ACdream 1032 Component

Component

Time Limit: 5000ms

Memory Limit: 64000KB

This problem will be judged on ACdream. Original ID: 1032
64-bit integer IO format: %lld      Java class name: (No Java Yet)

 

Given a tree with weight assigned to nodes, find out minimum total weight connected component with fixed number of node.

 

Input

The first line contains a single integer n.

The second line contains n integers $w_1,w_2,…,w_n. w_i$ denotes the weight of the node i.

The following (n−1) lines with two integers ai and bi, which denote the edge between ai and bi.

Note that the nodes are labled by $1,2,…,n.$

$(1leq nleq 2⋅10^3,1leq w_ileq 10^5)$

Output

$n$ integers $c_1,c_2,…,c_n. c_i$ stands for the minimum total weight component with i nodes.

Sample Input

3 
1 2 3
1 2
2 3

Sample Output

1 3 6

Source

ftiasch

 

解题：树形dp

 

#include <bits/stdc++.h>
using namespace std;
const int maxn = 2010;
vector<int>g[maxn];
int val[maxn],dp[maxn][maxn],n,son[maxn],ans[maxn];
void dfs(int u,int fa){
    dp[u][1] = val[u];
    dp[u][0] = 0;
    son[u] = 1;
    for(int i = g[u].size()-1; i >= 0; --i){
        if(g[u][i] == fa) continue;
        dfs(g[u][i],u);
        son[u] += son[g[u][i]];
        for(int j = son[u]; j > 0; --j){
            for(int k = 1; k <= j; ++k)
                dp[u][j] = min(dp[u][j],dp[g[u][i]][j - k] + dp[u][k]);
        }
    }
    for(int i = son[u]; i >= 0; --i)
        ans[i] = min(ans[i],dp[u][i]);
}
int main(){
    while(~scanf("%d",&n)){
        for(int i = 0; i < maxn; ++i) g[i].clear();
        for(int i = 1; i <= n; ++i) scanf("%d",val + i);
        memset(dp,0x3f,sizeof dp);
        memset(ans,0x3f,sizeof ans);
        for(int i = 1,u,v; i < n; ++i){
            scanf("%d%d",&u,&v);
            g[u].push_back(v);
            g[v].push_back(u);
        }
        dfs(1,-1);
        for(int i = 1; i <= n; ++i)
            printf("%d%c",ans[i],i == n?'
':' ');
    }
    return 0;
}