test/verify/yukicoder-650.test.cpp

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• Last update: 2024-05-01 23:44:47+09:00
• Problem: https://yukicoder.me/problems/no/650

Depends on

• Graph Template(グラフテンプレート) (graph/graph-template.hpp)
• Heavy-Light-Decomposition(HL分解) (graph/tree/heavy-light-decomposition.hpp)
• math/combinatorics/montgomery-mod-int.hpp
• Square-Matrix(正方行列) (math/matrix/square-matrix.hpp)
• Segment Tree(セグメント木) (structure/segment-tree/segment-tree.hpp)
• template/template.hpp

Code

// competitive-verifier: PROBLEM https://yukicoder.me/problems/no/650

#include "../../template/template.hpp"

#include "../../graph/tree/heavy-light-decomposition.hpp"

#include "../../structure/segment-tree/segment-tree.hpp"

#include "../../math/combinatorics/montgomery-mod-int.hpp"
#include "../../math/matrix/square-matrix.hpp"

using mint = modint1000000007;

int main() {
  int N;
  cin >> N;
  vector< int > X(N), Y(N);
  HeavyLightDecomposition<> g(N);
  for(int i = 1; i < N; i++) {
    cin >> X[i] >> Y[i];
    g.add_edge(X[i], Y[i]);
  }
  g.build();
  for(int i = 1; i < N; i++) {
    if(g.in[X[i]] > g.in[Y[i]]) swap(X[i], Y[i]);
  }
  using Mat = SquareMatrix< mint, 2 >;
  auto f = [](const Mat &a, const Mat &b) { return a * b; };
  auto seg = get_segment_tree(N, f, Mat::mul_identity());
  int Q;
  cin >> Q;
  while(Q--) {
    char x;
    cin >> x;
    if(x == 'x') {
      int v;
      cin >> v;
      Mat m;
      cin >> m[0][0] >> m[0][1] >> m[1][0] >> m[1][1];
      seg.set(g.in[Y[v + 1]], m);
    } else {
      int y, z;
      cin >> y >> z;
      auto mat = g.query(y, z, Mat::mul_identity(), [&](int a, int b) { return seg.prod(a, b); }, f, true);
      cout << mat[0][0] << " " << mat[0][1] << " " << mat[1][0] << " " << mat[1][1] << "\n";
    }
  }
}

#line 1 "test/verify/yukicoder-650.test.cpp"
// competitive-verifier: PROBLEM https://yukicoder.me/problems/no/650

#line 1 "template/template.hpp"
#include <bits/stdc++.h>

using namespace std;

using int64 = long long;

const int64 infll = (1LL << 62) - 1;
const int inf = (1 << 30) - 1;

struct IoSetup {
  IoSetup() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(10);
    cerr << fixed << setprecision(10);
  }
} iosetup;

template <typename T1, typename T2>
ostream &operator<<(ostream &os, const pair<T1, T2> &p) {
  os << p.first << " " << p.second;
  return os;
}

template <typename T1, typename T2>
istream &operator>>(istream &is, pair<T1, T2> &p) {
  is >> p.first >> p.second;
  return is;
}

template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
  for (int i = 0; i < (int)v.size(); i++) {
    os << v[i] << (i + 1 != v.size() ? " " : "");
  }
  return os;
}

template <typename T>
istream &operator>>(istream &is, vector<T> &v) {
  for (T &in : v) is >> in;
  return is;
}

template <typename T1, typename T2>
inline bool chmax(T1 &a, T2 b) {
  return a < b && (a = b, true);
}

template <typename T1, typename T2>
inline bool chmin(T1 &a, T2 b) {
  return a > b && (a = b, true);
}

template <typename T = int64>
vector<T> make_v(size_t a) {
  return vector<T>(a);
}

template <typename T, typename... Ts>
auto make_v(size_t a, Ts... ts) {
  return vector<decltype(make_v<T>(ts...))>(a, make_v<T>(ts...));
}

template <typename T, typename V>
typename enable_if<is_class<T>::value == 0>::type fill_v(T &t, const V &v) {
  t = v;
}

template <typename T, typename V>
typename enable_if<is_class<T>::value != 0>::type fill_v(T &t, const V &v) {
  for (auto &e : t) fill_v(e, v);
}

template <typename F>
struct FixPoint : F {
  explicit FixPoint(F &&f) : F(forward<F>(f)) {}

  template <typename... Args>
  decltype(auto) operator()(Args &&...args) const {
    return F::operator()(*this, forward<Args>(args)...);
  }
};

template <typename F>
inline decltype(auto) MFP(F &&f) {
  return FixPoint<F>{forward<F>(f)};
}
#line 4 "test/verify/yukicoder-650.test.cpp"

