&y);
g[x].push_back(y);
g[y].push_back(x);
}
dfs(1,-1);
vector<int> out;
int minn=(1<<28);
for (int i=1; i<=n; i++)
{
minn=min(minn,max(n-size[i],sonsize[i]));
}
for (int i=1; i<=n; i++)
if (max(n-size[i],sonsize[i])==minn)
out.push_back(i);
cout<<minn<<" "<<out.size()<<endl;
cout<<out[0];
for (int i=1; i<out.size(); i++)
cout<<" "<<out[i]<<endl;
return 0;
}