Tifa's CP Library

:heavy_check_mark: sbt (src/code/nt/sbt.hpp)

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#ifndef TIFALIBS_MATH_SBT
#define TIFALIBS_MATH_SBT

#include "../nt/gcd.hpp"

namespace tifa_libs::math {

// x / y (x > 0, y > 0). default 1 / 1
template <std::signed_integral T>
class SBT {
  T lx, ly, x, y, rx, ry;
  vec<T> seq;

 public:
  CEXPE SBT() : lx(0), ly(1), x(1), y(1), rx(1), ry(0) {}
  CEXPE SBT(spn<T> seq_) : SBT() {
    for (auto d : seq_) {
      assert(d != 0);
      if (d > 0) movr(d);
      if (d < 0) movl(d);
    }
  }
  CEXP SBT(T x_, T y_) : SBT() {
    assert(x_ > 0 && y_ > 0);
    if (T g = gcd(x_, y_); g > 1) x_ /= g, y_ /= g;
    while (min(x_, y_))
      if (x_ > y_) {
        const T _ = x_ / y_;
        movr(_ - !(x_ -= _ * y_));
      } else {
        const T _ = y_ / x_;
        movl(_ - !(y_ -= _ * x_));
      }
  }

  friend CEXP auto operator<=>(SBT CR l, SBT CR r) { return l.x * r.y - r.x * l.y; }
  friend CEXP bool operator==(SBT CR l, SBT CR r) { return l.x == r.x && l.y == r.y; }
  CEXP ptt<T> current() const { return {x, y}; }
  CEXP ptt<T> lbound() const { return {lx, ly}; }
  CEXP ptt<T> rbound() const { return {rx, ry}; }
  // path from (1, 1) to @current(). rchild be positive and vice versa
  CEXP vec<T> path() const { return seq; }
  CEXP T dep() const {
    T res = 0;
    for (auto &&s : seq) res += abs(s);
    return res;
  }
  // move towards lchild with @d steps
  CEXP void movl(T d = 1) {
    if (d <= 0) return;
    if (seq.empty() || seq.back() > 0) seq.push_back(0);
    seq.back() -= d, rx += lx * d, ry += ly * d, x = rx + lx, y = ry + ly;
  }
  // move towards rchild with @d steps
  CEXP void movr(T d = 1) {
    if (d <= 0) return;
    if (seq.empty() || seq.back() < 0) seq.push_back(0);
    seq.back() += d, lx += rx * d, ly += ry * d, x = rx + lx, y = ry + ly;
  }
  // move towards fa with @d steps
  // @return true if succeed, or false if falied
  CEXP bool movf(T d = 1) {
    if (d <= 0) return true;
    while (d) {
      if (seq.empty()) return false;
      T _ = min(d, abs(seq.back()));
      if (seq.back() > 0) x -= rx * _, y -= ry * _, lx = x - rx, ly = y - ry, seq.back() -= _;
      else x -= lx * _, y -= ly * _, rx = x - lx, ry = y - ly, seq.back() += _;
      if (d -= _; !seq.back()) seq.pop_back();
      if (!_) break;
    }
    return true;
  }
  static CEXP SBT lca(SBT CR l, SBT CR r) {
    SBT ret;
    for (u32 i = 0; i < min((u32)l.seq.size(), (u32)r.seq.size()); ++i) {
      T val1 = l.seq[i], val2 = r.seq[i];
      if ((val1 < 0) != (val2 < 0)) break;
      if (val1 < 0) ret.movl(min(-val1, -val2));
      if (val1 > 0) ret.movr(min(val1, val2));
      if (val1 != val2) break;
    }
    return ret;
  }
};

}  // namespace tifa_libs::math

#endif
#line 1 "src/code/nt/sbt.hpp"



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



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



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



#include <bits/extc++.h>

#define CEXP constexpr
#define CEXPE constexpr explicit
#define TPN typename
#define CR const&

