#392892 (C++17) No.650 行列木クエリ

提出ソース
結果

問題	No.650 行列木クエリ
ユーザー	beet
提出日時	2019-10-25 20:44:42
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	521 ms / 2,000 ms
コード長	15,874 bytes
コンパイル時間	3,720 ms
コンパイル使用メモリ	257,420 KB
実行使用メモリ	212,800 KB
最終ジャッジ日時	2024-07-22 07:34:23
合計ジャッジ時間	7,045 ms
ジャッジサーバーID （参考情報）	judge3 / judge4
このコードへのチャレンジ
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テストケース

テストケース表示
入力	結果	実行時間実行使用メモリ
testcase_00	AC	116 ms 190,940 KB
testcase_01	AC	228 ms 195,160 KB
testcase_02	AC	483 ms 212,688 KB
testcase_03	AC	67 ms 191,068 KB
testcase_04	AC	220 ms 195,144 KB
testcase_05	AC	498 ms 212,800 KB
testcase_06	AC	68 ms 190,940 KB
testcase_07	AC	68 ms 190,812 KB
testcase_08	AC	305 ms 195,276 KB
testcase_09	AC	521 ms 212,604 KB
testcase_10	AC	67 ms 190,812 KB
権限があれば一括ダウンロードができます
ソースコード

raw source code
#ifndef call_from_test
#include<bits/stdc++.h>
using namespace std;

#define call_from_test
#ifndef call_from_test
#include<bits/stdc++.h>
using namespace std;
#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
//INSERT ABOVE HERE
signed main(){
  return 0;
}
#endif

#undef call_from_test

#endif
//BEGIN CUT HERE
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);
  }
};
//END CUT HERE
#ifndef call_from_test

#define call_from_test
#ifndef call_from_test
#include<bits/stdc++.h>
using namespace std;
using Int = long long;
#endif
//BEGIN CUT HERE
struct FastIO{
  FastIO(){
    cin.tie(0);
    ios::sync_with_stdio(0);
  }
}fastio_beet;
//END CUT HERE
#ifndef call_from_test
signed main(){
  return 0;
}
#endif

#ifndef call_from_test
#include<bits/stdc++.h>
using namespace std;
using Int = long long;
#endif
//BEGIN CUT HERE
template<typename T,T MOD = 1000000007>
struct Mint{
  static constexpr T mod = MOD;
  T v;
  Mint():v(0){}
  Mint(signed v):v(v){}
  Mint(long long t){v=t%MOD;if(v<0) v+=MOD;}

  Mint pow(long long k){
    Mint res(1),tmp(v);
    while(k){
      if(k&1) res*=tmp;
      tmp*=tmp;
      k>>=1;
    }
    return res;
  }

  static Mint add_identity(){return Mint(0);}
  static Mint mul_identity(){return Mint(1);}

  Mint inv(){return pow(MOD-2);}

  Mint& operator+=(Mint a){v+=a.v;if(v>=MOD)v-=MOD;return *this;}
  Mint& operator-=(Mint a){v+=MOD-a.v;if(v>=MOD)v-=MOD;return *this;}
  Mint& operator*=(Mint a){v=1LL*v*a.v%MOD;return *this;}
  Mint& operator/=(Mint a){return (*this)*=a.inv();}

  Mint operator+(Mint a) const{return Mint(v)+=a;};
  Mint operator-(Mint a) const{return Mint(v)-=a;};
  Mint operator*(Mint a) const{return Mint(v)*=a;};
  Mint operator/(Mint a) const{return Mint(v)/=a;};

  Mint operator-() const{return v?Mint(MOD-v):Mint(v);}

  bool operator==(const Mint a)const{return v==a.v;}
  bool operator!=(const Mint a)const{return v!=a.v;}
  bool operator <(const Mint a)const{return v <a.v;}

  static Mint comb(long long n,int k){
    Mint num(1),dom(1);
    for(int i=0;i<k;i++){
      num*=Mint(n-i);
      dom*=Mint(i+1);
    }
    return num/dom;
  }
};
template<typename T,T MOD> constexpr T Mint<T, MOD>::mod;
template<typename T,T MOD>
ostream& operator<<(ostream &os,Mint<T, MOD> m){os<<m.v;return os;}
//END CUT HERE
#ifndef call_from_test
//INSERT ABOVE HERE
signed ABC127_E(){
  cin.tie(0);
  ios::sync_with_stdio(0);

  int h,w,k;
  cin>>h>>w>>k;
  using M = Mint<int>;

