test/yukicoder/510/main.test.cpp

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• Last update: 2021-04-23 23:44:44+09:00
• Problem: https://yukicoder.me/problems/no/510
• Link: View error logs on GitHub Actions

Depends on

• Dual monoid (Mylib/AlgebraicStructure/Monoid/dual.cpp)
• Product matrix monoid (Mylib/AlgebraicStructure/Monoid/product_matrix.cpp)
• Segment tree (Mylib/DataStructure/SegmentTree/segment_tree.cpp)
• Input tuple (Mylib/IO/input_tuple.cpp)
• Input tuples (Mylib/IO/input_tuples.cpp)
• Square matrix (Const size) (Mylib/LinearAlgebra/square_matrix_const_size.cpp)
• Modint (Mylib/Number/Mint/mint.cpp)

Code

#define PROBLEM "https://yukicoder.me/problems/no/510"

#include <iostream>
#include <vector>
#include "Mylib/AlgebraicStructure/Monoid/dual.cpp"
#include "Mylib/AlgebraicStructure/Monoid/product_matrix.cpp"
#include "Mylib/DataStructure/SegmentTree/segment_tree.cpp"
#include "Mylib/IO/input_tuples.cpp"
#include "Mylib/LinearAlgebra/square_matrix_const_size.cpp"
#include "Mylib/Number/Mint/mint.cpp"

namespace hl = haar_lib;

using mint   = hl::modint<1000000007>;
using Mat    = hl::square_matrix_const<mint, 4>;
using Monoid = hl::dual_monoid<hl::product_matrix_monoid<Mat>>;

auto f(mint x, mint y) {
  Mat ret = {
      {1, 0, x, 0},
      {0, y, 0, 1},
      {0, 2 * y, y * y, 1},
      {0, 0, 0, 1}};
  return ret;
}

int main() {
  int n, q;
  std::cin >> n >> q;

  hl::segment_tree<Monoid> seg(n);
  std::vector<mint> x(n), y(n);

  for (int i = 0; i < n; ++i) {
    seg.set(i, f(x[i], y[i]));
  }

  for (auto [c, i] : hl::input_tuples<char, int>(q)) {
    if (c == 'x') {
      int v;
      std::cin >> v;
      x[i] = v;

      seg.set(i, f(x[i], y[i]));
    } else if (c == 'y') {
      int v;
      std::cin >> v;
      y[i] = v;

      seg.set(i, f(x[i], y[i]));
    } else {
      auto m   = seg.fold(0, i);
      auto ans = dot(m[0], Mat::vector_type({1, 1, 1, 1}));
      std::cout << ans << "\n";
    }
  }

  return 0;
}

#line 1 "test/yukicoder/510/main.test.cpp"
#define PROBLEM "https://yukicoder.me/problems/no/510"

#include <iostream>
#include <vector>
#line 2 "Mylib/AlgebraicStructure/Monoid/dual.cpp"

namespace haar_lib {
  template <typename Monoid>
  struct dual_monoid {
    using value_type = typename Monoid::value_type;
    const static Monoid M;
    value_type operator()() const { return M(); }
    value_type operator()(const value_type &a, const value_type &b) const { return M(b, a); }
  };
}  // namespace haar_lib
#line 2 "Mylib/AlgebraicStructure/Monoid/product_matrix.cpp"

namespace haar_lib {
  template <typename T>
  struct product_matrix_monoid {
    using value_type = T;
    value_type operator()() const { return T::unit(); }
    value_type operator()(const value_type &a, const value_type &b) const { return a * b; }
  };
}  // namespace haar_lib
#line 2 "Mylib/DataStructure/SegmentTree/segment_tree.cpp"
#include <algorithm>
#include <cassert>
#include <functional>
#line 6 "Mylib/DataStructure/SegmentTree/segment_tree.cpp"

namespace haar_lib {
  template <typename Monoid>
  class segment_tree {
  public:
    using value_type = typename Monoid::value_type;

  private:
    Monoid M_;
    int depth_, size_, hsize_;
    std::vector<value_type> data_;

  public:
    segment_tree() {}
    segment_tree(int n) : depth_(n > 1 ? 32 - __builtin_clz(n - 1) + 1 : 1),
                          size_(1 << depth_),
                          hsize_(size_ / 2),
                          data_(size_, M_()) {}

    auto operator[](int i) const {
      assert(0 <= i and i < hsize_);
      return data_[hsize_ + i];
    }

    auto fold(int l, int r) const {
      assert(0 <= l and l <= r and r <= hsize_);
      value_type ret_left  = M_();
      value_type ret_right = M_();

      int L = l + hsize_, R = r + hsize_;
      while (L < R) {
        if (R & 1) ret_right = M_(data_[--R], ret_right);
        if (L & 1) ret_left = M_(ret_left, data_[L++]);
        L >>= 1, R >>= 1;
      }

