SGU 134 Centroid（树的重心）

思路：找树的重心，就是删除那个节点之后使得剩下子树的节点数最大的最小的点

#include<iostream>
#include<cstdio>
#include<cstring>
#include<vector>
using namespace std;
const int maxn = 16000+5;
#define inf 1e9
vector<int>e[maxn],ans;
int siz[maxn];
int dp[maxn];
int n,minx,res;
void dfs(int u,int fa)
{
siz[u]=1;
for(int i = 0;i<e[u].size();i++)
{
int v = e[u][i];
if(v==fa)
continue;
dfs(v,u);
siz[u]+=siz[v];
res = max(res,siz[v]);
}
dp[u]=max(res,n-siz[u]);
minx = min(dp[u],minx);
}
int main()
{
scanf("%d",&n);
{
for(int i = 0;i<=n;i++)
e[i].clear();
minx = inf;
res = 0;
for(int i = 1;i<n;i++)
{
int u,v;
scanf("%d%d",&u,&v);
e[u].push_back(v);
e[v].push_back(u);
}
dfs(1,-1);
//for(int i = 1;i<=n;i++)
// printf("%d\n",dp[i]);
for(int i = 1;i<=n;i++)
if(dp[i]==minx)
ans.push_back(i);

printf("%d %d\n",minx,ans.size());
for(int i = 0;i<ans.size();i++)
printf("%d ",ans[i]);
//printf("%d\n",ans[ans.size()-1]);
}
}


Description

You are given an undirected connected graph, with N vertices and N-1 edges (a tree). You must find the centroid(s) of the tree. 

In order to define the centroid, some integer value will be assosciated to every vertex. Let's consider the vertex k. If we remove the vertex k from the tree (along with its adjacent edges), the remaining graph will have only N-1 vertices
and may be composed of more than one connected components. Each of these components is (obviously) a tree. The value associated to vertex k is the largest number of vertices contained by some connected component in the remaining graph, after
the removal of vertex k. All the vertices for which the associated value is minimum are considered centroids.

Input
The first line of the input contains the integer number N (1<=N<=16 000). The next N-1 lines will contain two integers, a and b, separated by blanks, meaning
that there exists an edge between vertex a and vertex b.

Output
You should print two lines. The first line should contain the minimum value associated to the centroid(s) and the number of centroids. The second line should contain the list of vertices which are centroids, sorted in ascending order.

Sample Input

7
1 2
2 3
2 4
1 5
5 6
6 7

Sample Output

3 1
1