  M ans{0};
  for(int d=1;d<h;d++)
    ans+=M(d)*M(h-d)*M(w)*M(w);

  for(int d=1;d<w;d++)
    ans+=M(d)*M(w-d)*M(h)*M(h);

  ans*=M::comb(h*w-2,k-2);
  cout<<ans<<endl;
  return 0;
}
/*
  verified on 2019/06/12
  https://atcoder.jp/contests/abc127/tasks/abc127_e
*/

signed main(){
  //ABC127_E();
  return 0;
}
#endif

#ifndef call_from_test
#include<bits/stdc++.h>
using namespace std;
using Int = long long;
template<typename T1,typename T2> inline void chmin(T1 &a,T2 b){if(a>b) a=b;}
template<typename T1,typename T2> inline void chmax(T1 &a,T2 b){if(a<b) a=b;}
#endif
//BEGIN CUT HERE
template<typename R, size_t N>
struct SquareMatrix{
  typedef array<R, N> arr;
  typedef array<arr, N> mat;
  mat dat;

  SquareMatrix(){
    for(size_t i=0;i<N;i++)
      for(size_t j=0;j<N;j++)
        dat[i][j]=R::add_identity();
  }

  bool operator==(const SquareMatrix& a) const{
    return dat==a.dat;
  }

  size_t size() const{return N;};
  arr& operator[](size_t k){return dat[k];};
  const arr& operator[](size_t k) const {return dat[k];};

  static SquareMatrix add_identity(){return SquareMatrix();}
  static SquareMatrix mul_identity(){
    SquareMatrix res;
    for(size_t i=0;i<N;i++) res[i][i]=R::mul_identity();
    return res;
  }

  SquareMatrix operator*(const SquareMatrix &B) const{
    SquareMatrix res;
    for(size_t i=0;i<N;i++)
      for(size_t j=0;j<N;j++)
        for(size_t k=0;k<N;k++)
          res[i][j]=res[i][j]+(dat[i][k]*B[k][j]);
    return res;
  }

  SquareMatrix operator+(const SquareMatrix &B) const{
    SquareMatrix res;
    for(size_t i=0;i<N;i++)
      for(size_t j=0;j<N;j++)
        res[i][j]=dat[i][j]+B[i][j];
    return res;
  }

  SquareMatrix pow(long long n) const{
    SquareMatrix a=*this,res=mul_identity();
    while(n){
      if(n&1) res=res*a;
      a=a*a;
      n>>=1;
    }
    return res;
  }
};
//END CUT HERE
#ifndef call_from_test
template<typename T,T MOD = 1000000007>
struct Mint{
  T v;
  Mint():v(0){}
  Mint(signed v):v(v){}
  Mint(long long t){v=t%MOD;if(v<0) v+=MOD;}

  Mint pow(long long k){
    Mint res(1),tmp(v);
    while(k){
      if(k&1) res*=tmp;
      tmp*=tmp;
      k>>=1;
    }
    return res;
  }

  static Mint add_identity(){return Mint(0);}
  static Mint mul_identity(){return Mint(1);}

  Mint inv(){return pow(MOD-2);}

  Mint& operator+=(Mint a){v+=a.v;if(v>=MOD)v-=MOD;return *this;}
  Mint& operator-=(Mint a){v+=MOD-a.v;if(v>=MOD)v-=MOD;return *this;}
  Mint& operator*=(Mint a){v=1LL*v*a.v%MOD;return *this;}
  Mint& operator/=(Mint a){return (*this)*=a.inv();}

  Mint operator+(Mint a) const{return Mint(v)+=a;};
  Mint operator-(Mint a) const{return Mint(v)-=a;};
  Mint operator*(Mint a) const{return Mint(v)*=a;};
  Mint operator/(Mint a) const{return Mint(v)/=a;};

