Tree of Tree

描述

You're given a tree with weights of each node, you need to find the maximum subtree of specified size of this tree.

Tree Definition
A tree is a connected graph which contains no cycles.

输入

There are several test cases in the input.

The first line of each case are two integers N(1 <= N <= 100), K(1 <= K <= N), where N is the number of nodes of this tree, and K is the subtree's size, followed by a line with N nonnegative integers, where the k-th integer indicates the weight of k-th node. The following N - 1 lines describe the tree, each line are two integers which means there is an edge between these two nodes. All indices above are zero-base and it is guaranteed that the description of the tree is correct.

输出

One line with a single integer for each case, which is the total weights of the maximum subtree.

样例输入

3 1
10 20 30
0 1
0 2
3 2
10 20 30
0 1
0 2

样例输出

题目大意：给定一颗树，求结点数为k的子树的最大权值。

解题思路：树形dp，dp[i][j]表示以第i个结点为根，有j个结点的子树的最大权值。

#include <bits/stdc++.h>
using namespace std;
#define LL long long
const int N=105;
vector<int>G[N];
int dp[N][N],m,d[N],a[N];
void dfs(int u)
{
    dp[u][1]=a[u];
    for(int i=0;i<G[u].size();i++){
        int v=G[u][i];
        dfs(v);
        for(int j=m;j>=1;j--){
            for(int k=1;k<=j;k++){
                if(j-k>=0) dp[u][j]=max(dp[u][j],dp[u][k]+dp[v][j-k]);
            }
        }
    }

}
int main()
{
    int n;
    while(cin>>n>>m){
        for(int i=0;i<=n;i++){
            G[i].clear();d[i]=0;
            for(int j=0;j<=m;j++) dp[i][j]=0;
        }
        for(int i=0;i<n;i++) cin>>a[i];
        for(int i=1,u,v;i<n;i++){
            cin>>u>>v;
            G[u].push_back(v);
            d[v]++; 
        }
        int pos=-1;
        for(int i=0;i<n;i++) if(d[i]==0) dfs(i);
        int ans=-1;
    
        for(int i=0;i<n;i++) ans=max(ans,dp[i][m]);
        cout<<ans<<endl;
        
    }
}

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