#define cT_(...) std::conditional_t<sizeof(__VA_ARGS__) <= sizeof(size_t), __VA_ARGS__, __VA_ARGS__ CR>
#define fle_(T, i, l, r, ...) for (T i = (l), i##e = (r)__VA_OPT__(, ) __VA_ARGS__; i <= i##e; ++i)
#define flt_(T, i, l, r, ...) for (T i = (l), i##e = (r)__VA_OPT__(, ) __VA_ARGS__; i < i##e; ++i)

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

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

// clang-format off
template <class T, T v> using ic = std::integral_constant<T, v>;
template <class T> using ptt = std::pair<T, T>;
template <class T> struct edge_t {
  T w; u32 u, v;
  CEXP auto operator<=>(edge_t CR) const = default;
};
template <class T> struct pt3 {
  T _0, _1, _2;
  CEXP auto operator<=>(pt3 CR) const = default;
};
template <class T> struct pt4 {
  T _0, _1, _2, _3;
  CEXP auto operator<=>(pt4 CR) const = default;
};
template <class E> using itl = std::initializer_list<E>;
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 T> using vecpt = vec<ptt<T>>;
template <class T> using vvecpt = vvec<ptt<T>>;
template <class T> using ptvec = ptt<vec<T>>;
template <class T> using ptvvec = ptt<vvec<T>>;

template <class T, usz ext = std::dynamic_extent> using spn = std::span<T const, ext>;
template <class T, usz N> using arr = std::array<T, N>;
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, 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>>;
// clang-format on

#define mk_(V, A, T) using V##A = V<T>;
#define mk(A, T) mk_(edge_t, A, T) mk_(ptt, A, T) mk_(pt3, A, T) mk_(pt4, A, T) mk_(vec, A, T) mk_(vvec, A, T) mk_(v3ec, A, T) mk_(vecpt, A, T) mk_(vvecpt, A, T) mk_(ptvec, A, T) mk_(ptvvec, A, T) mk_(spn, A, T) mk_(itl, A, T)
mk(b, bool) mk(i, i32) mk(u, u32) mk(ii, i64) mk(uu, u64);
#undef mk
#undef mk_

using namespace std::literals;
CEXP i8 operator""_i8(unsigned long long x) { return (i8)x; }
CEXP i16 operator""_i16(unsigned long long x) { return (i16)x; }
CEXP i32 operator""_i32(unsigned long long x) { return (i32)x; }
CEXP i64 operator""_i64(unsigned long long x) { return (i64)x; }
CEXP isz operator""_iz(unsigned long long x) { return (isz)x; }
CEXP u8 operator""_u8(unsigned long long x) { return (u8)x; }
CEXP u16 operator""_u16(unsigned long long x) { return (u16)x; }
CEXP u32 operator""_u32(unsigned long long x) { return (u32)x; }
CEXP u64 operator""_u64(unsigned long long x) { return (u64)x; }
CEXP usz operator""_uz(unsigned long long x) { return (usz)x; }

using std::numbers::pi_v;
template <std::floating_point FP>
inline FP eps_v = std::sqrt(std::numeric_limits<FP>::epsilon());
template <std::floating_point FP>
CEXP void set_eps(FP v) { eps_v<FP> = v; }

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

namespace tifa_libs {
using std::min, std::max, std::swap;
template <class T>
constexpr T abs(T x) { return x < 0 ? -x : x; }
}  // namespace tifa_libs


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

namespace tifa_libs {

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

template <class T>
concept container_c = iterable_c<T> && !std::same_as<std::remove_cvref_t<T>, strn> && !std::same_as<std::remove_cvref_t<T>, strnv>;

template <class T>
CEXP 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>
CEXP 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>
CEXP 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>
CEXP 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>
CEXP 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>
CEXP 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>
CEXP 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>
concept dft_c = requires(T x, vec<TPN T::data_t> v, u32 n) {
  { x.size() } -> std::same_as<u32>;
  x.bzr(n);
  x.dif(v, n);
  x.dit(v, n);
};

template <class T>
concept ntt_c = dft_c<T> && requires(T x) {
  T::max_size;
  T::G;
};

template <class T>
CEXP 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 = TPN 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 = TPN to_uint<T>::type;

