#377852 (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
コンテスト
ユーザー	Haar
提出日時	2019-09-09 23:11:06
言語	C++17 (gcc 13.3.0 + boost 1.87.0)
結果	AC
実行時間	174 ms / 2,000 ms
コード長	11,829 bytes
コンパイル時間	3,314 ms
コンパイル使用メモリ	215,064 KB
最終ジャッジ日時	2025-01-07 17:32:17
ジャッジサーバーID （参考情報）	judge1 / judge3
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
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ソースコード

raw source code
#include <bits/stdc++.h>
#define LLI long long int
#define FOR(v, a, b) for(LLI v = (a); v < (b); ++v)
#define FORE(v, a, b) for(LLI v = (a); v <= (b); ++v)
#define REP(v, n) FOR(v, 0, n)
#define REPE(v, n) FORE(v, 0, n)
#define REV(v, a, b) for(LLI v = (a); v >= (b); --v)
#define ALL(x) (x).begin(), (x).end()
#define RALL(x) (x).rbegin(), (x).rend()
#define ITR(it, c) for(auto it = (c).begin(); it != (c).end(); ++it)
#define RITR(it, c) for(auto it = (c).rbegin(); it != (c).rend(); ++it)
#define EXIST(c,x) ((c).find(x) != (c).end())
#define fst first
#define snd second
#define popcount __builtin_popcount
#define UNIQ(v) (v).erase(unique(ALL(v)), (v).end())
#define bit(i) (1LL<<(i))

#ifdef DEBUG
#include <misc/C++/Debug.cpp>
#else
#define dump(...) ((void)0)
#endif

#define gcd __gcd

using namespace std;
template <class T> constexpr T lcm(T m, T n){return m/gcd(m,n)*n;}

template <typename I> void join(ostream &ost, I s, I t, string d=" "){for(auto i=s; i!=t; ++i){if(i!=s)ost<<d; ost<<*i;}ost<<endl;}
template <typename T> istream& operator>>(istream &is, vector<T> &v){for(auto &a : v) is >> a; return is;}

template <typename T, typename U> bool chmin(T &a, const U &b){return (a>b ? a=b, true : false);}
template <typename T, typename U> bool chmax(T &a, const U &b){return (a<b ? a=b, true : false);}
template <typename T, size_t N, typename U> void fill_array(T (&a)[N], const U &v){fill((U*)a, (U*)(a+N), v);}

struct Init{
  Init(){
    cin.tie(0);
    ios::sync_with_stdio(false);
  }
}init;

template <uint32_t M> class ModInt{
public:
  uint64_t val;
  ModInt(): val(0){}
  ModInt(int64_t n){
    if(n >= M) val = n % M;
    else if(n < 0) val = n % M + M;
    else val = n;
  }
  
  inline constexpr ModInt operator+(const ModInt &a) const {return ModInt((val+a.val)%M);}
  inline constexpr ModInt operator-(const ModInt &a) const {return ModInt((val-a.val+M)%M);}
  inline constexpr ModInt operator*(const ModInt &a) const {return ModInt((val*a.val)%M);}
  inline constexpr ModInt operator/(const ModInt &a) const {return ModInt((val*a.inv().val)%M);}
  
  inline constexpr ModInt& operator=(const ModInt &a){val = a.val; return *this;}
  inline constexpr ModInt& operator+=(const ModInt &a){if((val += a.val) >= M) val -= M; return *this;}
  inline constexpr ModInt& operator-=(const ModInt &a){if(val < a.val) val += M; val -= a.val; return *this;}
  inline constexpr ModInt& operator*=(const ModInt &a){(val *= a.val) %= M; return *this;}
  inline constexpr ModInt& operator/=(const ModInt &a){(val *= a.inv().val) %= M; return *this;}

  inline constexpr bool operator==(const ModInt &a) const {return val==a.val;}
  inline constexpr bool operator!=(const ModInt &a) const {return val!=a.val;}
  
