結果

問題 No.650 行列木クエリ
コンテスト
ユーザー Taiki0715
提出日時 2023-08-27 12:36:10
言語 C++17(clang)
(17.0.6 + boost 1.87.0)
結果
AC  
実行時間 1,268 ms / 2,000 ms
コード長 8,060 bytes
コンパイル時間 9,726 ms
コンパイル使用メモリ 182,376 KB
実行使用メモリ 219,036 KB
最終ジャッジ日時 2024-12-27 07:53:37
合計ジャッジ時間 16,356 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge2
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 1
other AC * 10
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

diff #
raw source code 

#include <bits/stdc++.h>
using namespace std;
#if __has_include(<atcoder/all>)
#include <atcoder/all>
using namespace atcoder;
template<int mod>istream &operator>>(istream &is,static_modint<mod> &a){long long b;is>>b;a=b;return is;}
istream &operator>>(istream &is,modint &a){long long b;cin>>b;a=b;return is;}
#endif
using ll=long long;
using ull=unsigned long long;
using P=pair<ll,ll>;
template<typename T>using minque=priority_queue<T,vector<T>,greater<T>>;
template<typename T>bool chmax(T &a,const T &b){return (a<b?(a=b,true):false);}
template<typename T>bool chmin(T &a,const T &b){return (a>b?(a=b,true):false);}
template<typename T1,typename T2>istream &operator>>(istream &is,pair<T1,T2>&p){is>>p.first>>p.second;return is;}
template<typename T>istream &operator>>(istream &is,vector<T> &a){for(auto &i:a)is>>i;return is;}
template<typename T1,typename T2>void operator++(pair<T1,T2>&a,int n){a.first++,a.second++;}
template<typename T1,typename T2>void operator--(pair<T1,T2>&a,int n){a.first--,a.second--;}
template<typename T>void operator++(vector<T>&a,int n){for(auto &i:a)i++;}
template<typename T>void operator--(vector<T>&a,int n){for(auto &i:a)i--;}
#define reps(i,a,n) for(int i=(a);i<(n);i++)
#define rep(i,n) reps(i,0,n)
#define all(x) x.begin(),x.end()
#define pcnt(x) __builtin_popcount(x)
ll myceil(ll a,ll b){return (a+b-1)/b;}
template<typename T>
vector<T> vec(T d,int sz){
  return vector<T>(sz,d);
}
template<typename T,typename... U>
auto vec(T d,int a,U...b){
  return vector<decltype(vec<T>(d,b...))>(a,vec<T>(d,b...));
}
#ifdef LOCAL
#include "debug.h"
#else
#define debug(...) static_cast<void>(0)
template<typename T1,typename T2>ostream &operator<<(ostream &os,const pair<T1,T2>&p){os<<p.first<<' '<<p.second;return os;}
#endif
void SOLVE();
int main(){
  ios::sync_with_stdio(false);
  cin.tie(nullptr);
  #ifdef LOCAL
  clock_t start=clock();
  #endif
  int testcase=1;
  //cin>>testcase;
  for(int i=0;i<testcase;i++){
    SOLVE();
  }
  #ifdef LOCAL
  cout<<"time:";
  cout<<(clock()-start)/1000;
  cout<<"ms\n";
  #endif
}
struct HeavyLightDecomposition{
private:
  int n;
  vector<vector<int>>to;
  int root;
  vector<int>par,pathtop,in,out;
public:
  vector<int>stsize;
private:
  void st_dfs(int x,int p){
    par[x]=p;
    stsize[x]=1;
    for(auto &i:to[x]){
      if(i==p){
        if(i==to[x].back())break;
        else swap(i,to[x].back());
      }
      st_dfs(i,x);
      stsize[x]+=stsize[i];
      if(stsize[i]>stsize[to[x][0]]){
        swap(i,to[x][0]);
      }
    }
  }
  void hld_dfs(int x,int p,int &id){
    in[x]=id++;
    for(auto i:to[x])if(i!=p){
      pathtop[i]=(i==to[x][0]?pathtop[x]:i);
      hld_dfs(i,x,id);
    }
    out[x]=id;
  }
public:
  HeavyLightDecomposition(int n,int root=0):n(n),to(n),stsize(n),par(n),in(n),out(n),root(root),pathtop(n){}
  void add_edge(int u,int v){
    to[u].emplace_back(v);
    to[v].emplace_back(u);
  }
  void build(){
    st_dfs(0,-1);
    pathtop[root]=root;
    int id=0;
    hld_dfs(0,-1,id);
  }
  inline int get(int x)const{return in[x];}
  int lca(int u,int v)const{
    int pu=pathtop[u],pv=pathtop[v];
    while(pathtop[u]!=pathtop[v]){
      if(in[pu]>in[pv])u=par[pu],pu=pathtop[u];
      else v=par[pv],pv=pathtop[v];
    }
    return (in[u]>in[v]?v:u);
  }
  void subtree_query(int u ,const function<void(int,int)> &f){
    f(in[u],out[u]);
  }
  void path_query(int u,int v,const function<void(int,int)>&f){
    int pu=pathtop[u],pv=pathtop[v];
    while(pathtop[u]!=pathtop[v]){
      if(in[u]>in[v])f(in[pu],in[u]+1),u=par[pu],pu=pathtop[u];
      else f(in[pv],in[v]+1),v=par[pv],pv=pathtop[v];
    }
    if(in[u]>in[v])swap(u,v);
    f(in[u],in[v]+1);
  }
  void noncommutative_path_query(int u,int v,const function<void(int,int)>&f){
    int l=lca(u,v);
    while(pathtop[u]!=pathtop[l]){
