#392876 (C++17) No.650 行列木クエリ

• 問題: No.650 行列木クエリ
• ユーザー: beet
• 提出日時: 2019-10-25 20:28:05
• 言語: C++17 (gcc 12.3.0 + boost 1.83.0)
• 結果: AC
• 実行時間: 403 ms / 2,000 ms
• コード長: 6,465 bytes
• コンパイル時間: 2,584 ms
• コンパイル使用メモリ: 232,408 KB
• 実行使用メモリ: 251,792 KB
• 最終ジャッジ日時: 2024-07-21 20:46:29
• 合計ジャッジ時間: 5,573 ms
• ジャッジサーバーID （参考情報）: judge4 / judge2

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	98 ms; 230,012 KB
testcase_01	AC	240 ms; 234,240 KB
testcase_02	AC	387 ms; 251,744 KB
testcase_03	AC	62 ms; 229,980 KB
testcase_04	AC	168 ms; 234,192 KB
testcase_05	AC	403 ms; 251,728 KB
testcase_06	AC	62 ms; 229,888 KB
testcase_07	AC	64 ms; 230,060 KB
testcase_08	AC	218 ms; 234,072 KB
testcase_09	AC	369 ms; 251,792 KB
testcase_10	AC	63 ms; 230,016 KB

ソースコード

#ifndef call_from_test
#include<bits/stdc++.h>
using namespace std;
using Int = long long;
#endif
//BEGIN CUT HERE
template<typename Node, size_t LIM>
struct LinkCutTreeBase{
  static array<Node, LIM> pool;
  size_t ptr;

  LinkCutTreeBase():ptr(0){}

  inline Node* create(){
    return &pool[ptr++];
  }

  inline Node* create(Node v){
    return &(pool[ptr++]=v);
  }

  virtual void toggle(Node *t) = 0;
  virtual void eval(Node *t) = 0;
  virtual void pushup(Node *t) = 0;

  void rotR(Node *t){
    Node *x=t->p,*y=x->p;
    x->sz-=t->sz;
    t->sz+=x->sz;
    if((x->l=t->r)) t->r->p=x,x->sz+=x->l->sz;
    t->r=x;x->p=t;
    pushup(x);pushup(t);
    if((t->p=y)){
      if(y->l==x) y->l=t;
      if(y->r==x) y->r=t;
      pushup(y);
    }
  }

  void rotL(Node *t){
    Node *x=t->p,*y=x->p;
    x->sz-=t->sz;
    t->sz+=x->sz;
    if((x->r=t->l)) t->l->p=x,x->sz+=x->r->sz;
    t->l=x;x->p=t;
    pushup(x);pushup(t);
    if((t->p=y)){
      if(y->l==x) y->l=t;
      if(y->r==x) y->r=t;
      pushup(y);
    }
  }

  bool is_root(Node *t){
    return !t->p||(t->p->l!=t&&t->p->r!=t);
  }

  void splay(Node *t){
    eval(t);
    while(!is_root(t)){
      Node *q=t->p;
      if(is_root(q)){
        eval(q);eval(t);
        if(q->l==t) rotR(t);
        else rotL(t);
      }else{
        auto *r=q->p;
        eval(r);eval(q);eval(t);
        if(r->l==q){
          if(q->l==t) rotR(q),rotR(t);
          else rotL(t),rotR(t);
        }else{
          if(q->r==t) rotL(q),rotL(t);
          else rotR(t),rotL(t);
        }
      }
    }
  }

  Node* expose(Node *t){
    Node *rp=nullptr;
    for(Node *c=t;c;c=c->p){
      splay(c);
      c->r=rp;
      pushup(c);
      rp=c;
    }
    splay(t);
    return rp;
  }

  void link(Node *par,Node *c){
    expose(c);
    expose(par);
    c->p=par;
    par->r=c;
    par->sz+=c->sz;
    pushup(par);
  }

  void cut(Node *c){
    expose(c);
    Node *par=c->l;
    c->l=nullptr;
    pushup(c);
    par->p=nullptr;
    c->sz-=par->sz;
  }
  void evert(Node *t){
    expose(t);
    toggle(t);
    eval(t);
  }

  Node *root(Node *t){
    expose(t);
    while(t->l) t=t->l;
    splay(t);
    return t;
  }

  bool is_connected(Node *a,Node *b){
    return root(a)==root(b);
  }

  Node *lca(Node *a,Node *b){
    expose(a);
    return expose(b);
  }
};
template<typename Node, size_t LIM>
array<Node, LIM> LinkCutTreeBase<Node, LIM>::pool;
//END CUT HERE
#ifndef call_from_test

template<typename Tp,typename Ep>
struct NodeBase{
  using T = Tp;
  using E = Ep;
  NodeBase *l,*r,*p;
  size_t sz;// tree size (only for root)
  int idx;
  bool rev;
  T val,dat;
  E laz;
  NodeBase():sz(1){}
  NodeBase(int idx,T val,E laz):
    sz(1),idx(idx),rev(0),val(val),dat(val),laz(laz){
    l=r=p=nullptr;}
};

template<typename Np, size_t LIM>
struct Path : LinkCutTreeBase<Np, LIM>{
  using super = LinkCutTreeBase<Np, LIM>;
  using Node = Np;
  using T = typename Node::T;
  using E = typename Node::E;

  using F = function<T(T, T)>;
  using G = function<T(T, E)>;
  using H = function<E(E, E)>;
  using S = function<T(T)>;
  F f;
  G g;
  H h;
  S flip;
  T ti;
  E ei;

