bzoj3572[Hnoi2014]世界树

Posted 2020-06-16

http://www.lydsy.com/JudgeOnline/problem.php?id=3572

首先我们先构建出虚树

然后在虚树上DP，求出虚树上每个点离最近的临时议事处在哪里

对于虚树上相邻的两个点$u$和$v$，他们连线上一定存在一个分界处，一边一定会去离$u$最近的临时议事处；另一边一定会去离$v$最近的临时议事处

然后就做完了

#include<cstdio>
#include<cstdlib>
#include<iostream>
#include<fstream>
#include<algorithm>
#include<cstring>
#include<string>
#include<cmath>
#include<queue>
#include<stack>
#include<map>
#include<utility>
#include<set>
#include<bitset>
#include<vector>
#include<functional>
#include<deque>
#include<cctype>
#include<climits>
#include<complex>
#include<cassert> 
//#include<bits/stdc++.h>适用于CF,UOJ，但不适用于poj
 
using namespace std;

typedef long long LL;
typedef double DB;
typedef pair<int,int> PII;
typedef pair<DB,DB> PDD;
typedef complex<DB> CP;
typedef vector<int> VI;

#define mmst(a,v) memset(a,v,sizeof(a))
#define mmcy(a,b) memcpy(a,b,sizeof(a))
#define fill(a,l,r,v) fill(a+l,a+r+1,v)
#define re(i,a,b)  for(i=(a);i<=(b);i++)
#define red(i,a,b) for(i=(a);i>=(b);i--)
#define fi first
#define se second
#define mp(a,b) make_pair(a,b)
#define pb(a) push_back(a)
#define SF scanf
#define PF printf
#define two(k) (1<<(k))
#define SZ(x) (int(x.size()))
#define all(x) (x).begin(),(x).end()
#define ire(i,v,x) for(i=0,v=i<SZ(x)?x[i]:0;i<SZ(x);v=x[++i])


template<class T>inline T sqr(T x){return x*x;}
template<class T>inline void upmin(T &t,T tmp){if(t>tmp)t=tmp;}
template<class T>inline void upmax(T &t,T tmp){if(t<tmp)t=tmp;}

inline int sgn(DB x){if(abs(x)<1e-9)return 0;return(x>0)?1:-1;}
const DB Pi=acos(-1.0);

int gint()
  {
        int res=0;bool neg=0;char z;
        for(z=getchar();z!=EOF && z!=‘-‘ && !isdigit(z);z=getchar());
        if(z==EOF)return 0;
        if(z==‘-‘){neg=1;z=getchar();}
        for(;z!=EOF && isdigit(z);res=res*10+z-‘0‘,z=getchar());
        return (neg)?-res:res; 
    }
LL gll()
  {
      LL res=0;bool neg=0;char z;
        for(z=getchar();z!=EOF && z!=‘-‘ && !isdigit(z);z=getchar());
        if(z==EOF)return 0;
        if(z==‘-‘){neg=1;z=getchar();}
        for(;z!=EOF && isdigit(z);res=res*10+z-‘0‘,z=getchar());
        return (neg)?-res:res; 
    }

const int maxn=300100;

int n;
VI e[maxn];

const int up=25;
int dep[maxn],jump[maxn][up+1];
int head,tail,que[maxn];
int sz[maxn],idx[maxn];
void  bfs()
  {
      int i,j;
      dep[que[head=tail=1]=1]=1;
      re(j,0,up)jump[1][j]=1;
      while(head<=tail)
        {
            int u=que[head++];
            re(i,0,SZ(e[u])-1)if(!dep[e[u][i]])
              {
                  int v=e[u][i];
                  dep[que[++tail]=v]=dep[u]+1;
                  jump[v][0]=u;
                  re(j,1,up)jump[v][j]=jump[jump[v][j-1]][j-1];
              }
        }
      red(i,tail,1)
        {
            int u=que[i];
            sz[u]=1;
            re(j,0,SZ(e[u])-1)if(dep[e[u][j]]>dep[u])sz[u]+=sz[e[u][j]];
        }
      idx[1]=1;
      re(i,1,tail)
        {
            int u=que[i],tmp=0;
            re(j,0,SZ(e[u])-1)if(dep[e[u][j]]>dep[u]){int v=e[u][j];idx[v]=idx[u]+tmp+1,tmp+=sz[v];}
        }
  }