      return M_(ret_left, ret_right);
    }

    auto fold_all() const {
      return data_[1];
    }

    void set(int i, const value_type &x) {
      assert(0 <= i and i < hsize_);
      i += hsize_;
      data_[i] = x;
      while (i > 1) i >>= 1, data_[i] = M_(data_[i << 1 | 0], data_[i << 1 | 1]);
    }

    void update(int i, const value_type &x) {
      assert(0 <= i and i < hsize_);
      i += hsize_;
      data_[i] = M_(data_[i], x);
      while (i > 1) i >>= 1, data_[i] = M_(data_[i << 1 | 0], data_[i << 1 | 1]);
    }

    template <typename T>
    void init_with_vector(const std::vector<T> &val) {
      data_.assign(size_, M_());
      for (int i = 0; i < (int) val.size(); ++i) data_[hsize_ + i] = val[i];
      for (int i = hsize_; --i >= 1;) data_[i] = M_(data_[i << 1 | 0], data_[i << 1 | 1]);
    }

    template <typename T>
    void init(const T &val) {
      init_with_vector(std::vector<value_type>(hsize_, val));
    }

  private:
    template <bool Lower, typename F>
    int bound(const int l, const int r, value_type x, F f) const {
      std::vector<int> pl, pr;
      int L = l + hsize_;
      int R = r + hsize_;
      while (L < R) {
        if (R & 1) pr.push_back(--R);
        if (L & 1) pl.push_back(L++);
        L >>= 1, R >>= 1;
      }

      std::reverse(pr.begin(), pr.end());
      pl.insert(pl.end(), pr.begin(), pr.end());

      value_type a = M_();

      for (int i : pl) {
        auto b = M_(a, data_[i]);

        if ((Lower and not f(b, x)) or (not Lower and f(x, b))) {
          while (i < hsize_) {
            const auto c = M_(a, data_[i << 1 | 0]);
            if ((Lower and not f(c, x)) or (not Lower and f(x, c))) {
              i = i << 1 | 0;
            } else {
              a = c;
              i = i << 1 | 1;
            }
          }

          return i - hsize_;
        }

        a = b;
      }

      return r;
    }

  public:
    template <typename F = std::less<value_type>>
    int lower_bound(int l, int r, value_type x, F f = F()) const {
      return bound<true>(l, r, x, f);
    }

    template <typename F = std::less<value_type>>
    int upper_bound(int l, int r, value_type x, F f = F()) const {
      return bound<false>(l, r, x, f);
    }
  };
}  // namespace haar_lib
#line 2 "Mylib/IO/input_tuples.cpp"
#include <initializer_list>
#line 4 "Mylib/IO/input_tuples.cpp"
#include <tuple>
#include <utility>
#line 6 "Mylib/IO/input_tuple.cpp"

namespace haar_lib {
  template <typename T, size_t... I>
  static void input_tuple_helper(std::istream &s, T &val, std::index_sequence<I...>) {
    (void) std::initializer_list<int>{(void(s >> std::get<I>(val)), 0)...};
  }

  template <typename T, typename U>
  std::istream &operator>>(std::istream &s, std::pair<T, U> &value) {
    s >> value.first >> value.second;
    return s;
  }

  template <typename... Args>
  std::istream &operator>>(std::istream &s, std::tuple<Args...> &value) {
    input_tuple_helper(s, value, std::make_index_sequence<sizeof...(Args)>());
    return s;
  }
}  // namespace haar_lib
#line 8 "Mylib/IO/input_tuples.cpp"

namespace haar_lib {
  template <typename... Args>
  class InputTuples {
    struct iter {
      using value_type = std::tuple<Args...>;
      value_type value;
      bool fetched = false;
      int N, c = 0;

      value_type operator*() {
        if (not fetched) {
          std::cin >> value;
        }
        return value;
      }

      void operator++() {
        ++c;
        fetched = false;
      }

      bool operator!=(iter &) const {
        return c < N;
      }

      iter(int N) : N(N) {}
    };

    int N;

  public:
    InputTuples(int N) : N(N) {}

    iter begin() const { return iter(N); }
    iter end() const { return iter(N); }
  };

  template <typename... Args>
  auto input_tuples(int N) {
    return InputTuples<Args...>(N);
  }
}  // namespace haar_lib
#line 2 "Mylib/LinearAlgebra/square_matrix_const_size.cpp"
#include <array>
#line 6 "Mylib/LinearAlgebra/square_matrix_const_size.cpp"

namespace haar_lib {
  template <typename T, int N>
  class vector_const {
  public:
    using value_type = T;

  private:
    std::array<T, N> data_;

