#689874 (C++17) No.1197 モンスターショー

• 問題: No.1197 モンスターショー
• ユーザー: beet
• 提出日時: 2021-08-14 14:37:45
• 言語: C++17 (gcc 12.3.0 + boost 1.83.0)
• 結果: AC
• 実行時間: 895 ms / 3,000 ms
• コード長: 13,298 bytes
• コンパイル時間: 2,743 ms
• コンパイル使用メモリ: 217,832 KB
• 実行使用メモリ: 55,168 KB
• 最終ジャッジ日時: 2024-10-05 08:33:04
• 合計ジャッジ時間: 21,928 ms
• ジャッジサーバーID （参考情報）: judge1 / judge3

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	30 ms; 53,400 KB
testcase_01	AC	33 ms; 53,376 KB
testcase_02	AC	33 ms; 53,376 KB
testcase_03	AC	33 ms; 53,376 KB
testcase_04	AC	33 ms; 53,376 KB
testcase_05	AC	33 ms; 53,504 KB
testcase_06	AC	32 ms; 53,376 KB
testcase_07	AC	160 ms; 55,040 KB
testcase_08	AC	201 ms; 54,272 KB
testcase_09	AC	466 ms; 54,656 KB
testcase_10	AC	707 ms; 54,528 KB
testcase_11	AC	374 ms; 53,760 KB
testcase_12	AC	196 ms; 53,760 KB
testcase_13	AC	257 ms; 54,016 KB
testcase_14	AC	514 ms; 54,272 KB
testcase_15	AC	342 ms; 53,888 KB
testcase_16	AC	724 ms; 54,912 KB
testcase_17	AC	686 ms; 55,168 KB
testcase_18	AC	283 ms; 53,760 KB
testcase_19	AC	651 ms; 54,528 KB
testcase_20	AC	145 ms; 53,632 KB
testcase_21	AC	268 ms; 53,524 KB
testcase_22	AC	57 ms; 53,632 KB
testcase_23	AC	633 ms; 54,272 KB
testcase_24	AC	454 ms; 54,272 KB
testcase_25	AC	238 ms; 53,888 KB
testcase_26	AC	389 ms; 54,144 KB
testcase_27	AC	554 ms; 54,912 KB
testcase_28	AC	451 ms; 54,016 KB
testcase_29	AC	324 ms; 54,144 KB
testcase_30	AC	282 ms; 54,400 KB
testcase_31	AC	287 ms; 54,016 KB
testcase_32	AC	228 ms; 53,504 KB
testcase_33	AC	197 ms; 53,888 KB
testcase_34	AC	890 ms; 55,168 KB
testcase_35	AC	892 ms; 55,168 KB
testcase_36	AC	895 ms; 55,168 KB
testcase_37	AC	881 ms; 55,168 KB
testcase_38	AC	889 ms; 55,040 KB
testcase_39	AC	885 ms; 55,168 KB
testcase_40	AC	577 ms; 55,040 KB
testcase_41	AC	34 ms; 53,376 KB
testcase_42	AC	33 ms; 53,504 KB

ソースコード

// verification-helper: PROBLEM https://yukicoder.me/problems/4862

#include<bits/stdc++.h>
using namespace std;

#define call_from_test
template<typename T=int>
vector<T> read(size_t n){
  vector<T> ts(n);
  for(size_t i=0;i<n;i++) cin>>ts[i];
  return ts;
}

template<typename Vertex, typename Cluster, size_t N>
struct TopTree{
  enum Type { Compress, Rake, Edge };
  struct Node{
    Vertex* vs[2];
    Cluster dat;
    Node* p;
    Node* q;
    Node* ch[2];
    bool rev,guard;
    Type type;
    Node():p(nullptr),q(nullptr),rev(false),guard(false){}
  };

  inline static array<Vertex, 2*N> pool_vertex;
  inline static size_t ptr_vertex = 0;

  inline static array<Node, 4*N> pool_node;
  inline static size_t ptr_node = 0;

  Cluster id;

  template<typename ...Args>
  inline Vertex* create(Args ...args){
    auto t=&pool_vertex[ptr_vertex++];
    auto dummy=&pool_vertex[ptr_vertex++];
    *t=Vertex(forward<Args>(args)...);
    link(t,id,dummy);
    return t;
  }

