POJ 2342 树状dp

Anniversary party

Description

There is going to be a party to celebrate the 80-th Anniversary of the Ural State University. The University has a hierarchical structure of employees. It means that the supervisor relation forms a tree rooted at the rector V. E. Tretyakov. In order to make the party funny for every one, the rector does not want both an employee and his or her immediate supervisor to be present. The personnel office has evaluated conviviality of each employee, so everyone has some number (rating) attached to him or her. Your task is to make a list of guests with the maximal possible sum of guests‘ conviviality ratings.

Input

Employees are numbered from 1 to N. A first line of input contains a number N. 1 <= N <= 6 000. Each of the subsequent N lines contains the conviviality rating of the corresponding employee. Conviviality rating is an integer number in a range from -128 to 127. After that go N – 1 lines that describe a supervisor relation tree. Each line of the tree specification has the form:
L K

It means that the K-th employee is an immediate supervisor of the L-th employee. Input is ended with the line

0 0

Output

Output should contain the maximal sum of guests‘ ratings.

Sample Input

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

Sample Output

5

Source

Ural State University Internal Contest October‘2000 Students Session

POJ 2342

题目意思：

求一棵树的最小点权覆盖;

解题思路：

树状dp,状态转移方程为：

dp[i][0]=max(dp[son1][0],dp[son1][1])+max(dp[son2][0],dp[son2][1])+...max(dp[sonm][0],dp[sonm][1]);

dp[i][1]=sum(dp[son][0]);

 1 #include<iostream>
 2 #include<cstdio>
 3 #include<cstring>
 4 #include<algorithm>
 5 #include<cstdio>
 6 using namespace std;
 7 const int maxn=6007;
 8 bool visit[maxn];
 9 int value[maxn];
10 int head[maxn];
11 int dp[maxn][2];
12 int sum=0;
13 int n;
14 struct node
15 {
16     int to,next;
17 };
18 node tree[maxn];
19 void init()
20 {
21     memset(head,-1,sizeof(head));
22     memset(visit,0,sizeof(visit));
23     memset(dp,0,sizeof(dp));
24     memset(value,0,sizeof(value));
25     sum=0;
26 }
27 void AddEdge(int u,int v)
28 {
29         tree[sum].to=v;
30         tree[sum].next=head[u];head[u]=sum;
31         sum++;
32 }
33 void dfs_tree(int point)
34 {
35     int res0=0,res1=0;
36     if(visit[point]) return;
37     visit[point]=1;
38     for(int i=head[point];i!=-1;i=tree[i].next)
39     {
40         if(!visit[tree[i].to]) dfs_tree(tree[i].to);
41         res1+=dp[tree[i].to][0];
42         res0+=max(dp[tree[i].to][0],dp[tree[i].to][1]);
43     }
44     dp[point][0]=res0;
45     dp[point][1]=res1+value[point];
46 }
47 int main()
48 {
49     // freopen("in.txt","r",stdin);
50     while(~scanf("%d",&n)){
51         init();
52         for(int i=1;i<=n;i++)
53         {
54             scanf("%d",&value[i]);
55         }
56         int a,b;
57         while(1)
58         {
59             scanf("%d %d",&a,&b);
60             if(a==0&&b==0) break;
61             AddEdge(b,a);
62             visit[a]=1;
63         }
64         int root;
65         for(int i=1;i<=n;i++)
66         {
67             if(visit[i]==0) root=i;
68         }
69         memset(visit,0,sizeof(visit));
70         dfs_tree(root);
71         int ans=max(dp[root][0],dp[root][1]);
72         printf("%d\n",ans);
73     }
74     return 0;
75 }