poj-1655-树的重心

Balancing Act

Time Limit: 1000MS		Memory Limit: 65536K
Total Submissions: 15526		Accepted: 6575

Description

Consider a tree T with N (1 <= N <= 20,000) nodes numbered 1...N. Deleting any node from the tree yields a forest: a collection of one or more trees. Define the balance of a node to be the size of the largest tree in the forest T created by deleting that node from T. 
For example, consider the tree: 

Deleting node 4 yields two trees whose member nodes are {5} and {1,2,3,6,7}. The larger of these two trees has five nodes, thus the balance of node 4 is five. Deleting node 1 yields a forest of three trees of equal size: {2,6}, {3,7}, and {4,5}. Each of these trees has two nodes, so the balance of node 1 is two. 

For each input tree, calculate the node that has the minimum balance. If multiple nodes have equal balance, output the one with the lowest number. 

Input

The first line of input contains a single integer t (1 <= t <= 20), the number of test cases. The first line of each test case contains an integer N (1 <= N <= 20,000), the number of congruence. The next N-1 lines each contains two space-separated node numbers that are the endpoints of an edge in the tree. No edge will be listed twice, and all edges will be listed.

Output

For each test case, print a line containing two integers, the number of the node with minimum balance and the balance of that node.

Sample Input

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

Sample Output

1 2

    求给定的一颗树的平衡点，就是这个点的最大的一颗子树森林的节点数尽量小。想到树形dp，但是子节点的最大子树可能来自
父亲，但是来自父亲的那棵树的节点数我们可以通过计算出当前节点为根的节点数再用N减去就好了，显然可以递归的时候顺便算出来。

#include<iostream>
#include<cstdio>
#include<cstring>
#include<vector>
using namespace std;
vector<int>g[20010];
int f[20010],num[20010],n;
void dfs(int u,int fa){
    f[u]=0,num[u]=1;
    for(int i=0;i<g[u].size();++i){
        if(g[u][i]==fa) continue;
        dfs(g[u][i],u);
        f[u]=max(f[u],num[g[u][i]]);
        num[u]+=num[g[u][i]];
    }
    f[u]=max(f[u],n-num[u]);
}
int main()
{
    int t,m,i,j;
    int u,v;
    cin>>t;
    while(t--){
        cin>>n;
        for(i=1;i<=n;++i) g[i].clear();
        for(i=1;i<n;++i){
            scanf("%d%d",&u,&v);
            g[u].push_back(v);
            g[v].push_back(u);
        }
        dfs(1,0);
        int ans1=0,ans2=999999;
        for(i=1;i<=n;++i){
            if(f[i]<ans2){
                ans1=i;
                ans2=f[i];
            }
        }
        cout<<ans1<<' '<<ans2<<endl;
    }
    return 0;
}