Tifa's CP Library

:heavy_check_mark: src/test_cpverifier/library-checker/point_set_range_composite.d31.test.cpp

Depends on

Code

#define AUTO_GENERATED
#define PROBLEM "https://judge.yosupo.jp/problem/point_set_range_composite"

#include "../../code/ds/segtree.hpp"

constexpr u32 MOD = 998244353;

#include "../../code/math/mint_d31.hpp"

using mint = tifa_libs::math::mint_d31<-1>;
using Ty = mint;
using T = std::pair<Ty, Ty>;
using F = T;

auto op(T a, T b) {  // b(a(x))
  swap(a, b);
  return T{a.first * b.first, a.first * b.second + a.second};
}
auto e() { return T{1, 0}; }
auto id() { return e(); }
auto mapping(F f, T a) { return op(f, a); }
auto composition(F, F) { return F(1, 0); }

int main() {
  mint::set_mod(MOD);
  std::ios::sync_with_stdio(false);
  std::cin.tie(nullptr);
  u32 n, q;
  std::cin >> n >> q;
  vec<T> a(n);
  for (auto& x : a) std::cin >> x.first >> x.second;
  tifa_libs::ds::segtree<T, op, e, F, mapping, composition, id> seg(a);
  for (u32 i = 0, opt; i < q; ++i) {
    std::cin >> opt;
    if (opt == 0) {
      u32 x;
      Ty y, z;
      std::cin >> x >> y >> z;
      seg.set(x, T{y, z});
    } else {
      u32 x, y;
      Ty z;
      std::cin >> x >> y >> z;
      auto ret = seg.query(x, y - 1);
      std::cout << ret.first * z + ret.second << '\n';
    }
  }
  return 0;
}
#line 1 "src/test_cpverifier/library-checker/point_set_range_composite.d31.test.cpp"
#define AUTO_GENERATED
#define PROBLEM "https://judge.yosupo.jp/problem/point_set_range_composite"

#line 1 "src/code/ds/segtree.hpp"



#line 1 "src/code/util/util.hpp"



#include <bits/stdc++.h>

template <class T>
constexpr T abs(T x) { return x < 0 ? -x : x; }

using i8 = int8_t;
using i16 = int16_t;
using i32 = int32_t;
using i64 = int64_t;
using i128 = __int128_t;
using isz = ptrdiff_t;

using u8 = uint8_t;
using u16 = uint16_t;
using u32 = uint32_t;
using u64 = uint64_t;
using u128 = __uint128_t;
using usz = size_t;

using f32 = float;
using f64 = double;
using f128 = long double;

template <class T>
using ptt = std::pair<T, T>;
template <class T>
using pt3 = std::tuple<T, T, T>;
template <class T>
using pt4 = std::tuple<T, T, T, T>;

template <class T, usz N>
using arr = std::array<T, N>;
template <class T>
using vec = std::vector<T>;
template <class T>
using vvec = vec<vec<T>>;
template <class T>
using v3ec = vec<vvec<T>>;
template <class U, class T>
using vecp = vec<std::pair<U, T>>;
template <class U, class T>
using vvecp = vvec<std::pair<U, T>>;
template <class T>
using vecpt = vec<ptt<T>>;
template <class T>
using vvecpt = vvec<ptt<T>>;

template <class T, class C = std::less<T>>
using pq = std::priority_queue<T, vec<T>, C>;
template <class T>
using pqg = std::priority_queue<T, vec<T>, std::greater<T>>;

using strn = std::string;
using strnv = std::string_view;

using vecu = vec<u32>;
using vvecu = vvec<u32>;
using v3ecu = v3ec<u32>;
using vecu64 = vec<u64>;
using vecb = vec<bool>;
using vvecb = vvec<bool>;

