cp-library

C++ Library for Competitive Programming

View the Project on GitHub emthrm/cp-library

:heavy_check_mark: データ構造/双対セグメント木
(test/data_structure/dual_segment_tree.test.cpp)

Depends on

Code

/*
 * @title データ構造/双対セグメント木
 *
 * verification-helper: PROBLEM https://judge.yosupo.jp/problem/range_affine_point_get
 */

#include <iostream>
#include <utility>
#include <vector>

#include "emthrm/data_structure/dual_segment_tree.hpp"
#include "emthrm/math/modint.hpp"

int main() {
  using ModInt = emthrm::MInt<998244353>;
  int n, q;
  std::cin >> n >> q;
  std::vector<ModInt> a(n);
  for (ModInt& a_i : a) std::cin >> a_i;
  struct M {
    using Elem = ModInt;
    using OperatorMonoid = std::pair<ModInt, ModInt>;
    static OperatorMonoid id() { return {ModInt::raw(1), ModInt::raw(0)}; }
    static OperatorMonoid merge(const OperatorMonoid& a,
                                const OperatorMonoid& b) {
      return {a.first * b.first, a.second * b.first + b.second};
    }
    static Elem apply(const Elem& a, const OperatorMonoid& b) {
      return a * b.first + b.second;
    }
  };
  emthrm::DualSegmentTree<M> dst(a);
  while (q--) {
    int type;
    std::cin >> type;
    if (type == 0) {
      int l, r;
      ModInt b, c;
      std::cin >> l >> r >> b >> c;
      dst.apply(l, r, {b, c});
    } else if (type == 1) {
      int i;
      std::cin >> i;
      std::cout << dst[i] << '\n';
    }
  }
  return 0;
}
#line 1 "test/data_structure/dual_segment_tree.test.cpp"
/*
 * @title データ構造/双対セグメント木
 *
 * verification-helper: PROBLEM https://judge.yosupo.jp/problem/range_affine_point_get
 */

#include <iostream>
#include <utility>
#include <vector>

#line 1 "include/emthrm/data_structure/dual_segment_tree.hpp"



#include <bit>
#include <concepts>
#include <cstdint>
#include <optional>
#line 10 "include/emthrm/data_structure/dual_segment_tree.hpp"

namespace emthrm {

template <typename T>
requires requires {
  typename T::Elem;
  typename T::OperatorMonoid;
  {T::id()} -> std::same_as<typename T::OperatorMonoid>;
  {T::merge(std::declval<typename T::OperatorMonoid>(),
            std::declval<typename T::OperatorMonoid>())}
      -> std::same_as<typename T::OperatorMonoid>;
  {T::apply(std::declval<typename T::Elem>(),
            std::declval<typename T::OperatorMonoid>())}
      -> std::same_as<typename T::Elem>;
}
struct DualSegmentTree {
  using Elem = typename T::Elem;
  using OperatorMonoid = typename T::OperatorMonoid;

  explicit DualSegmentTree(const std::vector<Elem>& data)
      : n(data.size()), height(std::countr_zero(std::bit_ceil(data.size()))),
        p2(1 << height), data(data), lazy(p2, T::id()) {}

  void set(const int idx, const Elem val) {
    propagate_line(idx);
    data[idx] = val;
  }

  void apply(const int idx, const OperatorMonoid val) {
    propagate_line(idx);
    data[idx] = T::apply(data[idx], val);
  }

  void apply(int left, int right, const OperatorMonoid val) {
    if (right <= left) [[unlikely]] return;
    propagate_line(left, std::countr_zero(static_cast<unsigned int>(left)));
    propagate_line(right, std::countr_zero(static_cast<unsigned int>(right)));
    left += p2;
    right += p2;
    if (left & 1) {
      data[left - p2] = T::apply(data[left - p2], val);
      ++left;
    }
    if (right & 1) {
      --right;
      data[right - p2] = T::apply(data[right - p2], val);
    }
    for (left >>= 1, right >>= 1; left < right; left >>= 1, right >>= 1) {
      if (left & 1) {
        lazy[left] = T::merge(lazy[left], val);
        ++left;
      }
      if (right & 1) {
        --right;
        lazy[right] = T::merge(lazy[right], val);
      }
    }
  }

