【树形DP+背包】 hdu1011 Starship Troopers

Starship Troopers

http://acm.hdu.edu.cn/showproblem.php?pid=1011

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
  

题意：n个洞穴，m个士兵，每个洞中有a个bug，b个brain，每个士兵可以处理20个bug，入口在洞穴1处，问最多可以得到多少个brain。 

题解：树形DP+背包。dp[x][j]=max{dp[x][j-k]+dp[i][k]}，其中x与i相连。

//树形DP+背包
#include<cstdio>
#include<cstring>
using namespace std;
#define MAX 105
#define max(a,b) ((a)>(b)?(a):(b))
int dp[MAX][MAX];//在第i个洞穴有j个人时获得的最大值
int mapt[MAX][MAX];
int n,m;
struct node
{
    int brain,bug;
}room[MAX];
void dfs(int x,int pre)
{
    int r=(room[x].bug+19)/20;//第x个洞需要的人数
    for(int i=m;i>=r;--i)
        dp[x][i]=room[x].brain;//初始化
    for(int i=1;i<=n;++i)
    {
        if((mapt[x][i])&&(pre!=i))
        {
            dfs(i,x);
            for(int j=m;j>=r;--j)
                for(int k=1;k<=j-r;++k)
                    dp[x][j]=max(dp[x][j],dp[x][j-k]+dp[i][k]);
        }
    }

}
int main()
{
    int a,b;
    for(;scanf("%d%d",&n,&m);)
    {
        if(n==-1&&m==-1) break;
        for(int i=1;i<=n;++i)
            scanf("%d%d",&room[i].bug,&room[i].brain);
        memset(mapt,0,sizeof(mapt));
        memset(dp,0,sizeof(dp));
        for(int i=1;i<n;++i)
        {
            scanf("%d%d",&a,&b);
            mapt[a][b]=mapt[b][a]=1;
        }
        if(m==0)
        {
            puts("0");
            continue;
        }
        dfs(1,-1);
        printf("%d\n",dp[1][m]);
    }
    return 0;
}

来源： http://blog.youkuaiyun.com/ACM_Ted