#ifdef ONLINE_JUDGE
#undef assert
#define assert(x) 42
#endif

using namespace std::literals;

constexpr i8 operator""_i8(unsigned long long x) { return (i8)x; }
constexpr i16 operator""_i16(unsigned long long x) { return (i16)x; }
constexpr i32 operator""_i32(unsigned long long x) { return (i32)x; }
constexpr i64 operator""_i64(unsigned long long x) { return (i64)x; }
constexpr isz operator""_iz(unsigned long long x) { return (isz)x; }

constexpr u8 operator""_u8(unsigned long long x) { return (u8)x; }
constexpr u16 operator""_u16(unsigned long long x) { return (u16)x; }
constexpr u32 operator""_u32(unsigned long long x) { return (u32)x; }
constexpr u64 operator""_u64(unsigned long long x) { return (u64)x; }
constexpr usz operator""_uz(unsigned long long x) { return (usz)x; }

inline const auto fn_0 = [](auto&&...) {};
inline const auto fn_is0 = [](auto x) { return x == 0; };


#line 5 "src/code/ds/segtree.hpp"

namespace tifa_libs::ds {
namespace segtree_impl_ {
template <bool use_tag, class T, auto op, auto e, class F, auto mapping, auto composition, auto id>
requires requires(T val, T val_l, T val_r, F tag) {
  { e() } -> std::same_as<T>;
  { op(val_l, val_r) } -> std::same_as<T>;
  { id() } -> std::same_as<F>;
  { mapping(tag, val) } -> std::same_as<T>;
}
class segtree {
  vec<T> t;
  vec<F> sign;
  vecb set_sign;
  u32 n;

 public:
  explicit constexpr segtree(vec<T> const &a) : t(a.size() * 4), sign(), set_sign(), n((u32)a.size()) {
    if constexpr (use_tag) sign.resize(t.size()), set_sign.resize(t.size());
    build(a, 1, 0, n - 1);
  }
  explicit constexpr segtree(u32 N = 0) : t(N * 4), sign(), set_sign(), n(N) {
    if constexpr (use_tag) sign.resize(t.size()), set_sign.resize(t.size());
    if (n) build(vec<T>(n, e()), 1, 0, n - 1);
  }

  constexpr void update(u32 L, u32 R, F f) { update(1, 0, n - 1, L, R, f); }
  constexpr void update(u32 pos, F f) { update(1, 0, n - 1, pos, pos, f); }
  constexpr void set(u32 L, u32 R, T f) { set(1, 0, n - 1, L, R, f); }
  constexpr void set(u32 pos, T f) { set(1, 0, n - 1, pos, pos, f); }
  constexpr T query(u32 L, u32 R) { return query(1, 0, n - 1, L, R); }
  constexpr T query(u32 pos) { return query(1, 0, n - 1, pos, pos); }

 private:
  constexpr void pushup(u32 x) { t[x] = op(t[x * 2], t[x * 2 + 1]); }
  constexpr void all_update(u32 x, F f) {
    t[x] = mapping(f, t[x]);
    if constexpr (use_tag) sign[x] = composition(f, sign[x]);
  }
  constexpr void all_set(u32 x, T f) {
    t[x] = f;
    if constexpr (use_tag) sign[x] = id(), set_sign[x] = 1;
  }
  constexpr void pushdown(u32 x) {
    if constexpr (use_tag) {
      if (set_sign[x]) all_set(x * 2, t[x]), all_set(x * 2 + 1, t[x]), set_sign[x] = 0;
      else all_update(x * 2, sign[x]), all_update(x * 2 + 1, sign[x]), sign[x] = id();
    }
  }
  constexpr void build(vec<T> const &a, u32 x, u32 l, u32 r) {
    if constexpr (use_tag) sign[x] = id();
    if (l == r) return void(t[x] = a[l]);
    u32 mid = l + (r - l) / 2;
    build(a, x * 2, l, mid), build(a, x * 2 + 1, mid + 1, r);
    pushup(x);
  }
  constexpr void update(u32 x, u32 l, u32 r, u32 L, u32 R, F f) {
    assert(R >= l && L <= r);
    if (L <= l && R >= r) return void(all_update(x, f));
    pushdown(x);
    u32 mid = l + (r - l) / 2;
    if (L <= mid) update(x * 2, l, mid, L, R, f);
    if (R > mid) update(x * 2 + 1, mid + 1, r, L, R, f);
    pushup(x);
  }
  constexpr void set(u32 x, u32 l, u32 r, u32 L, u32 R, T f) {
    assert(R >= l && L <= r);
    if (L <= l && R >= r) return void(all_set(x, f));
    pushdown(x);
    u32 mid = l + (r - l) / 2;
    if (L <= mid) set(x * 2, l, mid, L, R, f);
    if (R > mid) set(x * 2 + 1, mid + 1, r, L, R, f);
    pushup(x);
  }
  constexpr T query(u32 x, u32 l, u32 r, u32 L, u32 R) {
    assert(R >= l && L <= r);
    if (L <= l && R >= r) return t[x];
    pushdown(x);
    u32 mid = l + (r - l) / 2;
    T ret = e();
    if (L <= mid) ret = op(ret, query(x * 2, l, mid, L, R));
    if (R > mid) ret = op(ret, query(x * 2 + 1, mid + 1, r, L, R));
    return ret;
  }
};
}  // namespace segtree_impl_