  Elem operator[](const int idx) {
    propagate_line(idx);
    return data[idx];
  }

 private:
  const int n, height, p2;
  std::vector<Elem> data;
  std::vector<OperatorMonoid> lazy;

  void propagate(const int idx) {
    if (lazy[idx] == T::id()) return;
    const int child = idx << 1;
    if (child >= p2) {
      if (child - p2 < n) {
        data[child - p2] = T::apply(data[child - p2], lazy[idx]);
        if (child - p2 + 1 < n) {
          data[child - p2 + 1] = T::apply(data[child - p2 + 1], lazy[idx]);
        }
      }
    } else {
      lazy[child] = T::merge(lazy[child], lazy[idx]);
      lazy[child + 1] = T::merge(lazy[child + 1], lazy[idx]);
    }
    lazy[idx] = T::id();
  }

  void propagate_line(const int idx, const int until = 0) {
    const int node = idx + p2;
    for (int i = height; i > until; --i) {
      propagate(node >> i);
    }
  }
};

namespace monoid {

template <typename T>
struct RangeUpdateQuery {
  using Elem = T;
  using OperatorMonoid = std::optional<Elem>;
  static constexpr OperatorMonoid id() { return std::nullopt; }
  static OperatorMonoid merge(const OperatorMonoid& a,
                              const OperatorMonoid& b) {
    return b.has_value() ? b : a;
  }
  static Elem apply(const Elem& a, const OperatorMonoid& b) {
    return b.has_value() ? b.value() : a;
  }
};

template <typename T>
struct RangeAddQuery {
  using Elem = T;
  using OperatorMonoid = T;
  static constexpr OperatorMonoid id() { return 0; }
  static OperatorMonoid merge(const OperatorMonoid& a,
                              const OperatorMonoid& b) {
    return a + b;
  }
  static Elem apply(const Elem& a, const OperatorMonoid& b) { return a + b; }
};

}  // namespace monoid

}  // namespace emthrm


#line 1 "include/emthrm/math/modint.hpp"



#ifndef ARBITRARY_MODINT
# include <cassert>
#endif
#include <compare>
#line 9 "include/emthrm/math/modint.hpp"
// #include <numeric>
#line 12 "include/emthrm/math/modint.hpp"

namespace emthrm {

#ifndef ARBITRARY_MODINT
template <unsigned int M>
struct MInt {
  unsigned int v;

  constexpr MInt() : v(0) {}
  constexpr MInt(const long long x) : v(x >= 0 ? x % M : x % M + M) {}
  static constexpr MInt raw(const int x) {
    MInt x_;
    x_.v = x;
    return x_;
  }

  static constexpr int get_mod() { return M; }
  static constexpr void set_mod(const int divisor) {
    assert(std::cmp_equal(divisor, M));
  }

  static void init(const int x) {
    inv<true>(x);
    fact(x);
    fact_inv(x);
  }

  template <bool MEMOIZES = false>
  static MInt inv(const int n) {
    // assert(0 <= n && n < M && std::gcd(n, M) == 1);
    static std::vector<MInt> inverse{0, 1};
    const int prev = inverse.size();
    if (n < prev) return inverse[n];
    if constexpr (MEMOIZES) {
      // "n!" and "M" must be disjoint.
      inverse.resize(n + 1);
      for (int i = prev; i <= n; ++i) {
        inverse[i] = -inverse[M % i] * raw(M / i);
      }
      return inverse[n];
    }
    int u = 1, v = 0;
    for (unsigned int a = n, b = M; b;) {
      const unsigned int q = a / b;
      std::swap(a -= q * b, b);
      std::swap(u -= q * v, v);
    }
    return u;
  }

  static MInt fact(const int n) {
    static std::vector<MInt> factorial{1};
    if (const int prev = factorial.size(); n >= prev) {
      factorial.resize(n + 1);
      for (int i = prev; i <= n; ++i) {
        factorial[i] = factorial[i - 1] * i;
      }
    }
    return factorial[n];
  }

  static MInt fact_inv(const int n) {
    static std::vector<MInt> f_inv{1};
    if (const int prev = f_inv.size(); n >= prev) {
      f_inv.resize(n + 1);
      f_inv[n] = inv(fact(n).v);
      for (int i = n; i > prev; --i) {
        f_inv[i - 1] = f_inv[i] * i;
      }
    }
    return f_inv[n];
  }