#line 2 "graph/tree/heavy-light-decomposition.hpp"

#line 2 "graph/graph-template.hpp"

/**
 * @brief Graph Template(グラフテンプレート)
 */
template <typename T = int>
struct Edge {
  int from, to;
  T cost;
  int idx;

  Edge() = default;

  Edge(int from, int to, T cost = 1, int idx = -1)
      : from(from), to(to), cost(cost), idx(idx) {}

  operator int() const { return to; }
};

template <typename T = int>
struct Graph {
  vector<vector<Edge<T> > > g;
  int es;

  Graph() = default;

  explicit Graph(int n) : g(n), es(0) {}

  size_t size() const { return g.size(); }

  void add_directed_edge(int from, int to, T cost = 1) {
    g[from].emplace_back(from, to, cost, es++);
  }

  void add_edge(int from, int to, T cost = 1) {
    g[from].emplace_back(from, to, cost, es);
    g[to].emplace_back(to, from, cost, es++);
  }

  void read(int M, int padding = -1, bool weighted = false,
            bool directed = false) {
    for (int i = 0; i < M; i++) {
      int a, b;
      cin >> a >> b;
      a += padding;
      b += padding;
      T c = T(1);
      if (weighted) cin >> c;
      if (directed)
        add_directed_edge(a, b, c);
      else
        add_edge(a, b, c);
    }
  }

  inline vector<Edge<T> > &operator[](const int &k) { return g[k]; }

  inline const vector<Edge<T> > &operator[](const int &k) const { return g[k]; }
};

template <typename T = int>
using Edges = vector<Edge<T> >;
#line 4 "graph/tree/heavy-light-decomposition.hpp"

/**
 * @brief Heavy-Light-Decomposition(HL分解)
 * @see https://smijake3.hatenablog.com/entry/2019/09/15/200200
 */
template <typename T = int>
struct HeavyLightDecomposition : Graph<T> {
 public:
  using Graph<T>::Graph;
  using Graph<T>::g;
  vector<int> sz, in, out, head, rev, par, dep;

  void build() {
    sz.assign(g.size(), 0);
    in.assign(g.size(), 0);
    out.assign(g.size(), 0);
    head.assign(g.size(), 0);
    rev.assign(g.size(), 0);
    par.assign(g.size(), 0);
    dep.assign(g.size(), 0);
    dfs_sz(0, -1, 0);
    int t = 0;
    dfs_hld(0, -1, t);
  }

  /* k: 0-indexed */
  int la(int v, int k) {
    while (1) {
      int u = head[v];
      if (in[v] - k >= in[u]) return rev[in[v] - k];
      k -= in[v] - in[u] + 1;
      v = par[u];
    }
  }

  int lca(int u, int v) const {
    for (;; v = par[head[v]]) {
      if (in[u] > in[v]) swap(u, v);
      if (head[u] == head[v]) return u;
    }
  }

  int dist(int u, int v) const { return dep[u] + dep[v] - 2 * dep[lca(u, v)]; }

  template <typename E, typename Q, typename F, typename S>
  E query(int u, int v, const E &ti, const Q &q, const F &f, const S &s,
          bool edge = false) {
    E l = ti, r = ti;
    for (;; v = par[head[v]]) {
      if (in[u] > in[v]) swap(u, v), swap(l, r);
      if (head[u] == head[v]) break;
      l = f(q(in[head[v]], in[v] + 1), l);
    }
    return s(f(q(in[u] + edge, in[v] + 1), l), r);
  }

  template <typename E, typename Q, typename F>
  E query(int u, int v, const E &ti, const Q &q, const F &f,
          bool edge = false) {
    return query(u, v, ti, q, f, f, edge);
  }

  template <typename Q>
  void add(int u, int v, const Q &q, bool edge = false) {
    for (;; v = par[head[v]]) {
      if (in[u] > in[v]) swap(u, v);
      if (head[u] == head[v]) break;
      q(in[head[v]], in[v] + 1);
    }
    q(in[u] + edge, in[v] + 1);
  }