  Path(F f,G g,H h,T ti,E ei):
    super(),f(f),g(g),h(h),ti(ti),ei(ei){
    flip=[](T a){return a;};
  }

  Path(F f,G g,H h,S flip,T ti,E ei):
    super(),f(f),g(g),h(h),flip(flip),ti(ti),ei(ei){}

  void propagate(Node *t,E v){
    t->laz=h(t->laz,v);
    t->val=g(t->val,v);
    t->dat=g(t->dat,v);
  }

  void toggle(Node *t){
    swap(t->l,t->r);
    t->dat=flip(t->dat);
    t->rev^=1;
  }

  void eval(Node *t){
    if(t->laz!=ei){
      if(t->l) propagate(t->l,t->laz);
      if(t->r) propagate(t->r,t->laz);
      t->laz=ei;
    }
    if(t->rev){
      if(t->l) toggle(t->l);
      if(t->r) toggle(t->r);
      t->rev=false;
    }
  }

  void pushup(Node *t){
    t->dat=t->val;
    if(t->l) t->dat=f(t->l->dat,t->dat);
    if(t->r) t->dat=f(t->dat,t->r->dat);
  }

  using super::expose;

  T query(Node *t){
    expose(t);
    return t->dat;
  }

  void update(Node *t,E v){
    expose(t);
    propagate(t,v);
    eval(t);
  }
};

signed YUKI_650(){
  cin.tie(0);
  ios::sync_with_stdio(0);

  struct M{
    Int a,b,c,d;
    M():a(1),b(0),c(0),d(1){}
    M(Int a,Int b,Int c,Int d):a(a),b(b),c(c),d(d){}
    //M(const M &v):a(v.a),b(v.b),c(v.c),d(v.d){}
    bool operator!=(const M &x)const{
      return a!=x.a||b!=x.b||c!=x.c||d!=x.d;
    }
    bool operator==(const M &x)const{
      return !(*this!=x);
    }
  };

  constexpr int MOD = 1e9+7;
  using M2 = pair<M, M>;
  using Node = NodeBase<M2, M2>;
  constexpr size_t LIM = 1e6;
  using LCT = Path<Node, LIM>;

  auto f=[MOD](M x,M y){
           M r(0,0,0,0);
           r.a=x.a*y.a+x.b*y.c;
           r.b=x.a*y.b+x.b*y.d;
           r.c=x.c*y.a+x.d*y.c;
           r.d=x.c*y.b+x.d*y.d;
           r.a%=MOD;r.b%=MOD;r.c%=MOD;r.d%=MOD;
           return r;
         };
  auto f2=[&](M2 x,M2 y){
            return M2(f(x.first,y.first),f(y.second,x.second));
          };
  auto g=[](M2 x,M2 y){x.first.a++;return y;};
  auto s=[](M2 x){swap(x.first,x.second);return x;};

  int n;
  cin>>n;
  vector<vector<int> > G(n);
  vector<int> X,Y;
  for(int i=1;i<n;i++){
    int a,b;
    cin>>a>>b;
    X.emplace_back(a);
    Y.emplace_back(b);
    G[a].emplace_back(b);
    G[b].emplace_back(a);
  }
  M ti=M();
  M ei(-1,-1,-1,-1);
  LCT lct(f2,g,g,s,M2(ti,ti),M2(ei,ei));

  vector<LCT::Node*> vs(n*2-1);
  for(int i=0;i<(int)vs.size();i++)
    vs[i]=lct.create(Node(i,M2(ti,ti),M2(ei,ei)));

  vector<map<int, int> > rev(n);
  int idx=n;
  {
    using P = pair<int, int>;
    queue<P> q;
    q.emplace(0,-1);
    while(!q.empty()){
      int v,p;
      tie(v,p)=q.front();q.pop();
      if(~p){
        lct.link(vs[p],vs[idx]);
        lct.link(vs[idx],vs[v]);
        rev[p][v]=rev[v][p]=idx++;
      }
      for(int u:G[v])
        if(u!=p) q.emplace(u,v);
    }
  }

  int q;
  cin>>q;
  for(int i=0;i<q;i++){
    char c;
    cin>>c;
    if(c=='x'){
      Int v,a,b,c,d;
      cin>>v>>a>>b>>c>>d;
      int z=rev[X[v]][Y[v]];
      lct.expose(vs[z]);
      vs[z]->val=M2(M(a,b,c,d),M(a,b,c,d));
      lct.pushup(vs[z]);
    }
    if(c=='g'){
      Int x,y;
      cin>>x>>y;
      lct.evert(vs[x]);
      M ans=lct.query(vs[y]).first;
      cout<<ans.a<<" "<<ans.b<<" "<<ans.c<<" "<<ans.d<<"\n";
    }
  }
  cout<<flush;
  return 0;
}
/*
  verified on 2019/06/08
  https://yukicoder.me/problems/no/650
*/

//INSERT ABOVE HERE
signed main(){
  YUKI_650();
  return 0;
}
#endif