解题：NOIP 2018 保卫王国

题面

最小支配集=全集-最大独立集

所以先把点权改成正无穷/负无穷来保证强制选/不选某个点到独立集里，然后变成了洛谷的动态DP模板

GTMDNOIP2018ZTY

 #include<stack>
 #include<cstdio>
 #include<cstring>
 #include<algorithm>
 using namespace std;
 const int N=,M=,inf=1e9;
 int siz[N],far[N],imp[N],top[N],lst[N];
 int p[N],noww[M],goal[M],val[N],dfn[N];
 int n,m,t1,t2,t3,t4,t5,t6,cnt,tot;
 char typ[]; long long sum;
 struct a
 {
     long long mat[][];
     void Clean()
     {
         memset(mat,,sizeof mat);
     }
 }seg[*N],tre[N];
 a Matime(a x,a y)
 {
     a ret; ret.Clean();
     for(int i=;i<;i++)
         for(int j=;j<;j++)
             for(int k=;k<;k++)
                 ret.mat[i][j]=max(ret.mat[i][j],x.mat[i][k]+y.mat[k][j]);
     return ret;
 }
 void Link(int f,int t)
 {
     noww[++cnt]=p[f];
     goal[cnt]=t,p[f]=cnt;
     noww[++cnt]=p[t];
     goal[cnt]=f,p[t]=cnt;
 }
 void DFS(int nde,int fth)
 {
     int tmp=;
     siz[nde]=,far[nde]=fth;
     for(int i=p[nde];i;i=noww[i])
         if(goal[i]!=fth)
         {
             DFS(goal[i],nde);
             siz[nde]+=siz[goal[i]];
             if(siz[goal[i]]>tmp)
                 tmp=siz[goal[i]],imp[nde]=goal[i];
         }
 }
 void Mark(int nde,int tpp)
 {
     dfn[nde]=++tot,top[nde]=tpp;
     if(imp[nde])
     {
         Mark(imp[nde],tpp);
         for(int i=p[nde];i;i=noww[i])
             if(goal[i]!=imp[nde]&&goal[i]!=far[nde])
                 Mark(goal[i],goal[i]);
     }
     lst[nde]=imp[nde]?lst[imp[nde]]:nde;
 }
 a Query(int nde,int l,int r,int ll,int rr)
 {
     if(l>=ll&&r<=rr)
         return seg[nde];
     else
     {
         int mid=(l+r)/,ls=*nde,rs=*nde+;
         if(mid>=ll&&mid<rr)
             return Matime(Query(rs,mid+,r,ll,rr),Query(ls,l,mid,ll,rr));
         if(mid>=rr) return Query(ls,l,mid,ll,rr);
         if(mid<ll) return Query(rs,mid+,r,ll,rr);
     }
 }
 void Modify(int nde,int l,int r,int pos,a tsk)
 {
     if(l==r) seg[nde]=tsk;
     else
     {
         int mid=(l+r)/,ls=*nde,rs=*nde+;
         if(pos<=mid) Modify(ls,l,mid,pos,tsk);
         else Modify(rs,mid+,r,pos,tsk);
         seg[nde]=Matime(seg[rs],seg[ls]);
     }
 }
 void Prework(int nde)
 {
     stack<int> st;
     for(int i=nde;i;i=imp[i]) st.push(i);
     while(!st.empty())
     {
         int tn=st.top(); st.pop();
         long long x=,y=val[tn];
         for(int i=p[tn];i;i=noww[i])
             if(goal[i]!=imp[tn]&&goal[i]!=far[tn])
             {
                 Prework(goal[i]); a mtr=tre[goal[i]];
                 x+=max(mtr.mat[][],mtr.mat[][]),y+=mtr.mat[][];
             }
         a tmp; tmp.mat[][]=tmp.mat[][]=x,tmp.mat[][]=y,tmp.mat[][]=-inf;
         Modify(,,n,dfn[tn],tmp);
     }
     tre[nde]=Query(,,n,dfn[nde],dfn[lst[nde]]);
 }
 void Change(int nde,long long tsk)
 {
     a tmp=Query(,,n,dfn[nde],dfn[nde]);
     tmp.mat[][]+=tsk-val[nde];
     Modify(,,n,dfn[nde],tmp),val[nde]=tsk;
     for(int i=top[nde];i!=;i=top[i])
     {
         int fa=far[i];
         a tmp=Query(,,n,dfn[fa],dfn[fa]),tep=Query(,,n,dfn[i],dfn[lst[i]]);
         tmp.mat[][]+=max(tep.mat[][],tep.mat[][])-max(tre[i].mat[][],tre[i].mat[][]);
         tmp.mat[][]+=tep.mat[][]-tre[i].mat[][],tmp.mat[][]=tmp.mat[][];
         Modify(,,n,dfn[fa],tmp),tre[i]=tep,i=fa;
     }
 }
 int main()
 {
     scanf("%d%d%s",&n,&m,typ);
     for(int i=;i<=n;i++)
         scanf("%d",&val[i]),sum+=val[i];
     for(int i=;i<n;i++)
         scanf("%d%d",&t1,&t2),Link(t1,t2);
     DFS(,),Mark(,),Prework();
     while(m--)
     {
         scanf("%d%d%d%d",&t1,&t2,&t3,&t4);
         if(!t2&&!t4&&(far[t1]==t3||far[t3]==t1))
             printf("-1\n");
         else
         {
             t5=val[t1],t6=val[t3];
             Change(t1,t2?-inf:inf);
             Change(t3,t4?-inf:inf);
             a qry=Query(,,n,,dfn[lst[]]);
             long long ans=sum-max(qry.mat[][],qry.mat[][]);
             printf("%lld\n",ans+(inf-t5)*(t2^)+(inf-t6)*(t4^));
             Change(t1,t5),Change(t3,t6);
         }
     }
     return ;
 }