  Node* recycle=nullptr;
  inline void dispose_node(Node* t){
    t->p=recycle;
    recycle=t;
  }

  inline Node* get_new_node(){
    if(recycle) return new(exchange(recycle,recycle->p)) Node;
    return &(pool_node[ptr_node++]);
  }

  inline Node* edge(Vertex* u,Cluster w,Vertex* v){
    auto t=get_new_node();
    t->vs[0]=u;t->vs[1]=v;t->dat=w;t->type=Type::Edge;
    return pushup(t);
  }

  inline Node* compress(Node* l,Node* r){
    auto t=get_new_node();
    t->ch[0]=l;t->ch[1]=r;t->type=Type::Compress;
    return pushup(t);
  }

  inline Node* rake(Node* l,Node* r){
    auto t=get_new_node();
    t->ch[0]=l;t->ch[1]=r;t->type=Type::Rake;
    return pushup(t);
  }

  int parent_dir(Node* t){
    Node* p=t->p;
    if(!p) return -1;
    if(p->guard) return -1;
    if(p->ch[0]==t) return 0;
    if(p->ch[1]==t) return 1;
    return -1;
  }

  int parent_dir_ignore_guard(Node* t){
    Node* p=t->p;
    if(!p) return -1;
    if(p->ch[0]==t) return 0;
    if(p->ch[1]==t) return 1;
    return -1;
  }

  inline Node* pushup(Node* const t){
    Node* const l=t->ch[0];
    Node* const r=t->ch[1];

    if(t->type==Type::Compress){
      assert(l->vs[1]==r->vs[0]);
      t->vs[0]=l->vs[0];
      t->vs[1]=r->vs[1];

      Cluster lf=l->dat;
      if(t->q){
        assert(l->vs[1]==t->q->vs[1]);
        lf=Cluster::rake(l->dat,t->q->dat);
      }
      t->dat=Cluster::compress(lf,r->vs[0],r->dat);

      l->vs[1]->handle=t;
    }

    if(t->type==Type::Rake){
      propagate(t);
      assert(l->vs[1]==r->vs[1]);
      t->vs[0]=l->vs[0];
      t->vs[1]=l->vs[1];
      t->dat=Cluster::rake(l->dat,r->dat);
    }else{
      if(!t->p){
        t->vs[0]->handle=t;
        t->vs[1]->handle=t;
      }else if(t->p->type==Type::Compress){
        if(parent_dir(t)==-1)
          t->vs[0]->handle=t;
      }else if(t->p->type==Type::Rake){
        t->vs[0]->handle=t;
      }
    }
    return t;
  }

  inline void toggle(Node* t){
    if(t->type==Type::Edge){
      swap(t->vs[0],t->vs[1]);
      t->dat.toggle();
    }else if(t->type==Type::Compress){
      swap(t->vs[0],t->vs[1]);
      t->dat.toggle();
      t->rev^=true;
    }else if(t->type==Type::Rake){
    }else abort();
  }

  inline void propagate(Node* t){
    if(t->type==Type::Compress){
      if(t->rev){
        assert(t->ch[0] and t->ch[1]);
        swap(t->ch[0],t->ch[1]);
        toggle(t->ch[0]);
        toggle(t->ch[1]);
        t->rev=false;
      }
    }
  }

  void set_toggle(Node* v){
    toggle(v);propagate(v);
  }

  void pushdown(Node* t){
    if(!t) return;
    pushdown(t->p);
    propagate(t);
  }

  void rotate(Node* t,Node* x,size_t dir){
    Node* y=x->p;
    int par=parent_dir_ignore_guard(x);
    propagate(t->ch[dir]);
    x->ch[dir^1]=t->ch[dir];
    t->ch[dir]->p=x;
    t->ch[dir]=x;
    x->p=t;
    t->p=y;
    if(~par) y->ch[par]=t;
    else if(y and y->type==Type::Compress) y->q=t;
    pushup(x);pushup(t);
    if(y and !y->guard) pushup(y);
  }

  void splay(Node* t){
    assert(t->type!=Type::Edge);
    propagate(t);

