Contestants Division POJ - 3140

最新推荐文章于 2020-03-15 22:51:32 发布

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最新推荐文章于 2020-03-15 22:51:32 发布

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原文链接：http://www.cnblogs.com/zgglj-com/p/7748773.html

本文介绍了一种用于ACM-ICPC区域赛的特殊监控与提交系统的算法问题，该系统需将参赛学生分为两个连接区域，并使两区域间的学生数量差最小。文章通过深度优先搜索和动态规划的方法解决此问题。

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

题解：dp[ i ]表示以i为根的子树的重量，那么在回溯过程中更新答案就行(用总重减去2倍dp[ i ]就是差值).

 1 #include<cmath>
 2 #include<vector>
 3 #include<cstdio>
 4 #include<cstring>
 5 #include<iostream>
 6 #include<algorithm>
 7 using namespace std;
 8 typedef long long ll;
 9 
10 const int maxn=1e5+5;
11 
12 int n,m;
13 ll dp[maxn],ans,temp;
14 
15 vector<int> G[maxn];
16 
17 ll mabs(ll a){
18     return a>0 ? a:-a;
19 }
20 
21 void DFS(int pa,int u){
22     for(int i=0;i<G[u].size();i++){
23         int v=G[u][i];
24         if(pa==v) continue;
25         DFS(u,v);
26         dp[u]+=dp[v];
27         //ans=min(ans,mabs(temp-2*dp[v]));  错误的更新方式！！！！！
28         //ans=min(ans,mabs(temp-2*dp[u]));
29     }
30     ans=min(ans,mabs(temp-2*dp[u]));
31 }
32 
33 int main()
34 {   int cnt=0;
35     while(~scanf("%d%d",&n,&m)){
36         if(n==0&&m==0) break;
37         
38         temp=0;
39         for(int i=1;i<=n;i++){
40             G[i].clear();
41             scanf("%lld",&dp[i]);
42             temp+=dp[i];
43         }
44         for(int i=1;i<=m;i++){
45             int u,v;
46             scanf("%d%d",&u,&v);
47             G[u].push_back(v);
48             G[v].push_back(u);
49         }
50         
51         ans=temp;
52         DFS(0,1);
53         cnt++;
54         printf("Case %d: %lld\n",cnt,ans);
55     }
56     return 0;
57 }