  Mint operator-() const{return v?Mint(MOD-v):Mint(v);}

  bool operator==(const Mint a)const{return v==a.v;}
  bool operator!=(const Mint a)const{return v!=a.v;}
  bool operator <(const Mint a)const{return v <a.v;}
};


struct FastIO{
  FastIO(){
    cin.tie(0);
    ios::sync_with_stdio(0);
  }
}fastio_beet;


template<typename T>
vector<T> compress(vector<T> v){
  sort(v.begin(),v.end());
  v.erase(unique(v.begin(),v.end()),v.end());
  return v;
}

template<typename T>
map<T, Int> dict(const vector<T> &v){
  map<T, Int> res;
  for(Int i=0;i<(Int)v.size();i++)
    res[v[i]]=i;
  return res;
}

template <typename T, typename F>
struct SegmentTree{
  Int n;
  F f;
  T ti;
  vector<T> dat;
  SegmentTree(){};
  SegmentTree(F f,T ti):f(f),ti(ti){}
  void init(Int n_){
    n=1;
    while(n<n_) n<<=1;
    dat.assign(n<<1,ti);
  }
  void build(const vector<T> &v){
    Int n_=v.size();
    init(n_);
    for(Int i=0;i<n_;i++) dat[n+i]=v[i];
    for(Int i=n-1;i;i--)
      dat[i]=f(dat[(i<<1)|0],dat[(i<<1)|1]);
  }
  void set_val(Int k,T x){
    dat[k+=n]=x;
    while(k>>=1)
      dat[k]=f(dat[(k<<1)|0],dat[(k<<1)|1]);
  }
  T query(Int a,Int b){
    T vl=ti,vr=ti;
    for(Int l=a+n,r=b+n;l<r;l>>=1,r>>=1) {
      if(l&1) vl=f(vl,dat[l++]);
      if(r&1) vr=f(dat[--r],vr);
    }
    return f(vl,vr);
  }
};

//INSERT ABOVE HERE
signed YAHOO2019_FINAL_D(){
  using M = Mint<Int>;
  using MM = SquareMatrix<M, 2>;

  Int n,q;
  cin>>n>>q;
  vector<Int> ts(q),ls(q),rs(q),ps(q);
  for(Int i=0;i<q;i++){
    cin>>ts[i];
    if(ts[i]==1) cin>>ps[i];
    if(ts[i]==2) cin>>ls[i]>>rs[i];
  }
  vector<Int> vs;
  for(Int i=0;i<q;i++){
    if(ts[i]==1){
      vs.emplace_back(ps[i]);
      vs.emplace_back(ps[i]+1);
      vs.emplace_back(ps[i]+2);
      vs.emplace_back(ps[i]+3);
    }
    if(ts[i]==2){
      vs.emplace_back(ls[i]);
      vs.emplace_back(ls[i]+1);
      vs.emplace_back(rs[i]);
      vs.emplace_back(rs[i]+1);
    }
  }
  vs.emplace_back(0);
  vs.emplace_back(n+1);
  vs=compress(vs);
  auto ms=dict(vs);

  MM A;
  A[0][0]=M(1);A[0][1]=M(1);
  A[1][0]=M(1);A[1][1]=M(0);

  vector<MM> vt(vs.size()-1,A);
  for(Int i=0;i+1<(Int)vs.size();i++){
    vt[i]=A.pow(vs[i+1]-vs[i]);
  }

  MM I=MM::mul_identity();
  auto f=[&](MM a,MM b){return b*a;};
  SegmentTree<MM, decltype(f)> seg(f,I);
  seg.build(vt);

  vector<Int> used(vs.size(),0);
  for(Int i=0;i<q;i++){
    if(ts[i]==1){
      Int k=ms[ps[i]];
      used[k]^=1;
      MM B;
      for(Int j=k;j<=k+2;j++){
        if(used[j]){
          B[0][0]=M(0);B[0][1]=M(0);
          B[1][0]=M(1);B[1][1]=M(0);
        }else{
          B[0][0]=M(!used[j-1]);B[0][1]=M(!used[j-2]);
          B[1][0]=M(1);B[1][1]=M(0);
        }
        seg.set_val(j,B);
      }
    }
    if(ts[i]==2){
      Int l=ms[ls[i]],r=ms[rs[i]];
      if(used[l]){
        cout<<0<<"\n";
        continue;
      }
      auto B=seg.query(l+1,r+1);
      cout<<B[0][0].v<<"\n";
    }
  }
  cout<<flush;
  return 0;
}
/*
  verified on 2019/09/17
  https://atcoder.jp/contests/yahoo-procon2019-final/tasks/yahoo_procon2019_final_d
*/

signed DDCC2019_FINAL_D(){
  string s;
  cin>>s;