      f(in[u]+1,in[pathtop[u]]);
      u=par[pathtop[u]];
    }
    if(u!=l)f(in[u]+1,in[l]+1);
    f(in[l],in[l]+1);
    if(v==l)return;
    vector<pair<int,int>>query;
    while(true){
      if(pathtop[l]==pathtop[v]){
        query.emplace_back(in[l]+1,in[v]+1);
        break;
      }
      query.emplace_back(in[pathtop[v]],in[v]+1);
      v=par[pathtop[v]];
    }
    reverse(all(query));
    for(auto [i,j]:query)f(i,j);
  }
};
template<class T>
struct Matrix{
  vector<vector<T>>A;
  Matrix(int h,int w):A(h,vector<T>(w,0)){}
  Matrix(int n):A(n,vector<T>(n,0)){}
  size_t height()const{return A.size();}
  size_t width()const{return A[0].size();}
  const vector<T> &operator[](int k)const{return (A.at(k));}
  vector<T> &operator[](int k){return (A.at(k));}
  Matrix I(size_t n){
    Matrix m(n);
    rep(i,n)m[i][i]=1;
    return m;
  }
  Matrix &operator+=(const Matrix &B){
    size_t h=height(),w=width();
    assert(h==B.height());
    assert(w==B.width());
    rep(i,h)rep(j,w)(*this)[i][j]+=B[i][j];
    return *this;
  }
  Matrix &operator-=(const Matrix &B){
    size_t h=height(),w=width();
    assert(h==B.height());
    assert(w==B.width());
    rep(i,h)rep(j,w)(*this)[i][j]-=B[i][j];
    return *this;
  }
  Matrix &operator*=(const Matrix &B){
    size_t h=height(),w=B.width(),p=width();
    assert(B.height()==p);
    vector<vector<T>>C(h,vector<T>(w,0));
    rep(i,h)rep(k,p)rep(j,w)C[i][j]=(C[i][j]+(*this)[i][k]*B[k][j]);
    A.swap(C);
    return *this;
  }
  Matrix &operator^=(ll k){
    assert(height()==width());
    assert(k>=0);
    Matrix B=I(height());
    while(k){
      if(k&1)B*=*this;
      *this *= *this;
      k>>=1ll;
    }
    A.swap(B.A);
    return *this;
  }
  Matrix operator+(const Matrix &B)const{
    return (Matrix(*this)+=B);
  }
  Matrix operator-(const Matrix &B)const{
    return (Matrix(*this)-=B);
  }
  Matrix operator*(const Matrix &B)const{
    return (Matrix(*this)*=B);
  }
  Matrix operator^(const ll k)const{
    return (Matrix(*this)^=k);
  }
  T det(){
    Matrix<T>b(*this);
    assert(this->height()==this->width());
    T ret=1;
    rep(i,width()){
      int id=-1;
      reps(j,i,width()){
        if(b[j][i]!=0)id=j;
      }
      if(id==-1)return 0;
      if(i!=id){
        ret*=-1;
        swap(b[i],b[id]);
      }
      ret*=b[i][i];
      T inv=b[i][i].inv();
      rep(j,width()){
        b[i][j]*=inv;
      }
      reps(j,i+1,width()){
        T x=b[j][i];
        rep(k,width()){
          b[j][k]-=b[i][k]*x;
        }
      }
    }
    return ret;
  }
  Matrix inv(){
    assert(this->height()==this->width());
    int n=this->height();
    Matrix<T>b(*this);
    Matrix<T>ret=I(n);
    rep(i,n){
      int id=-1;
      reps(j,i,n){
        if(b[j][i]!=0)id=j;
      }
      assert(id!=-1);
      if(i!=id){
        swap(b[i],b[id]);
        swap(ret[i],ret[id]);
      }
      T inv=b[i][i].inv();
      rep(j,n){
        b[i][j]*=inv;
        ret[i][j]*=inv;
      }
      rep(j,n)if(i!=j){
        T x=b[j][i];
        rep(k,n){
          b[j][k]-=b[i][k]*x;
          ret[j][k]-=ret[i][k]*x;
        }
      }
    }
    return ret;
  }
};
using mint=modint1000000007;
Matrix<mint>op(Matrix<mint>a,Matrix<mint>b){return a*b;}
Matrix<mint>op2(Matrix<mint>a,Matrix<mint>b){return b*a;}
Matrix<mint>e(){
  Matrix<mint>ret(2);
  ret[0][0]=ret[1][1]=1;
  return ret;
}
void SOLVE(){
  int n;
  cin>>n;
  HeavyLightDecomposition hld(n*2-1);
  rep(i,n-1){
    int a,b;
    cin>>a>>b;
    hld.add_edge(a,i+n);
    hld.add_edge(i+n,b);
  }
  hld.build();
  int q;
  cin>>q;
  segtree<Matrix<mint>,op,e>seg(n*2-1);
  segtree<Matrix<mint>,op2,e>segrev(n*2-1);
  while(q--){
    char c;
    cin>>c;
    if(c=='x'){
      int i,a,b,c,d;
      cin>>i>>a>>b>>c>>d;
      int id=hld.get(i+n);
      Matrix<mint>nxt(2);
      nxt[0][0]=a;
      nxt[0][1]=b;
      nxt[1][0]=c;
      nxt[1][1]=d;
      seg.set(id,nxt);
      segrev.set(id,nxt);
    }
    else if(c=='g'){
      int u,v;
      cin>>u>>v;
      Matrix<mint>ans(2);
      ans[0][0]=ans[1][1]=1;
      hld.noncommutative_path_query(u,v,[&](int a,int b){
        if(a<b)ans*=seg.prod(a,b);
        else ans*=segrev.prod(b,a);
      });
      rep(i,2)rep(j,2)cout<<ans[i][j].val()<<' ';cout<<endl;
    }
  }
}
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