【LOJ#2124】【HAOI2015】—树上染色（树形dp）

传送门

简单dp即可

#include<bits/stdc++.h>
using namespace std;
#define cs const
#define re register
#define pb push_back
#define bg begin
#define pii pair<int,int>
#define fi first
#define ll long long
#define se second
cs int RLEN=1<<20|1;
inline char gc(){
	static char ibuf[RLEN],*ib,*ob;
	(ib==ob)&&(ob=(ib=ibuf)+fread(ibuf,1,RLEN,stdin));
	return (ib==ob)?EOF:*ib++;
}
#define gc getchar
inline int read(){
	char ch=gc();
	int res=0;bool f=1;
	while(!isdigit(ch))f^=ch=='-',ch=gc();
	while(isdigit(ch))res=(res+(res<<2)<<1)+(ch^48),ch=gc();
	return f?res:-res;
}
template<class tp>inline void chemx(tp &a,tp b){a<b?a=b:0;}
template<class tp>inline void chemn(tp &a,tp b){a>b?a=b:0;}
cs int N=2005;
vector<pii>e[N];
int n,k,siz[N];
ll f[N][N],tmp[N];
inline ll calc(int v,int ret,int num){
	return 1ll*v*num*(k-num)+1ll*v*ret*(n-k-ret);
}
void dfs(int u,int fa){
	siz[u]=1;
	f[u][0]=0,f[u][1]=0;
	for(pii &x:e[u]){
		int v=x.fi;
		if(v==fa)continue;
		dfs(v,u);
		memset(tmp,128,sizeof(ll)*(k+1));
		for(int i=min(k,siz[u]);~i;i--)if(f[u][i]>=0)
		for(int j=0;i+j<=k&&j<=siz[v];j++)if(f[v][j]>=0){
			chemx(tmp[i+j],f[u][i]+f[v][j]+calc(x.se,siz[v]-j,j));
		}
		for(int i=0;i<=k;i++)chemx(f[u][i],tmp[i]);
		siz[u]+=siz[v];
	}
}
int main(){
	#ifdef Stargazer
	freopen("lx.cpp","r",stdin);
	#endif
	n=read(),k=read();
	for(int i=1;i<n;i++){
		int u=read(),v=read(),w=read();
		e[u].pb(pii(v,w)),e[v].pb(pii(u,w));
	}
	memset(f,128,sizeof(f));
	dfs(1,0);
	cout<<f[1][k]<<'\n';
}