HDU1011 Starship Troopers 树形DP

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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 1050 1040 1040 2065 3070 301 21 32 42 51 120 7-1 -1

 

Sample Output

507

 

 

题意：给出每个房间拥有的BUG数和能得到的能量数，然后给出每个房间的联通图，要到下一个房间必须攻破上一个房间，每个士兵最多消灭20个BUG，就算不足20个BUG也要安排一个士兵

思路：先建立树，然后进行树形DP

 

#include <stdio.h>#include <string.h>#include <algorithm>using namespace std;int n,m,len;int dp[105][105];//dp表示在i点放j人能得到的能量int bug[105],p[105],vis[105],head[105];struct node{    int now,next;} tree[105];void add(int x,int y){    tree[len].now = y;    tree[len].next = head[x];    head[x] = len++;}void dfs(int root){    int cost,i,j,k,son;    vis[root] = 1;    cost = (bug[root]+19)/20;//不足20的部分也要安排一个    for(i = cost; i<=m; i++)        dp[root][i] = p[root];//小于cost的无法获得经验    for(i = head[root]; i!=-1; i = tree[i].next)    {        son = tree[i].now;        if(!vis[son])        {            dfs(son);            for(j = m; j>=cost; j--)            {                for(k = 1; j+k<=m; k++)                {                    if(dp[son][k])//到达r的有j+k人，如果留在r有j人，则到达后继节点有k人                        dp[root][j+k] = max(dp[root][j+k],dp[root][j]+dp[son][k]);                }            }        }    }}int main(){    int i,j,x,y;    while(~scanf("%d%d",&n,&m),n+m>0)    {        for(i = 1; i<=n; i++)            scanf("%d%d",&bug[i],&p[i]);        len = 0;        memset(vis,0,sizeof(vis));        memset(head,-1,sizeof(head));        for(i = 1; i<n; i++)        {            scanf("%d%d",&x,&y);            add(x,y);            add(y,x);        }        if(!m)        {            printf("0\n");            continue;        }        memset(dp,0,sizeof(dp));        dfs(1);        printf("%d\n",dp[1][m]);    }    return 0;}

 

           

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