    while(~parent_dir(t)){
      Node* q=t->p;
      if(q->type!=t->type) break;
      if(~parent_dir(q) and q->p and q->p->type==q->type){
        Node* r=q->p;
        if(r->p) propagate(r->p);
        propagate(r);propagate(q);propagate(t);
        int qt_dir=parent_dir(t);
        int rq_dir=parent_dir(q);
        if(rq_dir==qt_dir){
          rotate(q,r,rq_dir^1);
          rotate(t,q,qt_dir^1);
        }else{
          rotate(t,q,qt_dir^1);
          rotate(t,r,rq_dir^1);
        }
      }else{
        if(q->p) propagate(q->p);
        propagate(q);propagate(t);
        int qt_dir=parent_dir(t);
        rotate(t,q,qt_dir^1);
      }
    }
  }

  Node* expose(Node* t){
    pushdown(t);
    while(true){
      assert(t->type!=Type::Rake);
      if(t->type==Type::Compress) splay(t);
      Node* n=nullptr;
      {
        Node* p=t->p;
        if(!p) break;
        if(p->type==Type::Rake){
          propagate(p);
          splay(p);
          n=p->p;
        }
        if(p->type==Type::Compress){
          propagate(p);
          if(p->guard and ~parent_dir_ignore_guard(t)) break;
          n=p;
        }
      }
      splay(n);
      int dir=parent_dir_ignore_guard(n);
      if(dir==-1 or n->p->type==Type::Rake) dir=0;

      Node* const c=n->ch[dir];
      if(dir==1){
        set_toggle(c);
        set_toggle(t);
      }
      int n_dir=parent_dir(t);
      if(~n_dir){
        Node* const r=t->p;
        propagate(c);
        propagate(r);
        r->ch[n_dir]=c;
        c->p=r;
        n->ch[dir]=t;
        t->p=n;
        pushup(c);pushup(r);pushup(t);pushup(n);
        splay(r);
      }else{
        propagate(c);
        n->q=c;
        c->p=n;
        n->ch[dir]=t;
        t->p=n;
        pushup(c);pushup(t);pushup(n);
      }
      if(t->type==Type::Edge) t=n;
    }
    return t;
  }

  Node* expose(Vertex* v){
    return expose((Node*)(v->handle));
  }

  void soft_expose(Vertex* u,Vertex* v){
    pushdown((Node*)u->handle);
    pushdown((Node*)v->handle);
    Node* rt=expose(u);

    if(u->handle==v->handle){
      if(rt->vs[1]==u or rt->vs[0]==v)
        set_toggle(rt);
      return;
    }

    rt->guard=true;
    Node* soft=expose(v);
    rt->guard=false;

    pushup(rt);
    if(parent_dir(soft)==0) set_toggle(rt);
  }

  void bring(Node* rt){
    Node* rk=rt->q;
    if(!rk){
      Node* ll=rt->ch[0];
      dispose_node(ll->p);
      ll->p=nullptr;
      pushup(ll);
    }else if(rk->type==Type::Compress or rk->type==Type::Edge){
      Node* nr=rk;
      set_toggle(nr);
      rt->ch[1]=nr;
      nr->p=rt;
      rt->q=nullptr;

      pushup(nr);pushup(rt);
    }else if(rk->type==Type::Rake){
      propagate(rk);
      while(rk->ch[1]->type==Type::Rake){
        propagate(rk->ch[1]);
        rk=rk->ch[1];
      }
      pushdown(rk);

      rt->guard=true;
      splay(rk);
      rt->guard=false;

      Node* ll=rk->ch[0];
      Node* rr=rk->ch[1];
      propagate(ll);
      set_toggle(rr);

      rt->ch[1]=rr;
      rr->p=rt;

      rt->q=ll;
      ll->p=rt;

      dispose_node(rk);
      pushup(ll);pushup(rr);pushup(rt);
    }
  }

  Node* link(Vertex* u,Cluster w,Vertex* v){
    if(!u->handle and !v->handle) return edge(u,w,v);