  public:
    vector_const() { data_.fill(0); }
    vector_const(T value) { data_.fill(value); }
    vector_const(std::initializer_list<T> list) {
      int i = 0;
      for (auto it = list.begin(); it != list.end(); ++it) data_[i++] = *it;
    }
    vector_const(const vector_const &that) : data_(that.data_) {}

    bool operator==(const vector_const &that) { return data_ == that.data_; }
    bool operator!=(const vector_const &that) { return !(*this == that); }

    auto &operator=(const vector_const &that) {
      data_ = that.data_;
      return *this;
    }

    auto &operator+=(const vector_const &that) {
      for (int i = 0; i < N; ++i) data_[i] += that.data_[i];
      return *this;
    }

    auto &operator-=(const vector_const &that) {
      for (int i = 0; i < N; ++i) data_[i] -= that.data_[i];
      return *this;
    }

    friend auto dot(const vector_const &a, const vector_const &b) {
      T ret = 0;
      for (int i = 0; i < N; ++i) ret += a.data_[i] * b.data_[i];
      return ret;
    }

    auto operator+(const vector_const &that) const {
      return vector_const(*this) += that;
    }

    auto operator-(const vector_const &that) const {
      return vector_const(*this) -= that;
    }

    auto &operator[](int i) { return data_[i]; }
    const auto &operator[](int i) const { return data_[i]; }
    auto begin() const { return data_.begin(); }
    auto end() const { return data_.end(); }

    int size() const { return N; }

    friend std::ostream &operator<<(std::ostream &s, const vector_const &a) {
      s << "{";
      for (auto it = a.data_.begin(); it != a.data_.end(); ++it) {
        if (it != a.data_.begin()) s << ",";
        s << *it;
      }
      s << "}";
      return s;
    }
  };

  template <typename T, int N>
  class square_matrix_const {
  public:
    using value_type  = T;
    using vector_type = vector_const<T, N>;

  private:
    std::array<vector_type, N> data_;

  public:
    square_matrix_const() {
      for (int i = 0; i < N; ++i) data_[i] = vector_type();
    }
    square_matrix_const(const T &val) {
      for (int i = 0; i < N; ++i) data_[i] = vector_type(val);
    }
    square_matrix_const(std::initializer_list<std::initializer_list<T>> list) {
      int i = 0;
      for (auto it = list.begin(); it != list.end(); ++it) {
        data_[i++] = vector_type(*it);
      }
    }
    square_matrix_const(const square_matrix_const &that) : data_(that.data_) {}

    bool operator==(const square_matrix_const &that) const { return data_ == that.data_; }
    bool operator!=(const square_matrix_const &that) const { return !(*this == that); }

    auto &operator=(const square_matrix_const &that) {
      data_ = that.data_;
      return *this;
    }

    auto &operator+=(const square_matrix_const &that) {
      for (int i = 0; i < N; ++i) data_[i] += that.data_[i];
      return *this;
    }

    auto &operator-=(const square_matrix_const &that) {
      for (int i = 0; i < N; ++i) data_[i] -= that.data_[i];
      return *this;
    }

    auto &operator*=(const square_matrix_const &that) {
      square_matrix_const ret;
      for (int i = 0; i < N; ++i)
        for (int j = 0; j < N; ++j)
          for (int k = 0; k < N; ++k)
            ret[i][j] += data_[i][k] * that.data_[k][j];
      return *this = ret;
    }

    const auto &operator[](int i) const { return data_[i]; }
    auto &operator[](int i) { return data_[i]; }
    int size() const { return N; }

    static auto unit() {
      square_matrix_const ret;
      for (int i = 0; i < N; ++i) ret[i][i] = 1;
      return ret;
    }

    auto operator+(const square_matrix_const &that) const {
      return square_matrix_const(*this) += that;
    }
    auto operator-(const square_matrix_const &that) const {
      return square_matrix_const(*this) -= that;
    }
    auto operator*(const square_matrix_const &that) const {
      return square_matrix_const(*this) *= that;
    }

    auto pow(uint64_t p) const {
      auto ret = unit();
      auto a   = *this;

      while (p > 0) {
        if (p & 1) ret *= a;
        a *= a;
        p >>= 1;
      }

      return ret;
    }

    auto operator*(const vector_type &that) const {
      vector_type ret;
      for (int i = 0; i < N; ++i) ret[i] = dot(data_[i], that);
      return ret;
    }
  };
}  // namespace haar_lib
#line 4 "Mylib/Number/Mint/mint.cpp"

namespace haar_lib {
  template <int32_t M>
  class modint {
    uint32_t val_;

  public:
    constexpr static auto mod() { return M; }

    constexpr modint() : val_(0) {}
    constexpr modint(int64_t n) {
      if (n >= M)
        val_ = n % M;
      else if (n < 0)
        val_ = n % M + M;
      else
        val_ = n;
    }