  /* {parent, child} */
  vector<pair<int, int> > compress(vector<int> &remark) {
    auto cmp = [&](int a, int b) { return in[a] < in[b]; };
    sort(begin(remark), end(remark), cmp);
    remark.erase(unique(begin(remark), end(remark)), end(remark));
    int K = (int)remark.size();
    for (int k = 1; k < K; k++)
      remark.emplace_back(lca(remark[k - 1], remark[k]));
    sort(begin(remark), end(remark), cmp);
    remark.erase(unique(begin(remark), end(remark)), end(remark));
    vector<pair<int, int> > es;
    stack<int> st;
    for (auto &k : remark) {
      while (!st.empty() && out[st.top()] <= in[k]) st.pop();
      if (!st.empty()) es.emplace_back(st.top(), k);
      st.emplace(k);
    }
    return es;
  }

  explicit HeavyLightDecomposition(const Graph<T> &g) : Graph<T>(g) {}

 private:
  void dfs_sz(int idx, int p, int d) {
    dep[idx] = d;
    par[idx] = p;
    sz[idx] = 1;
    if (g[idx].size() && g[idx][0] == p) swap(g[idx][0], g[idx].back());
    for (auto &to : g[idx]) {
      if (to == p) continue;
      dfs_sz(to, idx, d + 1);
      sz[idx] += sz[to];
      if (sz[g[idx][0]] < sz[to]) swap(g[idx][0], to);
    }
  }

  void dfs_hld(int idx, int p, int &times) {
    in[idx] = times++;
    rev[in[idx]] = idx;
    for (auto &to : g[idx]) {
      if (to == p) continue;
      head[to] = (g[idx][0] == to ? head[idx] : to);
      dfs_hld(to, idx, times);
    }
    out[idx] = times;
  }
};
#line 6 "test/verify/yukicoder-650.test.cpp"

#line 1 "structure/segment-tree/segment-tree.hpp"
/**
 * @brief Segment Tree(セグメント木)
 *
 */
template <typename T, typename F>
struct SegmentTree {
  int n, sz;
  vector<T> seg;

  const F f;
  const T ti;

  SegmentTree() = default;

  explicit SegmentTree(int n, const F f, const T &ti) : n(n), f(f), ti(ti) {
    sz = 1;
    while (sz < n) sz <<= 1;
    seg.assign(2 * sz, ti);
  }

  explicit SegmentTree(const vector<T> &v, const F f, const T &ti)
      : SegmentTree((int)v.size(), f, ti) {
    build(v);
  }

  void build(const vector<T> &v) {
    assert(n == (int)v.size());
    for (int k = 0; k < n; k++) seg[k + sz] = v[k];
    for (int k = sz - 1; k > 0; k--) {
      seg[k] = f(seg[2 * k + 0], seg[2 * k + 1]);
    }
  }

  void set(int k, const T &x) {
    k += sz;
    seg[k] = x;
    while (k >>= 1) {
      seg[k] = f(seg[2 * k + 0], seg[2 * k + 1]);
    }
  }

  T get(int k) const { return seg[k + sz]; }

  T operator[](const int &k) const { return get(k); }

  void apply(int k, const T &x) {
    k += sz;
    seg[k] = f(seg[k], x);
    while (k >>= 1) {
      seg[k] = f(seg[2 * k + 0], seg[2 * k + 1]);
    }
  }

  T prod(int l, int r) const {
    T L = ti, R = ti;
    for (l += sz, r += sz; l < r; l >>= 1, r >>= 1) {
      if (l & 1) L = f(L, seg[l++]);
      if (r & 1) R = f(seg[--r], R);
    }
    return f(L, R);
  }

  T all_prod() const { return seg[1]; }

  template <typename C>
  int find_first(int l, const C &check) const {
    if (l >= n) return n;
    l += sz;
    T sum = ti;
    do {
      while ((l & 1) == 0) l >>= 1;
      if (check(f(sum, seg[l]))) {
        while (l < sz) {
          l <<= 1;
          auto nxt = f(sum, seg[l]);
          if (not check(nxt)) {
            sum = nxt;
            l++;
          }
        }
        return l + 1 - sz;
      }
      sum = f(sum, seg[l++]);
    } while ((l & -l) != l);
    return n;
  }

  template <typename C>
  int find_last(int r, const C &check) const {
    if (r <= 0) return -1;
    r += sz;
    T sum = ti;
    do {
      r--;
      while (r > 1 and (r & 1)) r >>= 1;
      if (check(f(seg[r], sum))) {
        while (r < sz) {
          r = (r << 1) + 1;
          auto nxt = f(seg[r], sum);
          if (not check(nxt)) {
            sum = nxt;
            r--;
          }
        }
        return r - sz;
      }
      sum = f(seg[r], sum);
    } while ((r & -r) != r);
    return -1;
  }
};

template <typename T, typename F>
SegmentTree<T, F> get_segment_tree(int N, const F &f, const T &ti) {
  return SegmentTree{N, f, ti};
}

template <typename T, typename F>
SegmentTree<T, F> get_segment_tree(const vector<T> &v, const F &f,
                                   const T &ti) {
  return SegmentTree{v, f, ti};
}
#line 8 "test/verify/yukicoder-650.test.cpp"

