Tifa's CP Library

:heavy_check_mark: is_on_s (src/code/geo2d/is_on_s.hpp)

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#ifndef TIFALIBS_GEO2D_IS_ON_S
#define TIFALIBS_GEO2D_IS_ON_S

#include "is_on_same_l.hpp"
#include "line.hpp"
#include "point_is_in_middle.hpp"

namespace tifa_libs::geo {

//! containing endpoints
template <class FP>
CEXP bool is_on_S(line<FP> CR s, point<FP> CR p) { return is_on_same_L(s.l, s.r, p) && is_in_middle(s.l, p, s.r); }
//! NOT containing endpoints
template <class FP>
CEXP bool is_on_S_strict(line<FP> CR s, point<FP> CR p) { return s.toleft(p) == 0 && sgn((p - s.l) * (s.l - s.r)) * sgn((p - s.r) * (s.l - s.r)) < 0; }

}  // namespace tifa_libs::geo

#endif
#line 1 "src/code/geo2d/is_on_s.hpp"



#line 1 "src/code/geo2d/is_on_same_l.hpp"



#line 1 "src/code/geo2d/cross.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/stdc++.h>

#define CEXP constexpr
#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;

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 E>
using itl = std::initializer_list<E>;
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>
using ptvec = ptt<vec<T>>;
template <class T>
using ptvvec = ptt<vvec<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;
template <class T, usz ext = std::dynamic_extent>
using spn = std::span<T const, ext>;

#define mk_(V, A, T) using V##A = V<T>;
#define mk(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; }

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

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; }
using std::numbers::pi_v;

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::derived_from<T, std::basic_string<TPN T::value_type>> && !std::derived_from<T, std::basic_string_view<TPN T::value_type>>;

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/geo2d/cross.hpp"

namespace tifa_libs::geo {

template <class P>
CEXP auto cross(P CR o, P CR a, P CR b) { return (a - o) ^ (b - o); }
template <class P>
requires std::floating_point<typename P::FP_t>
CEXP auto cross_unit(P CR o, P CR a, P CR b) { return (a - o).do_unit() ^ (b - o).do_unit(); }
template <class P>
requires std::floating_point<typename P::FP_t>
CEXP int sgn_cross(P CR o, P CR a, P CR b) { return sgn(cross_unit(o, a, b)); }
template <class P>
CEXP int sgn_cross(P CR o, P CR a, P CR b) { return sgn(cross(o, a, b)); }

}  // namespace tifa_libs::geo


#line 1 "src/code/geo2d/point.hpp"



#line 5 "src/code/geo2d/point.hpp"

namespace tifa_libs::geo {

template <class FP>
struct point {
  using FP_t = FP;
  
