随笔

#include<iostream>
#include<cstdio>
#include<algorithm>
#include<cstring>
#include<queue>
using namespace std;
#define N 120000
typedef long long ll;
#define M 410000
#define inf 0x6fffffff
#define K 180
int f[N],f2[N],ren[N],di[N],dn;
int n,m,k;
int get(int x){
    return f[x]==x?x:f[x]=get(f[x]);
}
int get2(int x){
    return f2[x]==x?x:f2[x]=get2(f2[x]);
}
struct P{
    int x,y;
    ll w;
    int bx,by;
    int num;
    bool operator<(P a)const{
       return w<a.w;
    }
}c[M],w[M],w1[M];
int xx[K],yy[K];
int e[M],ne[M*2],v[M*2];
ll ww[M*2];
int nn,wn,wn1;
int rank[N],sa[K],op;
ll dis[K][K];
ll ph[K];
int dep[N],fath[N];
ll up[N];
int e2[N],ne2[K],v2[K],tot;
int w2[K],cu[N];
void add2(int x,int y,int z){
    ne2[++tot]=e2[x],e2[x]=tot,v2[tot]=y,w2[tot]=z;
}
ll ans=-inf,s[N];
bool been[K];
void add(int x,int y,ll z){
    ne[++nn]=e[x],e[x]=nn,v[nn]=y,ww[nn]=z;
}
bool he(int x,int y){
    int x1=get(x),y1=get(y);
    if(x1==y1)return 0;
    return f[x1]=y1,1;
}
void he2(int x,int y){
    int x1=get2(x),y1=get2(y);
    if(x1!=y1)f2[x1]=y1;
}
ll DIS(int x,int y){
    ll ans=0;
    while(x!=y){
        if(dep[x]<dep[y])swap(x,y);
        ans+=up[x];
        x=fath[x];
    }
    return ans;
}
ll S[N];
void df(int x){
    S[x]=s[x];
    for(int i=e2[x];i;i=ne2[i]){
        if(fath[x]==v2[i])continue;
        fath[v2[i]]=x;
        cu[v2[i]]=w2[i];
        dep[v2[i]]=dep[x]+1;
        df(v2[i]);
        S[x]+=S[v2[i]];
    }
}
void geng(int x,int y,ll z){
    while(x!=y){
        if(dep[x]<dep[y])swap(x,y);
        if(w1[cu[x]].num){
            if(w1[cu[x]].w==-inf)w1[cu[x]].w=z;
            else w1[cu[x]].w=min(w1[cu[x]].w,z);
        }
        x=fath[x];
    }
}
ll rec;

void dfs3(int x,int fa,ll len){
    int fr,j,p,l2,pp;
    if(x==f2[1])fr=1;
    else fr=(w1[cu[x]].x==x?w1[cu[x]].bx:w1[cu[x]].by);
    for(int i=e2[x];i;i=ne2[i]){
      j=v2[i];
      if(fa==j)continue;
      if(w1[w2[i]].x==j)
      p=w1[w2[i]].bx,pp=p=w1[w2[i]].by;
      else p=w1[w2[i]].by,pp=w1[w2[i]].bx;
      l2=len+dis[rank[pp]][rank[fr]]+w1[w2[i]].w;
      rec+=l2*S[j]+ph[rank[p]];
      dfs3(j,x,l2);
    }
}
ll solv(int x){
    tot=0,rec=0;
    for(int i=1;i<=wn1;i++){
        if(w1[i].num){
            if(x&(1<<(w1[i].num-1))){
                w1[i].w=-inf;    
            }else{
                w1[i].w=inf;
            }
        }
    }
    sort(w1+1,w1+wn1+1);
    int q;
    for(int i=1;i<=dn;i++)q=di[i],f[q]=q,e2[q]=0,dep[q]=0,fath[q]=0,cu[q]=0;
    for(int i=1;i<=wn1;i++){
        been[i]=0;
        if(he(w1[i].x,w1[i].y)){
            been[i]=1;
            add2(w1[i].x,w1[i].y,i);
            add2(w1[i].y,w1[i].x,i);
        }
    }
    df(f2[1]);
    for(int i=1;i<=wn1;i++)if(!been[i]&&w1[i].w!=inf){
        geng(w1[i].x,w1[i].y,w1[i].w);
    }
    rec+=ph[rank[1]];
    dfs3(f2[1],0,0);
    ans=max(ans,rec);
}
void dfs(int x,int fa){
    for(int i=e[x];i;i=ne[i]){
        if(v[i]==fa)continue;        
        dep[v[i]]=dep[x]+1;
        up[v[i]]=ww[i];
        fath[v[i]]=x;
        dfs(v[i],x);
    }
}
ll bb[N],siz[N];
void dfs2(int x,int fa){
    siz[x]=ren[x];
    bb[x]=0;
    for(int i=e[x];i;i=ne[i]){
        if(v[i]==fa)continue;
        dfs2(v[i],x);
        siz[x]+=siz[v[i]];
        bb[x]+=bb[v[i]]+siz[v[i]]*ww[i];
    }
}
int main(){
    scanf("%d%d%d",&n,&m,&k);
    for(int i=1;i<=n;i++)f[i]=i;
    for(int i=1;i<=m;i++)scanf("%d%d%lld",&c[i].x,&c[i].y,&c[i].w);
    sort(c+1,c+m+1);
    for(int i=1;i<=m;i++)if(he(c[i].x,c[i].y))w[++wn]=c[i];
    for(int i=1;i<=k;i++)scanf("%d%d",&xx[i],&yy[i]);
        for(int i=1;i<=n;i++)scanf("%d",&ren[i]);
    for(int i=1;i<=k;i++){
        w[++wn].x=xx[i];
        w[wn].y=yy[i];
        w[wn].w=-inf;
        w[wn].num=i;
    }
    sort(w+1,w+wn+1);
    for(int i=1;i<=n;i++)f[i]=i,f2[i]=i;
    for(int i=1;i<=wn;i++){
        if(he(w[i].x,w[i].y)){
            if(!w[i].num){
            he2(w[i].x,w[i].y);    
            add(w[i].x,w[i].y,w[i].w);
            add(w[i].y,w[i].x,w[i].w);
            }
        }
    }
    for(int i=1;i<=n;i++)s[get2(i)]+=ren[i];
    for(int i=1;i<=n;i++)if(f2[i]==i)dfs(i,0),di[++dn]=i;
    for(int i=1;i<=wn;i++)if(get2(w[i].x)!=get2(w[i].y)){
        w1[++wn1]=w[i];
        w1[wn1].bx=w[i].x;
        w1[wn1].by=w[i].y;
        w1[wn1].x=f2[w[i].x];
        w1[wn1].y=f2[w[i].y];
        if(!rank[w[i].x]){
            sa[++op]=w[i].x;
            rank[w[i].x]=op;
        }
        if(!rank[w[i].y]){
            sa[++op]=w[i].y;
            rank[w[i].y]=op;
        }
    }
    if(!rank[1]){
        sa[++op]=1;
        rank[1]=op;
    }
    for(int i=1;i<=op;i++){
        dfs2(sa[i],0);
        ph[i]=bb[sa[i]];
          for(int j=i+1;j<=op;j++)if(f2[sa[i]]==f2[sa[j]])dis[j][i]=dis[i][j]=DIS(sa[i],sa[j]);
    }

    for(int i=0;i<(1<<k);i++)solv(i);
    cout<<ans;
}