#line 2 "math/combinatorics/montgomery-mod-int.hpp"

template <uint32_t mod_, bool fast = false>
struct MontgomeryModInt {
 private:
  using mint = MontgomeryModInt;
  using i32 = int32_t;
  using i64 = int64_t;
  using u32 = uint32_t;
  using u64 = uint64_t;

  static constexpr u32 get_r() {
    u32 ret = mod_;
    for (i32 i = 0; i < 4; i++) ret *= 2 - mod_ * ret;
    return ret;
  }

  static constexpr u32 r = get_r();

  static constexpr u32 n2 = -u64(mod_) % mod_;

  static_assert(r * mod_ == 1, "invalid, r * mod != 1");
  static_assert(mod_ < (1 << 30), "invalid, mod >= 2 ^ 30");
  static_assert((mod_ & 1) == 1, "invalid, mod % 2 == 0");

  u32 x;

 public:
  MontgomeryModInt() : x{} {}

  MontgomeryModInt(const i64 &a)
      : x(reduce(u64(fast ? a : (a % mod() + mod())) * n2)) {}

  static constexpr u32 reduce(const u64 &b) {
    return u32(b >> 32) + mod() - u32((u64(u32(b) * r) * mod()) >> 32);
  }

  mint &operator+=(const mint &p) {
    if (i32(x += p.x - 2 * mod()) < 0) x += 2 * mod();
    return *this;
  }

  mint &operator-=(const mint &p) {
    if (i32(x -= p.x) < 0) x += 2 * mod();
    return *this;
  }

  mint &operator*=(const mint &p) {
    x = reduce(u64(x) * p.x);
    return *this;
  }

  mint &operator/=(const mint &p) {
    *this *= p.inv();
    return *this;
  }

  mint operator-() const { return mint() - *this; }

  mint operator+(const mint &p) const { return mint(*this) += p; }

  mint operator-(const mint &p) const { return mint(*this) -= p; }

  mint operator*(const mint &p) const { return mint(*this) *= p; }

  mint operator/(const mint &p) const { return mint(*this) /= p; }

  bool operator==(const mint &p) const {
    return (x >= mod() ? x - mod() : x) == (p.x >= mod() ? p.x - mod() : p.x);
  }

  bool operator!=(const mint &p) const {
    return (x >= mod() ? x - mod() : x) != (p.x >= mod() ? p.x - mod() : p.x);
  }

  u32 val() const {
    u32 ret = reduce(x);
    return ret >= mod() ? ret - mod() : ret;
  }

  mint pow(u64 n) const {
    mint ret(1), mul(*this);
    while (n > 0) {
      if (n & 1) ret *= mul;
      mul *= mul;
      n >>= 1;
    }
    return ret;
  }

  mint inv() const { return pow(mod() - 2); }

  friend ostream &operator<<(ostream &os, const mint &p) {
    return os << p.val();
  }

  friend istream &operator>>(istream &is, mint &a) {
    i64 t;
    is >> t;
    a = mint(t);
    return is;
  }

  static constexpr u32 mod() { return mod_; }
};

template <uint32_t mod>
using modint = MontgomeryModInt<mod>;
using modint998244353 = modint<998244353>;
using modint1000000007 = modint<1000000007>;
#line 1 "math/matrix/square-matrix.hpp"
/**
 * @brief Square-Matrix(正方行列)
 */
template <class T, size_t N>
struct SquareMatrix {
  array<array<T, N>, N> A;

  SquareMatrix() : A{{}} {}

  size_t size() const { return N; }

  inline const array<T, N> &operator[](int k) const { return (A.at(k)); }

  inline array<T, N> &operator[](int k) { return (A.at(k)); }

  static SquareMatrix add_identity() { return SquareMatrix(); }

  static SquareMatrix mul_identity() {
    SquareMatrix mat;
    for (size_t i = 0; i < N; i++) mat[i][i] = 1;
    return mat;
  }