  FP x, y;
  explicit CEXP point(FP x = FP{}, FP y = FP{}) : x(x), y(y) {}

  friend std::istream &operator>>(std::istream &is, point &p) { return is >> p.x >> p.y; }
  friend std::ostream &operator<<(std::ostream &os, point CR p) { return os << p.x << ' ' << p.y; }
  // s * r + t * (1 - r)
  template <std::floating_point T>
  friend CEXP point lerp(point CR s, point CR t, T r) { return s * r + t * (1 - r); }
  friend CEXP point mid_point(point CR s, point CR t) { return lerp(s, t, .5); }
  template <arithm_c T>
  CEXP point &operator+=(T n) { return this->x += n, this->y += n, *this; }
  template <arithm_c T>
  CEXP point &operator-=(T n) { return this->x -= n, this->y -= n, *this; }
  template <arithm_c T>
  CEXP point &operator*=(T n) { return this->x *= n, this->y *= n, *this; }
  template <arithm_c T>
  CEXP point &operator/=(T n) { return this->x /= n, this->y /= n, *this; }
  template <arithm_c T>
  friend CEXP point operator+(point x, T n) { return x += n; }
  template <arithm_c T>
  friend CEXP point operator+(T n, point x) { return x += n; }
  template <arithm_c T>
  friend CEXP point operator-(point x, T n) { return x -= n; }
  template <arithm_c T>
  friend CEXP point operator-(T n, point x) { return x -= n; }
  template <arithm_c T>
  friend CEXP point operator*(point x, T n) { return x *= n; }
  template <arithm_c T>
  friend CEXP point operator*(T n, point x) { return x *= n; }
  template <arithm_c T>
  friend CEXP point operator/(point x, T n) { return x /= n; }
  template <arithm_c T>
  friend CEXP point operator/(T n, point x) { return x /= n; }
  CEXP point &operator+=(point CR p) { return this->x += p.x, this->y += p.y, *this; }
  CEXP point &operator-=(point CR p) { return this->x -= p.x, this->y -= p.y, *this; }
  CEXP point operator+(point CR p) const { return point(*this) += p; }
  CEXP point operator-(point CR p) const { return point(*this) -= p; }
  CEXP point operator-() const { return point{-x, -y}; }
  CEXP auto operator<=>(point CR p) const {
    if (auto CR c = comp(x, p.x); c) return c;
    return comp(y, p.y);
  }
  CEXP bool operator==(point CR p) const { return is_eq(x, p.x) && is_eq(y, p.y); }
  CEXP FP operator*(point CR p) const { return x * p.x + y * p.y; }
  CEXP FP operator^(point CR p) const { return x * p.y - y * p.x; }
  CEXP FP arg() const {
    static_assert(std::is_floating_point_v<FP>);
    return std::atan2(y, x);
  }
  CEXP FP arg_2pi() const {
    FP res = arg();
    return is_neg(res) ? res + 2 * pi_v<FP> : res;
  }
  CEXP FP norm2() const { return x * x + y * y; }
  CEXP FP norm() const {
    static_assert(std::is_floating_point_v<FP>);
    return std::hypot(x, y);
  }
  CEXP point &do_unit() {
    static_assert(std::is_floating_point_v<FP>);
    return *this /= norm();
  }
  static CEXP u32 QUAD__[9] = {6, 7, 8, 5, 0, 1, 4, 3, 2};
  // 4 3 2
  // 5 0 1
  // 6 7 8
  CEXP u32 quad() const { return QUAD__[(sgn(y) + 1) * 3 + sgn(x) + 1]; }
  CEXP int toleft(point CR p) const { return sgn(*this ^ p); }
  CEXP point &do_rot(FP theta) {
    const FP x0 = x, y0 = y, ct = std::cos(theta), st = std::sin(theta);
    return x = x0 * ct - y0 * st, y = x0 * st + y0 * ct, *this;
  }
  friend CEXP point rot(point p, FP theta) { return p.do_rot(theta); }
  CEXP point &do_rot90() {
    const FP _ = x;
    return x = -y, y = _, *this;
  }
  friend CEXP point rot90(point p) { return p.do_rot90(); }
  CEXP point &do_rot270() {
    const FP _ = y;
    return y = -x, x = _, *this;
  }
  friend CEXP point rot270(point p) { return p.do_rot270(); }
};

}  // namespace tifa_libs::geo


#line 6 "src/code/geo2d/is_on_same_l.hpp"

namespace tifa_libs::geo {

template <class FP>
CEXP bool is_on_same_L(point<FP> CR p1, point<FP> CR p2, point<FP> CR p3) { return is_zero(cross(p1, p2, p3)); }

}  // namespace tifa_libs::geo


#line 1 "src/code/geo2d/line.hpp"



#line 6 "src/code/geo2d/line.hpp"

namespace tifa_libs::geo {

template <class FP>
struct line {
  point<FP> l, r;