  static MInt nCk(const int n, const int k) {
    if (n < 0 || n < k || k < 0) [[unlikely]] return MInt();
    return fact(n) * (n - k < k ? fact_inv(k) * fact_inv(n - k) :
                                  fact_inv(n - k) * fact_inv(k));
  }
  static MInt nPk(const int n, const int k) {
    return n < 0 || n < k || k < 0 ? MInt() : fact(n) * fact_inv(n - k);
  }
  static MInt nHk(const int n, const int k) {
    return n < 0 || k < 0 ? MInt() : (k == 0 ? 1 : nCk(n + k - 1, k));
  }

  static MInt large_nCk(long long n, const int k) {
    if (n < 0 || n < k || k < 0) [[unlikely]] return MInt();
    inv<true>(k);
    MInt res = 1;
    for (int i = 1; i <= k; ++i) {
      res *= inv(i) * n--;
    }
    return res;
  }

  constexpr MInt pow(long long exponent) const {
    MInt res = 1, tmp = *this;
    for (; exponent > 0; exponent >>= 1) {
      if (exponent & 1) res *= tmp;
      tmp *= tmp;
    }
    return res;
  }

  constexpr MInt& operator+=(const MInt& x) {
    if ((v += x.v) >= M) v -= M;
    return *this;
  }
  constexpr MInt& operator-=(const MInt& x) {
    if ((v += M - x.v) >= M) v -= M;
    return *this;
  }
  constexpr MInt& operator*=(const MInt& x) {
    v = (unsigned long long){v} * x.v % M;
    return *this;
  }
  MInt& operator/=(const MInt& x) { return *this *= inv(x.v); }

  constexpr auto operator<=>(const MInt& x) const = default;

  constexpr MInt& operator++() {
    if (++v == M) [[unlikely]] v = 0;
    return *this;
  }
  constexpr MInt operator++(int) {
    const MInt res = *this;
    ++*this;
    return res;
  }
  constexpr MInt& operator--() {
    v = (v == 0 ? M - 1 : v - 1);
    return *this;
  }
  constexpr MInt operator--(int) {
    const MInt res = *this;
    --*this;
    return res;
  }

  constexpr MInt operator+() const { return *this; }
  constexpr MInt operator-() const { return raw(v ? M - v : 0); }

  constexpr MInt operator+(const MInt& x) const { return MInt(*this) += x; }
  constexpr MInt operator-(const MInt& x) const { return MInt(*this) -= x; }
  constexpr MInt operator*(const MInt& x) const { return MInt(*this) *= x; }
  MInt operator/(const MInt& x) const { return MInt(*this) /= x; }

  friend std::ostream& operator<<(std::ostream& os, const MInt& x) {
    return os << x.v;
  }
  friend std::istream& operator>>(std::istream& is, MInt& x) {
    long long v;
    is >> v;
    x = MInt(v);
    return is;
  }
};
#else  // ARBITRARY_MODINT
template <int ID>
struct MInt {
  unsigned int v;

  constexpr MInt() : v(0) {}
  MInt(const long long x) : v(x >= 0 ? x % mod() : x % mod() + mod()) {}
  static constexpr MInt raw(const int x) {
    MInt x_;
    x_.v = x;
    return x_;
  }

  static int get_mod() { return mod(); }
  static void set_mod(const unsigned int divisor) { mod() = divisor; }

  static void init(const int x) {
    inv<true>(x);
    fact(x);
    fact_inv(x);
  }

  template <bool MEMOIZES = false>
  static MInt inv(const int n) {
    // assert(0 <= n && n < mod() && std::gcd(x, mod()) == 1);
    static std::vector<MInt> inverse{0, 1};
    const int prev = inverse.size();
    if (n < prev) return inverse[n];
    if constexpr (MEMOIZES) {
      // "n!" and "M" must be disjoint.
      inverse.resize(n + 1);
      for (int i = prev; i <= n; ++i) {
        inverse[i] = -inverse[mod() % i] * raw(mod() / i);
      }
      return inverse[n];
    }
    int u = 1, v = 0;
    for (unsigned int a = n, b = mod(); b;) {
      const unsigned int q = a / b;
      std::swap(a -= q * b, b);
      std::swap(u -= q * v, v);
    }
    return u;
  }

  static MInt fact(const int n) {
    static std::vector<MInt> factorial{1};
    if (const int prev = factorial.size(); n >= prev) {
      factorial.resize(n + 1);
      for (int i = prev; i <= n; ++i) {
        factorial[i] = factorial[i - 1] * i;
      }
    }
    return factorial[n];
  }

