BZOJ 4033: [HAOI2015]树上染色

/**************************************************************
    Problem: 4033
    User: BeiYu
    Language: C++
    Result: Accepted
    Time:432 ms
    Memory:34192 kb
****************************************************************/
 
#include <bits/stdc++.h>
using namespace std;
 
#define mpr make_pair
#define x first
#define y second
 
typedef long long LL;
typedef pair<int,int> pr;
const int N = 2050;
 
inline int in(int x=0,char ch=getchar(),int v=1) {
    while(ch>‘9‘||ch<‘0‘) v=ch==‘-‘?-1:v,ch=getchar();
    while(ch>=‘0‘&&ch<=‘9‘)x=x*10+ch-‘0‘,ch=getchar();return x*v; }
 
int n,k;
vector<pr> g[N];
LL f[N][N],sz[N],tmp[N];
 
void AddEdge(int fr,int to,int dis) { g[fr].push_back(mpr(to,dis)); }
void DP(int u,int fa) {
    sz[u]=1;
    for(int t=0,v;t<(int)g[u].size();t++) if((v=g[u][t].x)!=fa){
        DP(v,u);
        for(int i=0;i<=sz[u]+sz[v];i++) tmp[i]=0;
        for(int i=0;i<=sz[u];i++) {
            for(int j=0;j<=sz[v];j++) {
                if(i+j>k) break;
                tmp[i+j]=max(tmp[i+j],f[u][i]+f[v][j]+g[u][t].y*(j*(k-j)+(sz[v]-j)*(n-k-(sz[v]-j))));
            }
        }sz[u]+=sz[v];
        for(int i=0;i<=sz[u];i++) f[u][i]=tmp[i];
    }
/*  cout<<"------"<<endl;
    cout<<u<<" "<<fa<<" "<<sz[u]<<endl;
    for(int i=0;i<=sz[u];i++) cout<<f[u][i]<<" ";cout<<endl;*/
}
 
int main() {
    n=in(),k=in();
    for(int i=1;i<n;i++) {
        int u=in(),v=in(),d=in();
        AddEdge(u,v,d),AddEdge(v,u,d);
    }
    DP(1,1);
    printf("%lld\n",f[1][k]);
    return 0;
}