树形动态规划 hdu1502 poj2342 Anniversary party

Anniversary party

一向惧怕DP动态规划和图论，而树形DP又把DP和树图结合起来了。

1、什么是树型动态规划 
顾名思义，树型动态规划就是在“树”的数据结构上的动态规划，平时作的动态规划都是线性的或者是建立在图上的，线性的动态规划有二种方向既向前和向后，相应的线性的动态规划有二种方法既顺推与逆推，而树型动态规划是建立在树上的，所以也相应的有二个方向： 
    1、叶－>根：在回溯的时候从叶子节点往上更新信息
    2、根 - >叶：往往是在从叶往根dfs一遍之后（相当于预处理），再重新往下获取最后的答案。

#include <cstdio>#include <cstring>#include <algorithm>#include <vector>using namespace std;const int maxn = 6007;int n, dp[maxn][2], f[maxn];vector<int> g[maxn];void work(int rt) {for(int i = 0; i < g[rt].size(); ++i) {work(g[rt][i]);} //DFS,嗯，深搜 for(int i = 0; i < g[rt].size(); ++i) {dp[rt][1] += dp[g[rt][i]][0];dp[rt][0] += max(dp[g[rt][i]][1], dp[g[rt][i]][0]);}}int main(){int n;while(~scanf("%d", &n)) {for(int i = 0; i <= n; ++i)g[i].clear();memset(dp, 0, sizeof dp);memset(f, -1, sizeof f);for (int i = 1; i <= n; ++i)scanf("%d", &dp[i][1]);int ch, fa;while(~scanf("%d%d", &ch, &fa), ch||fa) {f[ch] = fa;g[fa].push_back(ch);}int rt = 1;while(f[rt] != -1)rt = f[rt];work(rt);printf("%d\n", max(dp[rt][1], dp[rt][0]));}return 0;}

Anniversary party

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 11644    Accepted Submission(s): 4788

Problem 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 T 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