【POJ 1655】Balancing Act 【树的重心】

Balancing Act

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

Source

POJ Monthly--2004.05.15 IOI 2003 sample task

求树的重心。

任意选一个点为root，进行dfs，找到最大儿子最小的那个结点即可。

#include <iostream>
#include <algorithm>
#include <cstdio>
#include <cstring>
#include <cmath>
using namespace std;
int tot=0,ans1,n,ans2,h[20005],T,son[20005];
struct edge
{
	int y,ne;
}a[100005];
void Addedge(int x,int y)   //前向星也挺好写的，以后不用vector了
{
	tot++;
	a[tot].y=y;
	a[tot].ne=h[x];
	h[x]=tot;
}
void Dfs(int x)
{
	int i=h[x],now=0;
	son[x]=0;
	while (i)
	{
		int y=a[i].y;
		if (son[y]==-1)
		{
			Dfs(y);
	 	    son[x]=son[x]+son[y]+1;
		    if (son[y]+1>now) now=son[y]+1;
		}
		i=a[i].ne;
	}
	if (now<n-1-son[x]) now=n-1-son[x];
	if (now==ans1&&ans2>x) ans2=x;
	if (now<ans1)
		ans1=now,ans2=x;
}
int main()
{
    scanf("%d",&T);
	while (T--)
	{
		scanf("%d",&n);
		tot=0;
		for (int i=1;i<=n;i++)
			h[i]=0;
		for (int i=1;i<n;i++)
		{
			int x,y;
			scanf("%d%d",&x,&y);
			Addedge(x,y);
			Addedge(y,x);
		}
		for (int i=1;i<=n;i++)
			son[i]=-1;
		ans1=ans2=n;
		Dfs(1);
		printf("%d %d\n",ans2,ans1);
	}
	return 0;
}