}  // namespace tifa_libs


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

namespace tifa_libs::math {

namespace gcd_impl_ {
template <uint_c T, uint_c U>
CEXP std::common_type_t<T, U> gcd__(T u, U v) {
  using W = std::common_type_t<T, U>;
  if (!u || !v) return u ^ v;
  const auto k = std::__countr_zero(u | v);
  u >>= k, v >>= k;
  do {
    if (W _ = v >> std::__countr_zero(v); u > _) v = u - _, u = _;
    else v = _ - u;
  } while (v);
  return u << k;
}
}  // namespace gcd_impl_

template <int_c T, int_c U>
CEXP auto gcd(T a, U b) { return gcd_impl_::gcd__((to_uint_t<T>)abs(a), (to_uint_t<U>)abs(b)); }

}  // namespace tifa_libs::math


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

namespace tifa_libs::math {

// x / y (x > 0, y > 0). default 1 / 1
template <std::signed_integral T>
class SBT {
  T lx, ly, x, y, rx, ry;
  vec<T> seq;

 public:
  CEXPE SBT() : lx(0), ly(1), x(1), y(1), rx(1), ry(0) {}
  CEXPE SBT(spn<T> seq_) : SBT() {
    for (auto d : seq_) {
      assert(d != 0);
      if (d > 0) movr(d);
      if (d < 0) movl(d);
    }
  }
  CEXP SBT(T x_, T y_) : SBT() {
    assert(x_ > 0 && y_ > 0);
    if (T g = gcd(x_, y_); g > 1) x_ /= g, y_ /= g;
    while (min(x_, y_))
      if (x_ > y_) {
        const T _ = x_ / y_;
        movr(_ - !(x_ -= _ * y_));
      } else {
        const T _ = y_ / x_;
        movl(_ - !(y_ -= _ * x_));
      }
  }

  friend CEXP auto operator<=>(SBT CR l, SBT CR r) { return l.x * r.y - r.x * l.y; }
  friend CEXP bool operator==(SBT CR l, SBT CR r) { return l.x == r.x && l.y == r.y; }
  CEXP ptt<T> current() const { return {x, y}; }
  CEXP ptt<T> lbound() const { return {lx, ly}; }
  CEXP ptt<T> rbound() const { return {rx, ry}; }
  // path from (1, 1) to @current(). rchild be positive and vice versa
  CEXP vec<T> path() const { return seq; }
  CEXP T dep() const {
    T res = 0;
    for (auto &&s : seq) res += abs(s);
    return res;
  }
  // move towards lchild with @d steps
  CEXP void movl(T d = 1) {
    if (d <= 0) return;
    if (seq.empty() || seq.back() > 0) seq.push_back(0);
    seq.back() -= d, rx += lx * d, ry += ly * d, x = rx + lx, y = ry + ly;
  }
  // move towards rchild with @d steps
  CEXP void movr(T d = 1) {
    if (d <= 0) return;
    if (seq.empty() || seq.back() < 0) seq.push_back(0);
    seq.back() += d, lx += rx * d, ly += ry * d, x = rx + lx, y = ry + ly;
  }
  // move towards fa with @d steps
  // @return true if succeed, or false if falied
  CEXP bool movf(T d = 1) {
    if (d <= 0) return true;
    while (d) {
      if (seq.empty()) return false;
      T _ = min(d, abs(seq.back()));
      if (seq.back() > 0) x -= rx * _, y -= ry * _, lx = x - rx, ly = y - ry, seq.back() -= _;
      else x -= lx * _, y -= ly * _, rx = x - lx, ry = y - ly, seq.back() += _;
      if (d -= _; !seq.back()) seq.pop_back();
      if (!_) break;
    }
    return true;
  }
  static CEXP SBT lca(SBT CR l, SBT CR r) {
    SBT ret;
    for (u32 i = 0; i < min((u32)l.seq.size(), (u32)r.seq.size()); ++i) {
      T val1 = l.seq[i], val2 = r.seq[i];
      if ((val1 < 0) != (val2 < 0)) break;
      if (val1 < 0) ret.movl(min(-val1, -val2));
      if (val1 > 0) ret.movr(min(val1, val2));
      if (val1 != val2) break;
    }
    return ret;
  }
};

}  // namespace tifa_libs::math


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