POJ2342Anniversary party题解动态规划DP

Anniversary party

Time Limit: 1000MS Memory Limit: 65536KTotal Submissions: 1507 Accepted: 782

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

711111111 32 36 47 44 53 50 0

Sample Output

5

Source

Ural State University Internal Contest October'2000 Students Session

和POj1463类似的树型DP

状态：

d[i][0]表示不选i结点的最大值

d[i][1]表示选i结点的最大值

状态转移方程：

j是i的儿子结点

d[i][0]=sum{max(d[j][0],d[j][1])}

d[i][1]=sum{d[j][0]}

边界：

d[i][1]=a[i]

代码：

#include<cstdio>#include<vector>#include<algorithm>using namespace std;int n,a[6005],f[6005],d[6005][2];vector<int> v[6005];void dfs(int x){int i,j,m=v[x].size();for(i=0;i<m;i++)dfs(v[x][i]);d[x][1]=a[x];if(!m)return;for(i=0;i<m;i++){j=v[x][i];d[x][1]+=d[j][0];d[x][0]+=max(d[j][0],d[j][1]);}}int main(){int i,x,y;scanf("%d",&n);for(i=1;i<=n;i++)scanf("%d",a+i);while(scanf("%d%d",&y,&x),x+y){v[x].push_back(y);f[y]=1;}for(i=1;i<=n;i++)if(!f[i])break;dfs(i);printf("%d/n",max(d[i][0],d[i][1]));}