int swim(int x,int H){for(int i=0;H;H>>=1,i++)if(H&1)x=jump[x][i];return x;}
int ask_lca(int x,int y)
  {
      if(dep[x]<dep[y])swap(x,y);
      x=swim(x,dep[x]-dep[y]);
      if(x==y)return x;
      int i;red(i,up,0)if(jump[x][i]!=jump[y][i])x=jump[x][i],y=jump[y][i];
      return jump[x][0];
  }

int m,h[maxn],h2[maxn];
int mark[maxn],ans[maxn];
VI to[maxn];
int ge,w[maxn];

bool cmp(int a,int b){return idx[a]<idx[b];}

int top,sta[maxn];
void addedge(int u,int v){to[u].pb(v);to[v].pb(u);}
void build()
  {
      int i;
      re(i,1,ge)to[w[i]].clear();
      sort(h+1,h+m+1,cmp);
      ge=0;
      sta[top=1]=1;
      re(i,2,m)
        {
            while(1)
              {
                  int lca=ask_lca(h[i],sta[top]);
                  if(lca==sta[top])break;
                  if(idx[lca]>idx[sta[top-1]])
                    {
                        w[++ge]=sta[top];
                        addedge(sta[top],lca);
                        sta[top]=lca;
                    }
                  else
                    {
                        addedge(sta[top],sta[top-1]);
                        w[++ge]=sta[top--];
                    }
              }
            sta[++top]=h[i];
        }
      while(top>=2)addedge(sta[top],sta[top-1]),w[++ge]=sta[top--];
      w[++ge]=sta[top--];
  }

const int inf=0x3f3f3f3f;
PII f[maxn];
int fa[maxn];
void solve()
  {
      int i,j;
      re(i,1,ge)fa[w[i]]=0,f[w[i]]=mark[w[i]]?mp(0,w[i]):mp(inf,0);
      que[head=tail=1]=1;
      while(head<=tail)
        {
            int u=que[head++];
            re(j,0,SZ(to[u])-1)if(to[u][j]!=fa[u])fa[que[++tail]=to[u][j]]=u;
        }
      red(i,tail,2)
        {
            int u=que[i],v=fa[u];
            upmin(f[v],mp(f[u].fi+dep[u]-dep[v],f[u].se));
        }
      re(i,2,tail)
        {
            int u=que[i],v=fa[u];
            upmin(f[u],mp(f[v].fi+dep[u]-dep[v],f[v].se));
        }
      re(i,1,tail)
        {
            int x=que[i],tmp=sz[x];
            re(j,0,SZ(to[x])-1)if(to[x][j]!=fa[x])
                  {
                      int y=to[x][j],z=swim(y,dep[y]-dep[x]-1);
                        tmp-=sz[z];
                    }
                ans[f[x].se]+=tmp;
        }
      re(i,2,tail)
        {
            int x=que[i],y=fa[x],dist=dep[x]-dep[y],z=swim(x,dist-1);
            if(f[x].se==f[y].se)
              ans[f[x].se]+=sz[z]-sz[x];
            else
              {
                  int d=(f[y].fi-f[x].fi+dist)/2.0;
                  if((f[y].fi-f[x].fi+dist)%2==0 && f[y].se<f[x].se)d--;
                  int u=swim(x,d);
                  ans[f[y].se]+=sz[z]-sz[u];
                  ans[f[x].se]+=sz[u]-sz[x];
              }
        }
  }

int main()
  {
      freopen("worldtree.in","r",stdin);
        freopen("worldtree.out","w",stdout);
        int i;
        n=gint();
        re(i,1,n-1){int x=gint(),y=gint();e[x].pb(y);e[y].pb(x);}
        bfs();
        int Q=gint();
        while(Q--)
          {
              m=gint();
                re(i,1,m)mark[h2[i]=h[i]=gint()]=i;
                if(!mark[1])h[++m]=1;
                build();
                solve();
                re(i,1,m)if(mark[h2[i]])PF("%d ",ans[h2[i]]),ans[h2[i]]=mark[h2[i]]=0;PF("\n");
            }
        return 0;
  }

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