  struct M{
    uint32_t v;
    M(){*this=add_identity();}
    M(uint32_t v):v(v){}
    M operator+(const M &a)const{return M(v+a.v);}
    M operator*(const M &a)const{return M(v*a.v);}
    static M add_identity(){return M(0);}
    static M mul_identity(){return M(1);}
  };

  using SM = SquareMatrix<M, 6>;

  auto f=[](SM a,SM b){return a*b;};
  SM ti=SM::mul_identity();
  SegmentTree<SM, decltype(f)> seg(f,ti);
  vector<SM> vt(s.size(),ti);
  for(int i=0;i<(int)s.size();i++){
    if(s[i]=='D') vt[i][0][1]=1;
    if(s[i]=='I') vt[i][1][2]=1;
    if(s[i]=='S') vt[i][2][3]=1;
    if(s[i]=='C') vt[i][3][4]=1;
    if(s[i]=='O') vt[i][4][5]=1;
  }
  seg.build(vt);

  int q;
  cin>>q;
  for(int i=0;i<q;i++){
    int l,r;
    cin>>l>>r;
    l--;
    cout<<seg.query(l,r)[0][5].v<<"\n";
  }
  cout<<flush;
  return 0;
}
/*
  verified on 2019/09/17
  https://atcoder.jp/contests/ddcc2019-final/tasks/ddcc2019_final_d
*/

signed main(){
  //YAHOO2019_FINAL_D();
  //DDCC2019_FINAL_D();
  return 0;
}
#endif

#undef call_from_test

//INSERT ABOVE HERE

signed YUKI_650(){
  using M = Mint<int>;
  using SM = SquareMatrix<M, 2>;
  using SM2 = pair<SM, SM>;
  using Node = NodeBase<SM2, SM2>;
  constexpr size_t LIM = 1e6;
  using LCT = Path<Node, LIM>;

  auto f=[](SM2 x,SM2 y){return SM2(x.first*y.first,y.second*x.second);};
  auto g=[](SM2 x,SM2 y){(void)x;return y;};
  auto flip=[](SM2 x){swap(x.first,x.second);return x;};

  SM ti=SM::mul_identity();
  SM ei=SM::mul_identity();
  SM2 ti2(ti,ti),ei2(ei,ei);
  LCT lct(f,g,g,flip,ti2,ei2);

  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);
  }

  vector<LCT::Node*> vs(n*2-1);
  for(int i=0;i<(int)vs.size();i++)
    vs[i]=lct.create(Node(i,ti2,ei2));

  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]);
      SM sm;
      sm[0][0]=a;sm[0][1]=b;
      sm[1][0]=c;sm[1][1]=d;
      vs[z]->val=SM2(sm,sm);
      lct.pushup(vs[z]);
    }
    if(c=='g'){
      int x,y;
      cin>>x>>y;
      lct.evert(vs[x]);
      SM ans=lct.query(vs[y]).first;
      cout<<ans[0][0]<<" "<<ans[0][1]<<" ";
      cout<<ans[1][0]<<" "<<ans[1][1]<<"\n";
    }
  }
  cout<<flush;
  return 0;
}
/*
  verified on 2019/10/25
  https://yukicoder.me/problems/no/650
*/

signed SPOJ_DYNACON1(){
  int n,m;
  cin>>n>>m;
  using Node = NodeBase<int, int>;
  constexpr size_t LIM = 1e6;
  using LCT = Path<Node, LIM>;

  auto f=[](int a,int b){return a+b;};
  LCT lct(f,f,f,0,0);
  vector<LCT::Node*> vs(n);
  for(int i=0;i<n;i++) vs[i]=lct.create(Node(i,0,0));

  for(int i=0;i<m;i++){
    string s;
    int a,b;
    cin>>s>>a>>b;
    a--;b--;
    if(s=="add"s){
      lct.evert(vs[b]);
      lct.link(vs[a],vs[b]);
    }
    if(s=="rem"s){
      auto v=lct.lca(vs[a],vs[b])==vs[a]?vs[b]:vs[a];
      lct.cut(v);
    }
    if(s=="conn"s)
      cout<<(lct.is_connected(vs[a],vs[b])?"YES\n":"NO\n");
  }
  cout<<flush;
  return 0;
}
/*
  verified on 2019/10/25
  https://www.spoj.com/problems/DYNACON1/
*/

signed main(){
  YUKI_650();
  //SPOJ_DYNACON1();
  return 0;
}
#endif