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POJ 3140 樹形dp

編輯：C++入門知識

Contestants Division Time Limit: 2000MS Memory Limit: 65536K Total Submissions: 7725 Accepted: 2196

Description

In the new ACM-ICPC Regional Contest, a special monitoring and submitting system will be set up, and students will be able to compete at their own universities. However there’s one problem. Due to the high cost of the new judging system, the organizing committee can only afford to set the system up such that there will be only one way to transfer information from one university to another without passing the same university twice. The contestants will be divided into two connected regions, and the difference between the total numbers of students from two regions should be minimized. Can you help the juries to find the minimum difference?

Input

There are multiple test cases in the input file. Each test case starts with two integers N and M, (1 ≤ N ≤ 100000, 1 ≤ M ≤ 1000000), the number of universities and the number of direct communication line set up by the committee, respectively. Universities are numbered from 1 to N. The next line has N integers, the K^th integer is equal to the number of students in university numbered K. The number of students in any university does not exceed 100000000. Each of the following M lines has two integers s, t, and describes a communication line connecting university s and university t. All communication lines of this new system are bidirectional.

N = 0, M = 0 indicates the end of input and should not be processed by your program.

Output

For every test case, output one integer, the minimum absolute difference of students between two regions in the format as indicated in the sample output.

Sample Input

7 6
1 1 1 1 1 1 1
1 2
2 7
3 7
4 6
6 2
5 7
0 0

Sample Output

Case 1: 1

Source

Shanghai 2006

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題意：將一顆樹分成兩顆子樹，使得差值盡可能的小。

很簡單，直接dp出以每一個點為根的子樹的權值，然後根據總權值求出剩余部分的權值，枚舉更新得到最小值。

代碼：

/* ***********************************************
Author :xianxingwuguan
Created Time :2014-2-6 16:15:10
File Name :1.cpp
************************************************ */
#pragma comment(linker, "/STACK:102400000,102400000")
#include 
#include 
#include 
#include 
#include 
#include 
#include 
#include 
#include 
#include 
#include 
#include 
#include 
#include 
using namespace std;
#define INF 1000000000000000LL
#define eps 1e-8
#define pi acos(-1.0)
typedef long long ll;
const ll maxn=100100;
ll head[maxn],tol,weight[maxn],dp[maxn];
struct node{
	ll next,to;
	node(){};
	node(ll _next,ll _to):next(_next),to(_to){}
}edge[5*maxn];
void add(ll u,ll v){
	edge[tol]=node(head[u],v);
	head[u]=tol++;
}
void dfs(ll u,ll fa){
	dp[u]=weight[u];
	for(ll i=head[u];i!=-1;i=edge[i].next){
		ll v=edge[i].to;
		if(v==fa)continue;
		dfs(v,u);
		dp[u]+=dp[v];
	}
}
ll ABS(ll x){
	if(x<=0)x=-x;
	return x;
}
int main(){
	ll i,j,k,m,n,p,T=0;
	while(cin>>n>>m){
		if(n==0&&m==0)break;
		memset(head,-1,sizeof(head));
		ll sum=0,ans=INF;
		for(i=1;i<=n;i++)cin>>weight[i],sum+=weight[i];
		while(m--){
			cin>>j>>k;
			add(j,k);
			add(k,j);
		}
		dfs(1,-1);
		for(i=1;i<=n;i++){
			ll pp=ABS(dp[i]-(sum-dp[i]));
			ans=min(ans,pp);
		}
		cout<<"Case "<<++T<<": "<