    constexpr auto &operator=(const modint &a) {
      val_ = a.val_;
      return *this;
    }
    constexpr auto &operator+=(const modint &a) {
      if (val_ + a.val_ >= M)
        val_ = (uint64_t) val_ + a.val_ - M;
      else
        val_ += a.val_;
      return *this;
    }
    constexpr auto &operator-=(const modint &a) {
      if (val_ < a.val_) val_ += M;
      val_ -= a.val_;
      return *this;
    }
    constexpr auto &operator*=(const modint &a) {
      val_ = (uint64_t) val_ * a.val_ % M;
      return *this;
    }
    constexpr auto &operator/=(const modint &a) {
      val_ = (uint64_t) val_ * a.inv().val_ % M;
      return *this;
    }

    constexpr auto operator+(const modint &a) const { return modint(*this) += a; }
    constexpr auto operator-(const modint &a) const { return modint(*this) -= a; }
    constexpr auto operator*(const modint &a) const { return modint(*this) *= a; }
    constexpr auto operator/(const modint &a) const { return modint(*this) /= a; }

    constexpr bool operator==(const modint &a) const { return val_ == a.val_; }
    constexpr bool operator!=(const modint &a) const { return val_ != a.val_; }

    constexpr auto &operator++() {
      *this += 1;
      return *this;
    }
    constexpr auto &operator--() {
      *this -= 1;
      return *this;
    }

    constexpr auto operator++(int) {
      auto t = *this;
      *this += 1;
      return t;
    }
    constexpr auto operator--(int) {
      auto t = *this;
      *this -= 1;
      return t;
    }

    constexpr static modint pow(int64_t n, int64_t p) {
      if (p < 0) return pow(n, -p).inv();

      int64_t ret = 1, e = n % M;
      for (; p; (e *= e) %= M, p >>= 1)
        if (p & 1) (ret *= e) %= M;
      return ret;
    }

    constexpr static modint inv(int64_t a) {
      int64_t b = M, u = 1, v = 0;

      while (b) {
        int64_t t = a / b;
        a -= t * b;
        std::swap(a, b);
        u -= t * v;
        std::swap(u, v);
      }

      u %= M;
      if (u < 0) u += M;

      return u;
    }

    constexpr static auto frac(int64_t a, int64_t b) { return modint(a) / modint(b); }

    constexpr auto pow(int64_t p) const { return pow(val_, p); }
    constexpr auto inv() const { return inv(val_); }

    friend constexpr auto operator-(const modint &a) { return modint(M - a.val_); }

    friend constexpr auto operator+(int64_t a, const modint &b) { return modint(a) + b; }
    friend constexpr auto operator-(int64_t a, const modint &b) { return modint(a) - b; }
    friend constexpr auto operator*(int64_t a, const modint &b) { return modint(a) * b; }
    friend constexpr auto operator/(int64_t a, const modint &b) { return modint(a) / b; }

    friend std::istream &operator>>(std::istream &s, modint &a) {
      s >> a.val_;
      return s;
    }
    friend std::ostream &operator<<(std::ostream &s, const modint &a) {
      s << a.val_;
      return s;
    }

    template <int N>
    static auto div() {
      static auto value = inv(N);
      return value;
    }

    explicit operator int32_t() const noexcept { return val_; }
    explicit operator int64_t() const noexcept { return val_; }
  };
}  // namespace haar_lib
#line 11 "test/yukicoder/510/main.test.cpp"

namespace hl = haar_lib;

using mint   = hl::modint<1000000007>;
using Mat    = hl::square_matrix_const<mint, 4>;
using Monoid = hl::dual_monoid<hl::product_matrix_monoid<Mat>>;

auto f(mint x, mint y) {
  Mat ret = {
      {1, 0, x, 0},
      {0, y, 0, 1},
      {0, 2 * y, y * y, 1},
      {0, 0, 0, 1}};
  return ret;
}

int main() {
  int n, q;
  std::cin >> n >> q;

  hl::segment_tree<Monoid> seg(n);
  std::vector<mint> x(n), y(n);

  for (int i = 0; i < n; ++i) {
    seg.set(i, f(x[i], y[i]));
  }

  for (auto [c, i] : hl::input_tuples<char, int>(q)) {
    if (c == 'x') {
      int v;
      std::cin >> v;
      x[i] = v;

      seg.set(i, f(x[i], y[i]));
    } else if (c == 'y') {
      int v;
      std::cin >> v;
      y[i] = v;

      seg.set(i, f(x[i], y[i]));
    } else {
      auto m   = seg.fold(0, i);
      auto ans = dot(m[0], Mat::vector_type({1, 1, 1, 1}));
      std::cout << ans << "\n";
    }
  }

  return 0;
}

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