template <class T, auto op, auto e, class F, auto mapping, auto composition, auto id>
requires requires(F tag_l, F tag_r) {
  { composition(tag_l, tag_r) } -> std::same_as<F>;
}
using segtree = segtree_impl_::segtree<true, T, op, e, F, mapping, composition, id>;
template <class T, auto op, auto e>
using segtree_notag = segtree_impl_::segtree<false, T, op, e, T, op, op, e>;

}  // namespace tifa_libs::ds


#line 5 "src/test_cpverifier/library-checker/point_set_range_composite.d31.test.cpp"

constexpr u32 MOD = 998244353;

#line 1 "src/code/math/mint_d31.hpp"



#line 1 "src/code/math/mint.hpp"



#line 1 "src/code/nt/inverse.hpp"



#line 1 "src/code/nt/inv_gcd.hpp"



#line 1 "src/code/math/safe_mod.hpp"



#line 1 "src/code/util/traits.hpp"



#line 5 "src/code/util/traits.hpp"

namespace tifa_libs {

template <class T>
concept iterable_c = requires(T v) {
  { v.begin() } -> std::same_as<typename T::iterator>;
  { v.end() } -> std::same_as<typename T::iterator>;
};

template <class T>
concept container_c = iterable_c<T> && !std::derived_from<T, std::basic_string<typename T::value_type>>;

template <class T>
constexpr bool is_char_v = std::is_same_v<T, char> || std::is_same_v<T, signed char> || std::is_same_v<T, unsigned char>;
template <class T>
concept char_c = is_char_v<T>;

template <class T>
constexpr bool is_s128_v = std::is_same_v<T, __int128_t> || std::is_same_v<T, __int128>;
template <class T>
concept s128_c = is_s128_v<T>;

template <class T>
constexpr bool is_u128_v = std::is_same_v<T, __uint128_t> || std::is_same_v<T, unsigned __int128>;
template <class T>
concept u128_c = is_u128_v<T>;

template <class T>
constexpr bool is_i128_v = is_s128_v<T> || is_u128_v<T>;
template <class T>
concept i128_c = is_u128_v<T>;

template <class T>
constexpr bool is_int_v = std::is_integral_v<T> || is_i128_v<T>;
template <class T>
concept int_c = is_int_v<T>;

template <class T>
constexpr bool is_sint_v = is_s128_v<T> || (is_int_v<T> && std::is_signed_v<T>);
template <class T>
concept sint_c = is_sint_v<T>;

template <class T>
constexpr bool is_uint_v = is_u128_v<T> || (is_int_v<T> && std::is_unsigned_v<T>);
template <class T>
concept uint_c = is_uint_v<T>;

template <class T>
concept mint_c = requires(T x) {
  { x.mod() } -> uint_c;
  { x.val() } -> uint_c;
};

template <class T>
constexpr bool is_arithm_v = std::is_arithmetic_v<T> || is_int_v<T>;
template <class T>
concept arithm_c = is_arithm_v<T>;

template <class T>
struct to_sint : std::make_signed<T> {};
template <>
struct to_sint<u128> {
  using type = u128;
};
template <>
struct to_sint<i128> {
  using type = u128;
};
template <class T>
using to_sint_t = typename to_sint<T>::type;

template <class T>
struct to_uint : std::make_unsigned<T> {};
template <>
struct to_uint<u128> {
  using type = u128;
};
template <>
struct to_uint<i128> {
  using type = u128;
};
template <class T>
using to_uint_t = typename to_uint<T>::type;