  inline constexpr static ModInt power(LLI n, LLI p){
    ModInt ret = 1, e = n;
    for(; p; e *= e, p >>= 1) if(p&1) ret *= e;

    return ret;
  }

  inline constexpr ModInt power(LLI p) const{return power(val,p);}
  
  inline constexpr ModInt inv() const{
    int64_t a = val, b = M, u = 1, v = 0;

    while(b){
      int64_t t = a/b;
      a -= t*b; swap(a,b);
      u -= t*v; swap(u,v);
    }
    u %= M;
    if(u < 0) u += M;
    
    return u;
  }
};

template <uint32_t M> ModInt<M> operator-(const ModInt<M> &a){return M-a.val;}

template <uint32_t M> ModInt<M> operator+(int64_t a, const ModInt<M> &b){return ModInt<M>(ModInt<M>(a)+b.val);}
template <uint32_t M> ModInt<M> operator-(int64_t a, const ModInt<M> &b){return ModInt<M>(ModInt<M>(a)-b.val);}
template <uint32_t M> ModInt<M> operator*(int64_t a, const ModInt<M> &b){return ModInt<M>(ModInt<M>(a)*b.val);}
template <uint32_t M> ModInt<M> operator/(int64_t a, const ModInt<M> &b){return ModInt<M>(ModInt<M>(a)/b.val);}

template <uint32_t M> istream& operator>>(istream &is, ModInt<M> &a){is >> a.val; return is;}
template <uint32_t M> ostream& operator<<(ostream &os, const ModInt<M> &a){ os << a.val; return os;}

template <typename T, int N> struct SquareMatrix{
  array<array<T,N>,N> matrix;

  SquareMatrix(): matrix(){}
  SquareMatrix(const T &val){
    REP(i,N) matrix[i].fill(val);
  }
  SquareMatrix(const SquareMatrix<T,N> &) = default;
  SquareMatrix(SquareMatrix<T,N> &&) = default;
  SquareMatrix(initializer_list<initializer_list<T>> list){
    int i = 0;
    ITR(it1,list){
      int j = 0;
      ITR(it2,*it1){
        matrix[i][j] = *it2;
        ++j;
      }
      ++i;
    }
  }

  bool operator==(const SquareMatrix<T,N> &val) const {
    return matrix == val.matrix;
  }

  bool operator!=(const SquareMatrix<T,N> &val) const {
    return !(*this == val);
  }

  SquareMatrix& operator=(const SquareMatrix &) = default;

  SquareMatrix& operator+=(const SquareMatrix &val){
    REP(i,N) REP(j,N) matrix[i][j] = matrix[i][j] + val[i][j];
    return *this;
  }

  SquareMatrix& operator-=(const SquareMatrix &val){
    REP(i,N) REP(j,N) matrix[i][j] = matrix[i][j] - val[i][j];
    return *this;
  }

  SquareMatrix& operator*=(const SquareMatrix &val){
    array<array<T,N>,N> temp = {};
    REP(i,N) REP(j,N) REP(k,N) temp[i][j] = temp[i][j] + matrix[i][k] * val[k][j];
    swap(matrix, temp);
    return *this;
  }

  inline const auto& operator[](size_t i) const {return matrix[i];}
  inline auto& operator[](size_t i){return matrix[i];}
  inline int size() const {return N;}
  
  static SquareMatrix<T,N> make_unit(){
    SquareMatrix<T,N> ret;
    REP(i,N) ret[i][i] = 1;
    return ret;
  }

  SquareMatrix<T,N> transpose() const {
    SquareMatrix<T,N> ret;
    REP(i,N) REP(j,N) ret[i][j] = matrix[j][i];
    return ret;
  }
 
  T determinant(){
    int s = 0;
    REP(i,N){
      if(matrix[i][i] == 0){
        FOR(j,i+1,N){
          if(matrix[j][i] != 0){
            matrix[i].swap(matrix[j]);
            (s += 1) %= 2;
            break; 
          }
          if(j == N-1) return 0;
        }
      }
    