  static MInt fact_inv(const int n) {
    static std::vector<MInt> f_inv{1};
    if (const int prev = f_inv.size(); n >= prev) {
      f_inv.resize(n + 1);
      f_inv[n] = inv(fact(n).v);
      for (int i = n; i > prev; --i) {
        f_inv[i - 1] = f_inv[i] * i;
      }
    }
    return f_inv[n];
  }

  static MInt nCk(const int n, const int k) {
    if (n < 0 || n < k || k < 0) [[unlikely]] return MInt();
    return fact(n) * (n - k < k ? fact_inv(k) * fact_inv(n - k) :
                                  fact_inv(n - k) * fact_inv(k));
  }
  static MInt nPk(const int n, const int k) {
    return n < 0 || n < k || k < 0 ? MInt() : fact(n) * fact_inv(n - k);
  }
  static MInt nHk(const int n, const int k) {
    return n < 0 || k < 0 ? MInt() : (k == 0 ? 1 : nCk(n + k - 1, k));
  }

  static MInt large_nCk(long long n, const int k) {
    if (n < 0 || n < k || k < 0) [[unlikely]] return MInt();
    inv<true>(k);
    MInt res = 1;
    for (int i = 1; i <= k; ++i) {
      res *= inv(i) * n--;
    }
    return res;
  }

  MInt pow(long long exponent) const {
    MInt res = 1, tmp = *this;
    for (; exponent > 0; exponent >>= 1) {
      if (exponent & 1) res *= tmp;
      tmp *= tmp;
    }
    return res;
  }

  MInt& operator+=(const MInt& x) {
    if ((v += x.v) >= mod()) v -= mod();
    return *this;
  }
  MInt& operator-=(const MInt& x) {
    if ((v += mod() - x.v) >= mod()) v -= mod();
    return *this;
  }
  MInt& operator*=(const MInt& x) {
    v = (unsigned long long){v} * x.v % mod();
    return *this;
    }
  MInt& operator/=(const MInt& x) { return *this *= inv(x.v); }

  auto operator<=>(const MInt& x) const = default;

  MInt& operator++() {
    if (++v == mod()) [[unlikely]] v = 0;
    return *this;
  }
  MInt operator++(int) {
    const MInt res = *this;
    ++*this;
    return res;
  }
  MInt& operator--() {
    v = (v == 0 ? mod() - 1 : v - 1);
    return *this;
  }
  MInt operator--(int) {
    const MInt res = *this;
    --*this;
    return res;
  }

  MInt operator+() const { return *this; }
  MInt operator-() const { return raw(v ? mod() - v : 0); }

  MInt operator+(const MInt& x) const { return MInt(*this) += x; }
  MInt operator-(const MInt& x) const { return MInt(*this) -= x; }
  MInt operator*(const MInt& x) const { return MInt(*this) *= x; }
  MInt operator/(const MInt& x) const { return MInt(*this) /= x; }

  friend std::ostream& operator<<(std::ostream& os, const MInt& x) {
    return os << x.v;
  }
  friend std::istream& operator>>(std::istream& is, MInt& x) {
    long long v;
    is >> v;
    x = MInt(v);
    return is;
  }

 private:
  static unsigned int& mod() {
    static unsigned int divisor = 0;
    return divisor;
  }
};
#endif  // ARBITRARY_MODINT

}  // namespace emthrm


#line 13 "test/data_structure/dual_segment_tree.test.cpp"

int main() {
  using ModInt = emthrm::MInt<998244353>;
  int n, q;
  std::cin >> n >> q;
  std::vector<ModInt> a(n);
  for (ModInt& a_i : a) std::cin >> a_i;
  struct M {
    using Elem = ModInt;
    using OperatorMonoid = std::pair<ModInt, ModInt>;
    static OperatorMonoid id() { return {ModInt::raw(1), ModInt::raw(0)}; }
    static OperatorMonoid merge(const OperatorMonoid& a,
                                const OperatorMonoid& b) {
      return {a.first * b.first, a.second * b.first + b.second};
    }
    static Elem apply(const Elem& a, const OperatorMonoid& b) {
      return a * b.first + b.second;
    }
  };
  emthrm::DualSegmentTree<M> dst(a);
  while (q--) {
    int type;
    std::cin >> type;
    if (type == 0) {
      int l, r;
      ModInt b, c;
      std::cin >> l >> r >> b >> c;
      dst.apply(l, r, {b, c});
    } else if (type == 1) {
      int i;
      std::cin >> i;
      std::cout << dst[i] << '\n';
    }
  }
  return 0;
}
Back to top page