}  // namespace tifa_libs


#line 5 "src/code/math/safe_mod.hpp"

namespace tifa_libs::math {

template <sint_c T>
constexpr T safe_mod(T x, to_uint_t<T> mod) { return ((x %= (T)mod) < 0 ? x + (T)mod : x); }

}  // namespace tifa_libs::math


#line 1 "src/code/nt/exgcd.hpp"



#line 5 "src/code/nt/exgcd.hpp"

namespace tifa_libs::math {

// Binary exgcd
template <uint_c U, bool only_x = false>
constexpr auto exgcd_b(U a, U b) {
  using T = to_sint_t<U>;
  if constexpr (only_x) {
    if (!a) return std::make_tuple(b, (T)0);
    if (!b) return std::make_tuple(a, (T)1);
  } else {
    if (!a) return std::make_tuple(b, (T)0, (T) !!b);
    if (!b) return std::make_tuple(a, (T)1, (T)0);
  }
  auto r = std::__countr_zero(a | b);
  a >>= r, b >>= r;
  T x = (T)a, y = (T)b;
  T s = 1, t = 0, u = 0, v = 1;
  while (x) {
    while (!(x & 1)) {
      x /= 2;
      if (!((s | t) & 1)) s /= 2, t /= 2;
      else s = (s + (T)b) / 2, t = (t - (T)a) / 2;
    }
    while (!(y & 1)) {
      y /= 2;
      if (!((u | v) & 1)) u /= 2, v /= 2;
      else u = (u + (T)b) / 2, v = (v - (T)a) / 2;
    }
    if (x >= y) x -= y, s -= u, t -= v;
    else y -= x, u -= s, v -= t;
  }
  if (y > 1) a /= (U)y, b /= (U)y;
  if (a && (U)abs(v) >= a) {
    T _ = v / (T)a;
    v -= _ * (T)a, u += _ * (T)b;
  }
  if (b && (U)abs(u) >= b) {
    T _ = u / (T)b;
    u -= _ * (T)b, v += _ * (T)a;
  }
  if (T u_ = u + (T)b, v_ = v - (T)a; abs(u_) + abs(v_) <= abs(u) + abs(v)) u = u_, v = v_;
  if (T u_ = u - (T)b, v_ = v + (T)a; abs(u_) + abs(v_) <= abs(u) + abs(v)) u = u_, v = v_;
  if constexpr (only_x) return std::make_tuple(U(y << r), u);
  else return std::make_tuple(U(y << r), u, v);
}
// @return then return tuple(g, x[, y]) s.t. g = gcd(a, b), xa + yb = g, |x| + |y| is the minimal (primary) and x <= y (secondarily)
template <sint_c T, bool only_x = false>
constexpr auto exgcd(T a, T b) {
  using U = to_uint_t<T>;
  if (auto [x, y] = std::minmax(a, b); x >= 0 && y <= T(U(-1) >> sizeof(U))) return exgcd_b<U, only_x>((U)a, (U)b);
  if constexpr (only_x) {
    T s = 1, u = 0;
    while (b) {
      T c = a / b;
      std::tie(s, u, a, b) = std::make_tuple(u, s - u * c, b, a - b * c);
    }
    return std::make_tuple((U)a, s);
  } else {
    T s = 1, t = 0, u = 0, v = 1;
    while (b) {
      T c = a / b;
      std::tie(s, t, u, v, a, b) = std::make_tuple(u, v, s - u * c, t - v * c, b, a - b * c);
    }
    return std::make_tuple((U)a, s, t);
  }
}

}  // namespace tifa_libs::math


#line 6 "src/code/nt/inv_gcd.hpp"

namespace tifa_libs::math {

template <uint_c T>
constexpr ptt<T> inv_gcd(T n, T mod) {
  using U = to_sint_t<T>;
  auto [g, x] = exgcd<U, true>(U(n % mod), (U)mod);
  return {g, safe_mod(x, mod)};
}

}  // namespace tifa_libs::math


#line 5 "src/code/nt/inverse.hpp"

namespace tifa_libs::math {

template <uint_c T, uint_c U>
constexpr U inverse(T n, U mod) {
  auto [g, x] = inv_gcd(U(n % mod), mod);
  assert(g == 1);
  return x;
}