    Node* nnu=(Node*)u->handle;
    Node* nnv=(Node*)v->handle;
    Node* ee=edge(u,w,v);
    Node* ll=nullptr;

    assert(nnv);
    Node* vv=expose(nnv);
    propagate(vv);
    if(vv->vs[1]==v) set_toggle(vv);
    if(vv->vs[0]==v){
      Node* nv=compress(ee,vv);
      ee->p=nv;
      pushup(ee);
      vv->p=nv;
      pushup(vv);pushup(nv);
      ll=nv;
    }else{
      Node* nv=vv;
      Node* ch=nv->ch[0];
      propagate(ch);
      nv->ch[0]=ee;
      ee->p=nv;
      pushup(ee);

      Node* bt=nv->q;
      Node* rk=nullptr;
      if(bt){
        propagate(bt);
        rk=rake(bt,ch);
        bt->p=rk;
        ch->p=rk;
        pushup(bt);pushup(ch);
      }else{
        rk=ch;
      }
      nv->q=rk;
      rk->p=nv;
      pushup(rk);pushup(nv);
      ll=nv;
    }

    assert(nnu);
    Node* uu=expose(nnu);
    propagate(uu);
    if(uu->vs[0]==u) set_toggle(uu);
    if(uu->vs[1]==u){
      Node* tp=compress(uu,ll);
      uu->p=tp;
      ll->p=tp;
      pushup(uu);pushup(ll);pushup(tp);
    }else{
      Node* nu=uu;
      Node* ch=nu->ch[1];
      toggle(ch);
      propagate(ch);

      nu->ch[1]=ll;
      ll->p=nu;
      pushup(ll);

      Node* al=nu->q;
      Node* rk=nullptr;
      if(al){
        propagate(al);
        rk=rake(al,ch);
        al->p=rk;
        ch->p=rk;
        pushup(al);pushup(ch);
      }else{
        rk=ch;
      }
      nu->q=rk;
      rk->p=nu;
      pushup(rk);pushup(nu);
    }
    return ee;
  }

  void cut(Vertex* u,Vertex *v){
    soft_expose(u,v);
    Node* rt=(Node*)u->handle;
    propagate(rt);
    Node* rr=rt->ch[1];
    rr->p=nullptr;
    set_toggle(rr);
    assert(rr->ch[1]->type==Type::Edge);
    dispose_node(rr->ch[1]);
    bring(rr);bring(rt);
  }

  Node* path(Vertex* u,Vertex* v){
    assert(u!=v);
    soft_expose(u,v);
    Node* rt=(Node*)u->handle;
    propagate(rt);
    propagate(rt->ch[1]);
    return rt->ch[1]->ch[0];
  }

  void set_vertex(Vertex* u,Vertex v){
    auto t=expose(u);
    *u=v;
    pushup(t);
  }

  void set_edge(Vertex* u,Vertex* v,const Cluster &w){
    auto t=path(u,v);
    assert(t->type==Type::Edge);
    t->dat=w;
    while(t) pushup(t),t=t->p;
  }

  Cluster get_path(Vertex* u,Vertex* v){
    return path(u,v)->dat;
  }

  Cluster get_subtree(Vertex* v){
    return expose(v)->dat;
  }

  // subtree of v when p is root
  Cluster get_subtree(Vertex* p,Vertex* v){
    Node* t=path(p,v);
    Cluster res=t->p->ch[1]->dat;
    res.toggle();
    Node* rk=t->p->q;
    if(t->p->q){
      assert(rk->vs[1]==t->p->ch[1]->vs[0]);
      res=Cluster::rake(res,rk->dat);
    }
    return res;
  }
};


template<typename T, size_t N>
struct DistanceSum{
  struct Vertex{
    void* handle;
    T color;
    Vertex(T color=0):handle(nullptr),color(color){}
  };

  struct Cluster{
    struct pi{
      T cnt;
      Vertex* ptr;
      pi():cnt(-1),ptr(nullptr){}
      pi(T cnt,Vertex* ptr):cnt(cnt),ptr(ptr){}
      bool operator<(const pi &o)const{return cnt<o.cnt;}
    };

    T len,cnt,chd,ans;
    T sum_l,sum_r;
    pi md;

