HDU-1011 Starship Troopers (树上背包)

Starship Troopers

Time Limit: 10000/5000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 20627    Accepted Submission(s): 5487

Problem Description

You, the leader of Starship Troopers, are sent to destroy a base of the bugs. The base is built underground. It is actually a huge cavern, which consists of many rooms connected with tunnels. Each room is occupied by some bugs, and their brains hide in some of the rooms. Scientists have just developed a new weapon and want to experiment it on some brains. Your task is to destroy the whole base, and capture as many brains as possible.

To kill all the bugs is always easier than to capture their brains. A map is drawn for you, with all the rooms marked by the amount of bugs inside, and the possibility of containing a brain. The cavern's structure is like a tree in such a way that there is one unique path leading to each room from the entrance. To finish the battle as soon as possible, you do not want to wait for the troopers to clear a room before advancing to the next one, instead you have to leave some troopers at each room passed to fight all the bugs inside. The troopers never re-enter a room where they have visited before.

A starship trooper can fight against 20 bugs. Since you do not have enough troopers, you can only take some of the rooms and let the nerve gas do the rest of the job. At the mean time, you should maximize the possibility of capturing a brain. To simplify the problem, just maximize the sum of all the possibilities of containing brains for the taken rooms. Making such a plan is a difficult job. You need the help of a computer.

 

Input

The input contains several test cases. The first line of each test case contains two integers N (0 < N <= 100) and M (0 <= M <= 100), which are the number of rooms in the cavern and the number of starship troopers you have, respectively. The following N lines give the description of the rooms. Each line contains two non-negative integers -- the amount of bugs inside and the possibility of containing a brain, respectively. The next N - 1 lines give the description of tunnels. Each tunnel is described by two integers, which are the indices of the two rooms it connects. Rooms are numbered from 1 and room 1 is the entrance to the cavern.

The last test case is followed by two -1's.

 

Output

For each test case, print on a single line the maximum sum of all the possibilities of containing brains for the taken rooms.

 

Sample Input

5 10
50 10
40 10
40 20
65 30
70 30
1 2
1 3
2 4
2 5
1 1
20 7
-1 -1

 

Sample Output

50
7

#include <stdio.h>
#include <vector>
#include <string.h>
using namespace std;
int bug[101], p[101], dp[101][101];
vector<vector<int> > g(101);
void dfs(int x, int fa, int m){
	int v = bug[x] / 20 + (bug[x] % 20 != 0);
	for(int i = v; i <= m; ++i){
		dp[x][i] = p[x];
	}
	int cur;
	for(int i = 0; i < g[x].size(); ++i){
		cur = g[x][i];
		if(cur == fa) continue;
		dfs(cur, x, m);
		for(int j = m; j >= v; --j){
			for(int s = 1; s <= j - v; ++s){
				dp[x][j] = max(dp[x][j], dp[x][j - s] + dp[cur][s]);
			}
		}
	}
}
int main(){
	int n, m, u, v;
	while(scanf("%d %d", &n, &m) != EOF){
		if(n == -1 && m == -1) return 0;
		for(int i = 1; i <= n; ++i){
			scanf("%d %d", &bug[i], &p[i]);
		}
		for(int i = 1; i <= n; ++i){
			g[i].clear();
		}
		for(int i = 1; i < n; ++i){
			scanf("%d %d", &u, &v);
			g[u].push_back(v);
			g[v].push_back(u);
		}
		if(m == 0){
			puts("0");
			continue;
		}
		memset(dp, 0, sizeof(dp));
		dfs(1, 0, m);
		printf("%d\n", dp[1][m]);
	}
}

/*
题意：
一棵树，3000个节点，每个节点有一些bugs，需要花一些士兵去杀死，杀bugs的士兵就只能留在该节点了，
士兵不可以走回头路，不足20个bugs也要花费一个士兵，每个节点有一个出现大bug的概率，目标是让这个概率和最大。

思路：
这题需要跑树上的背包，对于每个节点维护一个背包容量对应的概率和。dp[i][j]表示在i节点有j个士兵时可以获得的
最大概率和。按儿子节点的顺序去转移一下即可。注意没有小bugs的时候，想要获得该点的
*/