}  // namespace tifa_libs::math


#line 6 "src/code/math/mint.hpp"

namespace tifa_libs::math {

template <class D, uint_c Rt>
class mint {
  constexpr D const &d() const { return static_cast<D const &>(*this); }
  constexpr D &d() { return static_cast<D &>(*this); }

 protected:
  Rt v_{};

 public:
  constexpr mint() {}
  template <int_c T>
  constexpr mint(T v) : v_(D::mod_(v)) {}
  constexpr operator D() { return d(); }

  using raw_type = Rt;
  using sraw_type = to_sint_t<Rt>;
  static constexpr raw_type mod() { return D::mod_(); }
  static constexpr sraw_type smod() { return (sraw_type)D::mod_(); }
  constexpr raw_type val() const { return d().val_(); }
  constexpr sraw_type sval() const { return (sraw_type)d().val_(); }
  constexpr raw_type &data() { return d().data_(); }

  template <int_c T>
  explicit constexpr operator T() const { return (T)val(); }
  constexpr mint &operator+=(mint const &r) { return d().adde_(r.d()); }
  constexpr mint &operator-=(mint const &r) { return d().sube_(r.d()); }
  constexpr mint &operator*=(mint const &r) { return d().mule_(r.d()); }
  constexpr mint &operator/=(mint const &r) { return *this = *this * r.inv(); }
  constexpr mint const &operator+() const { return *this; }
  constexpr mint operator-() const { return d().neg_(); }
  constexpr mint inv() const { return inverse(val(), mod()); }
  friend constexpr mint operator+(mint l, mint const &r) { return l += r; }
  friend constexpr mint operator-(mint l, mint const &r) { return l -= r; }
  friend constexpr mint operator*(mint l, mint const &r) { return l *= r; }
  friend constexpr mint operator/(mint l, mint const &r) { return l /= r; }
  friend constexpr bool operator==(mint const &l, mint const &r) { return l.val() == r.val(); }
  friend constexpr auto operator<=>(mint const &l, mint const &r) { return l.sval() - r.sval(); }
  friend std::istream &operator>>(std::istream &is, mint &x) {
    i64 _;
    is >> _;
    x = mint(_);
    return is;
  }
  friend std::ostream &operator<<(std::ostream &os, mint const &x) { return os << x.val(); }
  friend constexpr mint abs(mint const &x) { return x.val(); }
};

}  // namespace tifa_libs::math


#line 5 "src/code/math/mint_d31.hpp"

namespace tifa_libs::math {

template <int ID>
class mint_d31 : public mint<mint_d31<ID>, u32> {
  using base = mint<mint_d31<ID>, u32>;
  friend base;

  static inline u32 R, R2, MOD, MOD_ODD, OFFSET, MASK;

  static constexpr u32 norm(i32 x) { return u32(x + (-(x < 0) & (i32)MOD)); }
  static constexpr u32 redc(u64 x) {
    u32 t = u32((x + u64((u32)x * R) * MOD_ODD) >> 32);
    return t - (MOD_ODD & -((MOD_ODD - 1 - t) >> 31));
  }
  static constexpr u32 tsf(u32 x) { return redc(u64(x % MOD_ODD) * R2) << OFFSET | (x & MASK); }

 public:
  static constexpr bool FIXED_MOD = false;
  static constexpr void set_mod(u32 m) {
    assert(!(m == 1 || m >> 31));
    for (MOD = MOD_ODD = m, OFFSET = 0; (MOD_ODD & 1) == 0; ++OFFSET, MOD_ODD /= 2);
    MASK = (1 << OFFSET) - 1;
    u32 t = 2, iv = MOD_ODD * (t - MOD_ODD * MOD_ODD);
    iv *= t - MOD_ODD * iv, iv *= t - MOD_ODD * iv;
    R = iv * (MOD_ODD * iv - t);
    R2 = u32(-u64(MOD_ODD) % MOD_ODD);
  }

  constexpr mint_d31() {}
  template <int_c T>
  constexpr mint_d31(T v) { this->v_ = mod_(v); }

 private:
  using raw_t = typename base::raw_type;
  using sraw_t = typename base::sraw_type;
  template <int_c T>
  static constexpr raw_t mod_(T v) { return tsf(norm(i32(v % (std::conditional_t<sint_c<T>, i32, u32>)mod_()))); }
  static constexpr raw_t mod_() { return MOD; }
  constexpr raw_t val_() const {
    raw_t h = redc(this->v_ >> OFFSET);
    return ((h - this->v_) * R & MASK) * MOD_ODD + h;
  }
  constexpr raw_t &data_() { return this->v_; }