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

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

  SquareMatrix &operator*=(const SquareMatrix &B) {
    array<array<T, N>, N> C;
    for (size_t i = 0; i < N; i++) {
      for (size_t j = 0; j < N; j++) {
        for (size_t k = 0; k < N; k++) {
          C[i][j] = (C[i][j] + (*this)[i][k] * B[k][j]);
        }
      }
    }
    A.swap(C);
    return (*this);
  }

  SquareMatrix &operator^=(uint64_t k) {
    SquareMatrix B = SquareMatrix::mul_identity();
    while (k > 0) {
      if (k & 1) B *= *this;
      *this *= *this;
      k >>= 1LL;
    }
    A.swap(B.A);
    return *this;
  }

  SquareMatrix operator+(const SquareMatrix &B) const {
    return SquareMatrix(*this) += B;
  }

  SquareMatrix operator-(const SquareMatrix &B) const {
    return SquareMatrix(*this) -= B;
  }

  SquareMatrix operator*(const SquareMatrix &B) const {
    return SquareMatrix(*this) *= B;
  }

  SquareMatrix operator^(uint64_t k) const { return SquareMatrix(*this) ^= k; }

  friend ostream &operator<<(ostream &os, SquareMatrix &p) {
    for (int i = 0; i < N; i++) {
      os << "[";
      for (int j = 0; j < N; j++) {
        os << p[i][j] << (j + 1 == N ? "]\n" : ",");
      }
    }
    return os;
  }
};
#line 11 "test/verify/yukicoder-650.test.cpp"

using mint = modint1000000007;

int main() {
  int N;
  cin >> N;
  vector< int > X(N), Y(N);
  HeavyLightDecomposition<> g(N);
  for(int i = 1; i < N; i++) {
    cin >> X[i] >> Y[i];
    g.add_edge(X[i], Y[i]);
  }
  g.build();
  for(int i = 1; i < N; i++) {
    if(g.in[X[i]] > g.in[Y[i]]) swap(X[i], Y[i]);
  }
  using Mat = SquareMatrix< mint, 2 >;
  auto f = [](const Mat &a, const Mat &b) { return a * b; };
  auto seg = get_segment_tree(N, f, Mat::mul_identity());
  int Q;
  cin >> Q;
  while(Q--) {
    char x;
    cin >> x;
    if(x == 'x') {
      int v;
      cin >> v;
      Mat m;
      cin >> m[0][0] >> m[0][1] >> m[1][0] >> m[1][1];
      seg.set(g.in[Y[v + 1]], m);
    } else {
      int y, z;
      cin >> y >> z;
      auto mat = g.query(y, z, Mat::mul_identity(), [&](int a, int b) { return seg.prod(a, b); }, f, true);
      cout << mat[0][0] << " " << mat[0][1] << " " << mat[1][0] << " " << mat[1][1] << "\n";
    }
  }
}

Test cases

Env	Name	Status	Elapsed	Memory
g++	0.0_100000_200001.txt	AC	52 ms	19 MB
g++	0.0_10_10.txt	AC	7 ms	4 MB
g++	0.0_20000_20000.txt	AC	25 ms	7 MB
g++	0.1_100000_20000_1.txt	AC	50 ms	18 MB
g++	0.1_10_10.txt	AC	7 ms	4 MB
g++	0.1_20000_20000.txt	AC	25 ms	7 MB
g++	00_sample1.txt	AC	6 ms	4 MB
g++	1.0_100000_20000_1.txt	AC	48 ms	23 MB
g++	1.0_10_10.txt	AC	7 ms	4 MB
g++	1.0_20000_20000.txt	AC	25 ms	8 MB
g++	99_challenge1.txt	AC	6 ms	4 MB
clang++	0.0_100000_200001.txt	AC	52 ms	18 MB
clang++	0.0_10_10.txt	AC	7 ms	4 MB
clang++	0.0_20000_20000.txt	AC	25 ms	7 MB
clang++	0.1_100000_20000_1.txt	AC	50 ms	18 MB
clang++	0.1_10_10.txt	AC	7 ms	4 MB
clang++	0.1_20000_20000.txt	AC	25 ms	7 MB
clang++	00_sample1.txt	AC	6 ms	4 MB
clang++	1.0_100000_20000_1.txt	AC	55 ms	27 MB
clang++	1.0_10_10.txt	AC	7 ms	4 MB
clang++	1.0_20000_20000.txt	AC	26 ms	8 MB
clang++	99_challenge1.txt	AC	7 ms	4 MB

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