      FOR(j,i+1,N){
        T t = matrix[j][i] / matrix[i][i];
        REP(k,N) matrix[j][k] -= matrix[i][k] * t;
      }
    }
  
    T ret = s ? -1 : 1;
    REP(i,N) ret *= matrix[i][i];
    return ret;
  }

  void show(int w = 10) const {
    REP(i,N){
      cerr << (i==0 ? "⎛" : (i==N-1 ? "⎝" : "⎜"));
      REP(j,N) cerr << setw(w) << matrix[i][j] << " ";
      cerr << (i==0 ? "⎞" : (i==N-1 ? "⎠" : "⎟"));
      cerr << endl;
    }
  }
};

template <typename T, int N> SquareMatrix<T,N> operator+(const SquareMatrix<T,N> &a, const SquareMatrix<T,N> &b){auto ret = a; ret += b; return ret;}
template <typename T, int N> SquareMatrix<T,N> operator-(const SquareMatrix<T,N> &a, const SquareMatrix<T,N> &b){auto ret = a; ret -= b; return ret;}
template <typename T, int N> SquareMatrix<T,N> operator*(const SquareMatrix<T,N> &a, const SquareMatrix<T,N> &b){auto ret = a; ret *= b; return ret;}

template <typename T, int N> SquareMatrix<T,N> power(SquareMatrix<T,N> a, uint64_t p){
  if(p == 0) return SquareMatrix<T,N>::make_unit();
  if(p == 1) return a;
  
  SquareMatrix<T,N> temp = power(a, p/2);
  auto ret = temp * temp;

  if(p%2) ret *= a;
 
  return ret;
}

template <typename T, int N> vector<T> operator*(const SquareMatrix<T,N> &a, const vector<T> &b){
  vector<T> ret(N);

  REP(i,N){
    REP(j,N){
      ret[i] += a[i][j] * b[j];
    }
  }

  return ret;
}

template <typename T, int N> vector<T> operator*(const vector<T> &b, const SquareMatrix<T,N> &a){
  vector<T> ret(N);

  REP(i,N){
    REP(j,N){
      ret[j] += b[i] * a[i][j];
    }
  }

  return ret;
}

template <typename T> class SegmentTreeRangeProductQuery{
private:
  int size;
  vector<T> vec;
  T e;
  
  inline T aux(int x, int y, int i, int l, int r){
    if(r<=x || y<=l) return e;
    else if(x<=l && r<=y) return vec[i];
    else return aux(x,y,i*2+1,l,(l+r)/2) * aux(x,y,i*2+2,(l+r)/2,r);
  };

public:
  SegmentTreeRangeProductQuery(int n, const T &e): e(e){
    size = 1;
    while(size < n) size *= 2;
    size = size*2-1;
    vec = vector<T>(size, e);
  }

  inline void update(int i, const T &x){
    int j = i+(size+1)/2-1;
    vec[j] = x;
    --j;
    while(j>=0){
      vec[j/2] = vec[(j/2)*2+1] * vec[(j/2)*2+2];
      (j /= 2) -= 1;
    }
  }
  
  inline T at(int i){
  	return vec[(size+1)/2 + i - 1];
  }

  inline T get(int x, int y){ // [x,y)
    return aux(x,y,0,0,(size+1)/2);
  }
};

template <typename Cost = int> class Edge{
public:
  int from,to;
  Cost cost;
  Edge() {}
  Edge(int to, Cost cost): to(to), cost(cost){}
  Edge(int from, int to, Cost cost): from(from), to(to), cost(cost){}