  constexpr mint_d31 neg_() const {
    mint_d31 res;
    raw_t h = this->v_ >> OFFSET;
    res.v_ = (((MOD_ODD & -(h != 0)) - h) << OFFSET) | (-this->v_ & MASK);
    return res;
  }
  constexpr mint_d31 &adde_(mint_d31 const &r) {
    raw_t h = (this->v_ >> OFFSET) + (r.v_ >> OFFSET) - MOD_ODD;
    this->v_ = ((h + (MOD_ODD & -(h >> 31))) << OFFSET) | ((this->v_ + r.v_) & MASK);
    return *this;
  }
  constexpr mint_d31 &sube_(mint_d31 const &r) {
    raw_t h = (this->v_ >> OFFSET) - (r.v_ >> OFFSET);
    this->v_ = ((h + (MOD_ODD & -(h >> 31))) << OFFSET) | ((this->v_ - r.v_) & MASK);
    return *this;
  }
  constexpr mint_d31 &mule_(mint_d31 const &r) {
    this->v_ = (redc((u64)(this->v_ >> OFFSET) * (r.v_ >> OFFSET)) << OFFSET) | ((this->v_ * r.v_) & MASK);
    return *this;
  }
};

}  // namespace tifa_libs::math


#line 9 "src/test_cpverifier/library-checker/point_set_range_composite.d31.test.cpp"

using mint = tifa_libs::math::mint_d31<-1>;
using Ty = mint;
using T = std::pair<Ty, Ty>;
using F = T;

auto op(T a, T b) {  // b(a(x))
  swap(a, b);
  return T{a.first * b.first, a.first * b.second + a.second};
}
auto e() { return T{1, 0}; }
auto id() { return e(); }
auto mapping(F f, T a) { return op(f, a); }
auto composition(F, F) { return F(1, 0); }

int main() {
  mint::set_mod(MOD);
  std::ios::sync_with_stdio(false);
  std::cin.tie(nullptr);
  u32 n, q;
  std::cin >> n >> q;
  vec<T> a(n);
  for (auto& x : a) std::cin >> x.first >> x.second;
  tifa_libs::ds::segtree<T, op, e, F, mapping, composition, id> seg(a);
  for (u32 i = 0, opt; i < q; ++i) {
    std::cin >> opt;
    if (opt == 0) {
      u32 x;
      Ty y, z;
      std::cin >> x >> y >> z;
      seg.set(x, T{y, z});
    } else {
      u32 x, y;
      Ty z;
      std::cin >> x >> y >> z;
      auto ret = seg.query(x, y - 1);
      std::cout << ret.first * z + ret.second << '\n';
    }
  }
  return 0;
}

Test cases

Env Name Status Elapsed Memory
g++-12 example_00 :heavy_check_mark: AC 8 ms 4 MB
g++-12 max_random_00 :heavy_check_mark: AC 1080 ms 39 MB
g++-12 max_random_01 :heavy_check_mark: AC 1074 ms 39 MB
g++-12 max_random_02 :heavy_check_mark: AC 1084 ms 39 MB
g++-12 max_random_03 :heavy_check_mark: AC 1070 ms 39 MB
g++-12 max_random_04 :heavy_check_mark: AC 1087 ms 39 MB
g++-12 random_00 :heavy_check_mark: AC 873 ms 31 MB
g++-12 random_01 :heavy_check_mark: AC 894 ms 36 MB
g++-12 random_02 :heavy_check_mark: AC 548 ms 7 MB
g++-12 random_03 :heavy_check_mark: AC 130 ms 34 MB
g++-12 random_04 :heavy_check_mark: AC 234 ms 23 MB
g++-12 small_00 :heavy_check_mark: AC 8 ms 4 MB
g++-12 small_01 :heavy_check_mark: AC 8 ms 4 MB
g++-12 small_02 :heavy_check_mark: AC 7 ms 4 MB
g++-12 small_03 :heavy_check_mark: AC 8 ms 4 MB
g++-12 small_04 :heavy_check_mark: AC 7 ms 4 MB
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