  CEXP line() {}
  CEXP line(point<FP> CR s, point<FP> CR t) : l(s), r(t) {}
  CEXP line(point<FP> CR s, FP angle_x) : l(s), r(s + is_eq(angle_x, pi_v<FP> / 2) ? point<FP>{0, 1} : point<FP>{1, std::tan(angle_x)}) { assert(angle_x > 0 && angle_x < pi_v<FP>); }
  // ax + by + c = 0
  CEXP line(FP a, FP b, FP c) {
    if (is_zero(a)) l = {0, -c / b}, r = {1, -c / b};
    else if (is_zero(b)) l = {-c / a, 0}, r = {-c / a, 1};
    else l = {0, -c / b}, r = {1, -(c + a) / b};
  }
  CEXP line(FP s_x, FP s_y, FP t_x, FP t_y) : l(s_x, s_y), r(t_x, t_y) {}

  friend std::istream& operator>>(std::istream& is, line& l) { return is >> l.l >> l.r; }
  friend std::ostream& operator<<(std::ostream& os, line CR l) { return os << l.l << ' ' << l.r; }
  CEXP point<FP> direction() const { return r - l; }
  CEXP bool is_parallel(line CR r) const { return is_zero(direction() ^ r.direction()); }
  friend CEXP bool is_parallel(line CR l, line CR r) { return l.is_parallel(r); }
  CEXP bool is_same_dir(line CR r) const { return is_parallel(r) && is_pos(direction() * r.direction()); }
  friend CEXP bool is_same_dir(line CR l, line CR r) { return l.is_same_dir(r); }
  friend CEXP bool operator==(line CR l, line CR r) { return l.l == r.l && l.r == r.r; }
  friend CEXP auto operator<=>(line CR l, line CR r) {
    if (l == r) return 0;
    if (l.is_same_dir(r)) return r.is_include_strict(l.l) ? -1 : 1;
    if (const auto vl = l.direction(), vr = r.direction(); vl.quad() != vr.quad()) return (i32)vl.quad() - (i32)vr.quad();
    else return -sgn(vl ^ vr);
  }
  CEXP int toleft(point<FP> CR p) const { return sgn_cross(l, r, p); }
  // half plane
  CEXP bool is_include_strict(point<FP> CR p) const { return toleft(p) > 0; }
  // half plane
  CEXP bool is_include(point<FP> CR p) const { return toleft(p) >= 0; }
  // translate @dist along the direction of half plane
  CEXP line& do_push(FP dist) {
    const point delta = direction().do_rot90().do_unit() * dist;
    return l += delta, r += delta, *this;
  }
};

}  // namespace tifa_libs::geo


#line 1 "src/code/geo2d/point_is_in_middle.hpp"



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



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

namespace tifa_libs {

//! containing endpoints
template <arithm_c FP>
CEXP bool is_in_middle(FP l, FP mid, FP r) { return is_eq(l, mid) || is_eq(r, mid) || ((l < mid) ^ (r < mid)); }

}  // namespace tifa_libs


#line 6 "src/code/geo2d/point_is_in_middle.hpp"

namespace tifa_libs::geo {

//! containing endpoints
template <class FP>
CEXP bool is_in_middle(point<FP> CR a, point<FP> CR m, point<FP> CR b) { return tifa_libs::is_in_middle(a.x, m.x, b.x) && tifa_libs::is_in_middle(a.y, m.y, b.y); }

}  // namespace tifa_libs::geo


#line 7 "src/code/geo2d/is_on_s.hpp"

namespace tifa_libs::geo {

//! containing endpoints
template <class FP>
CEXP bool is_on_S(line<FP> CR s, point<FP> CR p) { return is_on_same_L(s.l, s.r, p) && is_in_middle(s.l, p, s.r); }
//! NOT containing endpoints
template <class FP>
CEXP bool is_on_S_strict(line<FP> CR s, point<FP> CR p) { return s.toleft(p) == 0 && sgn((p - s.l) * (s.l - s.r)) * sgn((p - s.r) * (s.l - s.r)) < 0; }

}  // namespace tifa_libs::geo


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