Tifa's CP Library

:warning: basis_r (src/code/math/basis_r.hpp)

Depends on

Code

#ifndef TIFALIBS_MATH_BASIS_R
#define TIFALIBS_MATH_BASIS_R

#include "../util/fp_comp.hpp"

namespace tifa_libs::math {

template <std::floating_point FP>
struct basisR {
  vvec<FP> basis;
  const u32 vec_len;

  CEXPE basisR(u32 vec_len) : vec_len(vec_len) {}

  CEXP bool insert(vec<FP> x) {
    x.resize(vec_len);
    bool status = 0;
    for (u32 i = (u32)basis.size() - 1; ~i; --i) {
      if (is_zero(x[i])) continue;
      if (!is_zero(basis[i][i])) {
        const FP _ = x[i] / basis[i][i];
        x[i] = 0;
        flt_ (u32, j, 0, i) x[j] -= basis[i][j] * _;
      } else {
        flt_ (u32, j, 0, i)
          if (!is_zero(x[j]) && !is_zero(basis[j][j])) {
            const FP _ = x[j] / basis[j][j];
            x[j] = 0;
            flt_ (u32, k, 0, j) x[k] -= basis[j][k] * _;
          }
        flt_ (u32, j, i + 1, (u32)basis.size())
          if (!is_zero(basis[j][i]) && !is_zero(x[i])) {
            const FP _ = basis[j][i] / x[i];
            basis[j][i] = 0;
            flt_ (u32, k, 0, i) basis[j][k] -= x[k] * _;
          }
        basis[i] = x, status = 1;
        break;
      }
    }
    return status;
  }
  CEXP bool test(vec<FP> x) const {
    for (u32 i = (u32)basis.size() - 1; ~i; --i) {
      if (is_zero(x[i])) continue;
      if (!is_zero(basis[i][i])) {
        const FP _ = x[i] / basis[i][i];
        x[i] = 0;
        flt_ (u32, j, 0, i) x[j] -= basis[i][j] * _;
      } else return 0;
    }
    return 1;
  }
  CEXP u32 rank() const {
    u32 res = 0;
    flt_ (u32, i, 0, (u32)basis.size()) res += !is_zero(basis[i][i]);
    return res;
  }
  // @return std::nullopt if x is linear independent with current basis, else
  // return the solution
  CEXP std::optional<vec<FP>> coord(vec<FP> x) {
    vec<FP> res(vec_len);
    for (u32 i = basis.size() - 1; ~i; --i)
      if (!is_zero(x[i])) {
        if (is_zero(basis[i][i])) return {};
        const FP _ = x[i] / basis[i][i];
        res[i] = _, x[i] = 0;
        fle_ (u32, j, 0, i) x[j] -= basis[i][j] * _;
      }
    return res;
  }
};

}  // namespace tifa_libs::math

#endif
#line 1 "src/code/math/basis_r.hpp"



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

namespace tifa_libs {

template <sint_c T>
CEXP int sgn(T x) { return (!!x) | (x >> (sizeof(T) * 8 - 1)); }
template <uint_c T>
CEXP int sgn(T x) { return !!x; }
template <std::floating_point FP>
CEXP int sgn(FP x) { return (x > eps_v<FP>)-(x < -eps_v<FP>); }

template <class FP>
CEXP bool is_neg(FP x) { return sgn(x) < 0; }
template <class FP>
CEXP bool is_zero(FP x) { return !sgn(x); }
template <class FP>
CEXP bool is_pos(FP x) { return sgn(x) > 0; }

template <int_c T>
CEXP int comp(T l, T r) { return sgn(l - r); }
template <std::floating_point FP>
CEXP int comp(FP l, FP r) { return sgn((l - r) / max({abs(l), abs(r), FP(1)})); }

template <class FP>
CEXP bool is_lt(FP l, FP r) { return comp(l, r) < 0; }
template <class FP>
CEXP bool is_eq(FP l, FP r) { return !comp(l, r); }
template <class FP>
CEXP bool is_gt(FP l, FP r) { return comp(l, r) > 0; }

}  // namespace tifa_libs


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

namespace tifa_libs::math {

template <std::floating_point FP>
struct basisR {
  vvec<FP> basis;
  const u32 vec_len;

  CEXPE basisR(u32 vec_len) : vec_len(vec_len) {}

  CEXP bool insert(vec<FP> x) {
    x.resize(vec_len);
    bool status = 0;
    for (u32 i = (u32)basis.size() - 1; ~i; --i) {
      if (is_zero(x[i])) continue;
      if (!is_zero(basis[i][i])) {
        const FP _ = x[i] / basis[i][i];
        x[i] = 0;
        flt_ (u32, j, 0, i) x[j] -= basis[i][j] * _;
      } else {
        flt_ (u32, j, 0, i)
          if (!is_zero(x[j]) && !is_zero(basis[j][j])) {
            const FP _ = x[j] / basis[j][j];
            x[j] = 0;
            flt_ (u32, k, 0, j) x[k] -= basis[j][k] * _;
          }
        flt_ (u32, j, i + 1, (u32)basis.size())
          if (!is_zero(basis[j][i]) && !is_zero(x[i])) {
            const FP _ = basis[j][i] / x[i];
            basis[j][i] = 0;
            flt_ (u32, k, 0, i) basis[j][k] -= x[k] * _;
          }
        basis[i] = x, status = 1;
        break;
      }
    }
    return status;
  }
  CEXP bool test(vec<FP> x) const {
    for (u32 i = (u32)basis.size() - 1; ~i; --i) {
      if (is_zero(x[i])) continue;
      if (!is_zero(basis[i][i])) {
        const FP _ = x[i] / basis[i][i];
        x[i] = 0;
        flt_ (u32, j, 0, i) x[j] -= basis[i][j] * _;
      } else return 0;
    }
    return 1;
  }
  CEXP u32 rank() const {
    u32 res = 0;
    flt_ (u32, i, 0, (u32)basis.size()) res += !is_zero(basis[i][i]);
    return res;
  }
  // @return std::nullopt if x is linear independent with current basis, else
  // return the solution
  CEXP std::optional<vec<FP>> coord(vec<FP> x) {
    vec<FP> res(vec_len);
    for (u32 i = basis.size() - 1; ~i; --i)
      if (!is_zero(x[i])) {
        if (is_zero(basis[i][i])) return {};
        const FP _ = x[i] / basis[i][i];
        res[i] = _, x[i] = 0;
        fle_ (u32, j, 0, i) x[j] -= basis[i][j] * _;
      }
    return res;
  }
};

}  // namespace tifa_libs::math


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