    Cluster(T len=0):len(len),cnt(0),chd(0),ans(0),sum_l(0),sum_r(0){}

    void toggle(){swap(sum_l,sum_r);}

    static Cluster compress(const Cluster& x,Vertex *v,const Cluster& y){
      Cluster nxt;
      nxt.len=x.len+y.len;
      nxt.cnt=x.cnt+x.chd+(v->color)+y.cnt;
      nxt.chd=0;
      assert(y.chd==0);

      nxt.ans=x.sum_l+y.sum_r;

      nxt.sum_l+=x.sum_l;
      nxt.sum_l+=y.sum_l;
      nxt.sum_l+=(x.cnt+x.chd+(v->color))*y.len;

      nxt.sum_r+=x.sum_r;
      nxt.sum_r+=y.sum_r;
      nxt.sum_r+=(x.chd+(v->color)+y.cnt)*x.len;

      nxt.md=pi(nxt.cnt,v);

      return nxt;
    }

    static Cluster rake(const Cluster& x,const Cluster& y){
      Cluster nxt;
      nxt.len=x.len;
      nxt.cnt=x.cnt;
      nxt.chd=x.chd+y.cnt+y.chd;

      nxt.ans=x.sum_l+y.sum_l;

      nxt.sum_l+=x.sum_l;
      nxt.sum_l+=y.sum_l;

      nxt.sum_r+=x.sum_r;
      nxt.sum_r+=y.sum_l;

      nxt.md=max(x.md,y.md);

      return nxt;
    }
  };

  TopTree<Vertex, Cluster, N> G;
  using Type = typename decltype(G)::Type;

  Vertex* centroid(Vertex* v){
    auto rt=G.expose(v);
    if(rt->type==Type::Edge) return v;

    auto cc=rt;
    Vertex* ctr=nullptr;

    T lv=0,rv=0,sum=rt->dat.cnt;
    while(cc->type==Type::Compress){
      G.propagate(cc);

      auto ll=cc->ch[0];
      if((ll->dat.cnt+lv)*2>sum){
        assert(ll->type!=Type::Edge);
        rv+=cc->dat.md.cnt-ll->dat.cnt;
        cc=ll;
        continue;
      }

      auto rr=cc->ch[1];
      if((rr->dat.cnt+rv)*2>sum){
        assert(rr->type!=Type::Edge);
        lv+=cc->dat.md.cnt-rr->dat.cnt;
        cc=rr;
        continue;
      }

      auto mm=cc->q;
      if(mm and mm->dat.md.cnt*2>sum){
        assert(mm->type!=Type::Edge);
        rv+=lv;lv=0;
        rv+=cc->dat.md.cnt-mm->dat.md.cnt;
        cc=(decltype(cc))mm->dat.md.ptr->handle;
        continue;
      }

      ctr=cc->dat.md.ptr;
      break;
    }
    return ctr;
  }
  Vertex* create(T color){return G.create(color);}
  void link(Vertex* u,Cluster w,Vertex* v){G.link(u,Cluster(w),v);}
  void cut(Vertex* u,Vertex* v){G.cut(u,v);}
  void set_vertex(Vertex* u,T color){G.set_vertex(u,Vertex(color));}
  T query(Vertex* v){return G.get_subtree(v).ans;}
};

#undef call_from_test

signed main(){
  cin.tie(0);
  ios::sync_with_stdio(0);
  using ll = long long;
  const char newl = '\n';

  int n,m,q;
  cin>>n>>m>>q;

  auto cs=read(m);
  vector<ll> cnt(n,0);
  for(int &c:cs) cnt[--c]++;

  constexpr size_t N = 1e5;
  DistanceSum<ll, N> G;
  vector<decltype(G)::Vertex*> vs(n);
  for(int i=0;i<n;i++) vs[i]=G.create(cnt[i]);

  for(int i=1;i<n;i++){
    int a,b;
    cin>>a>>b;
    a--;b--;
    G.link(vs[a],1,vs[b]);
  }

  int flg=0;
  for(int i=0;i<q;i++){
    int t;
    cin>>t;
    if(t==1){
      int p,d;
      cin>>p>>d;
      p--;d--;
      G.set_vertex(vs[cs[p]],--cnt[cs[p]]);
      cs[p]=d;
      G.set_vertex(vs[cs[p]],++cnt[cs[p]]);
    }
    if(t==2){
      int e;
      cin>>e;
      e--;
      cout<<G.query(vs[e])<<newl;
      flg=1;
    }
  }
  if(!flg) cout<<newl;
  return 0;
}