  Edge rev() const {return Edge(to,from,cost);}
  
  friend ostream& operator<<(ostream &os, const Edge &e){
    os << "(FROM: " << e.from << "," << "TO: " << e.to << "," << "COST: " << e.cost << ")";
    return os;
  }
};

template <typename T> using Graph = vector<vector<Edge<T>>>;
template <typename T> using Tree = vector<vector<Edge<T>>>;

template <typename C, typename T> void add_edge(C &g, int from, int to, T w){
  g[from].push_back(Edge<T>(from, to, w));  
}

template <typename C, typename T> void add_undirected(C &g, int a, int b, T w){
  g[a].push_back(Edge<T>(a, b, w));
  g[b].push_back(Edge<T>(b, a, w));
}


template <typename T> class HLDecomposition{
  Tree<T> tree;
  int n;

  vector<int> sub, par, head, id, rid, next, end;

  int dfs_sub(int cur, int p){
    par[cur] = p;
    int t = 0;
    for(auto &e : tree[cur]){
      if(e.to == p) continue;
      sub[cur] += dfs_sub(e.to, cur);
      if(sub[e.to] > t){
        t = sub[e.to];
        next[cur] = e.to;
        swap(e, tree[cur][0]);
      }
    }
    return sub[cur];
  }

  void dfs_build(int cur, int &i){
    id[cur] = i;
    rid[i] = cur;
    ++i;

    for(auto &e : tree[cur]){
      if(e.to == par[cur]) continue;
      head[e.to] = (e.to == tree[cur][0].to ? head[cur] : e.to);
      dfs_build(e.to, i);
    }

    end[cur] = i;
  }
  

public:
  HLDecomposition(const Tree<T> &tree):
    tree(tree), n(tree.size()), sub(n,1), par(n,-1), head(n), id(n), rid(n), next(n,-1), end(n, -1){
    dfs_sub(0, -1);
    int i=0;
    dfs_build(0, i);
  }

  void path_query_vertex(int x, int y, const function<void(int,int)> &f){
    while(1){
      if(id[x] > id[y]) swap(x, y);
      f(max(id[head[y]], id[x]), id[y]+1);
      if(head[x] == head[y]) return;
      y = par[head[y]];
    }
  }

  void path_query_edge(int x, int y, const function<void(int,int)> &f){
    while(1){
      if(id[x] > id[y]) swap(x, y);
      if(head[x] == head[y]){
        if(x != y) f(id[x]+1, id[y]+1);
        return;
      }
      f(id[head[y]], id[y]+1);
      y = par[head[y]];
    }
  }
  
  void subtree_query_edge(int x, const function<void(int,int)> &f){
    f(id[x]+1, end[x]);
  }

  int get_edge_id(int u, int v){ // 辺に対応するid
    if(par[u] == v){
      return id[u];
    }else if(par[v] == u){
      return id[v];
    }
 
    return -1;
  }

  int parent(int x){return par[x];};
};

const LLI mod = 1e9+7;
using mint = ModInt<mod>;
using M = SquareMatrix<mint,2>;







int main(){
  int n; cin >> n;

  Tree<int> tree(n);
  vector<Edge<int>> edges(n-1);
  REP(i,n-1){
    int a,b; cin >> a >> b;
    add_undirected(tree, a, b, 1);
    edges[i] = Edge<int>(a,b,1);
  }

  int q; cin >> q;

  
  HLDecomposition hld(tree);
  SegmentTreeRangeProductQuery<M> seg(n, M::make_unit());
  

  REP(_,q){
    char c; cin >> c;

    if(c == 'x'){
      int i,x00,x01,x10,x11; cin >> i >> x00 >> x01 >> x10 >> x11;

      M m({{x00,x01}, {x10,x11}});

      auto &e = edges[i];
      int id = hld.get_edge_id(e.from, e.to);

      seg.update(id, m);
    }else{
      int i,j; cin >> i >> j;

      M ans = M::make_unit();

      auto f = [&](int x, int y){
                 ans = seg.get(x,y) * ans;
               };

      hld.path_query_edge(i,j,f);

      cout << ans[0][0] << " " << ans[0][1] << " " << ans[1][0] << " " << ans[1][1] << endl;

      //ans.show();
    }
  }
  



  return 0;
}
yukicoder

結果

ソースコード
