#pragma once
#include "../../dis/pp_p/lib.hpp"
#include "../../ds/c/lib.hpp"
namespace tifa_libs {
// relation between circle and circle
// clang-format off
enum class RELCC : u8 { lyingin, touchin, intersect, touchex, lyingout };
// clang-format on
template <class FP>
CEXP RELCC relation_CC(circle<FP> CR c1, circle<FP> CR c2) NE {
if (const auto d1 = comp_distp(c1.o, c2.o, c1.r + c2.r); d1 > 0) return RELCC::lyingout;
else if (d1 == 0) return RELCC::touchex;
if (const auto d2 = comp_distp(c1.o, c2.o, abs(c1.r - c2.r)); d2 > 0) return RELCC::intersect;
else if (d2 == 0) return RELCC::touchin;
return RELCC::lyingin;
}
} // namespace tifa_libs
#line 2 "src/geo2d/rel/cc/lib.hpp"
#line 2 "src/geo2d/dis/pp_p/lib.hpp"
#line 2 "src/math/qpow/basic/lib.hpp"
#line 2 "src/util/alias/num/lib.hpp"
#line 2 "src/util/util/lib.hpp"
// https://github.com/Tiphereth-A/CP-lib
#include <bits/extc++.h>
// clang-format off
namespace tifa_libs {
#define CEXP constexpr
#define CEXPE constexpr explicit
#define CR const&
#define CP const*
#define PC *const
#define CPC const*const
#define TPN typename
#define NE noexcept
#define CNE const noexcept
#define ND [[nodiscard]]
#define cT_(...) std::conditional_t<sizeof(__VA_ARGS__) <= sizeof(size_t) * 2, __VA_ARGS__, __VA_ARGS__ CR>
// NOLINTNEXTLINE(misc-const-correctness)
#define flt_(T, i, l, r, ...) for (T i = (l), i##e = (r)__VA_OPT__(, ) __VA_ARGS__; i < i##e; ++i)
#define retif_(cond, if_true, ...) if cond return if_true __VA_OPT__(; else return __VA_ARGS__)
#ifdef ONLINE_JUDGE
#undef assert
#define assert(x) 42
#endif
using namespace std::ranges;
using namespace std::literals;
template <class T>
CEXP T abs(T x) NE { retif_((x < 0), -x, x); }
} // namespace tifa_libs
// clang-format on
#line 4 "src/util/alias/num/lib.hpp"
// clang-format off
namespace tifa_libs {
#define mk0_(w, t) using w = t; using c##w = const t
#define mk_(w, t) mk0_(w, t); CEXP w operator""_##w(unsigned long long x) NE { return (w)x; }
mk_(i8, int8_t) mk_(u8, uint8_t) mk_(i16, int16_t) mk_(u16, uint16_t) mk_(i32, int32_t) mk_(u32, uint32_t) mk_(i64, int64_t) mk_(u64, uint64_t) mk_(isz, ssize_t) mk_(usz, size_t) mk_(chr, char) mk_(schr, signed char) mk_(uchr, unsigned char) mk_(sint, signed) mk_(uint, unsigned);
mk0_(i128, __int128_t); mk0_(u128, __uint128_t); mk0_(f32, float); mk0_(f64, double); mk0_(f128, long double);
#undef mk0_
#undef mk_
} // namespace tifa_libs
// clang-format on
#line 4 "src/math/qpow/basic/lib.hpp"
namespace tifa_libs {
template <class T>
CEXP T qpow(T a, u64 b, cT_(T) init_v = T{1}) NE {
T res = init_v;
for (; b; b >>= 1, a = a * a) {
while (!(b & 1)) b >>= 1, a = a * a;
res = res * a;
}
return res;
}
} // namespace tifa_libs
#line 2 "src/geo2d/dis/pp/lib.hpp"
#line 2 "src/geo2d/ds/p/lib.hpp"
#line 2 "src/util/func_fp/lib.hpp"
#line 2 "src/util/consts/lib.hpp"
#line 4 "src/util/consts/lib.hpp"
// clang-format off
namespace tifa_libs {
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) NE { eps_v<FP> = v; }
CEXP u32 TIME = ((__TIME__[0] & 15) << 20) | ((__TIME__[1] & 15) << 16) | ((__TIME__[3] & 15) << 12) | ((__TIME__[4] & 15) << 8) | ((__TIME__[6] & 15) << 4) | (__TIME__[7] & 15);
CEXP auto STR2U16 = [] { std::array<u32, 65536> table{}; table.fill(-1_u32); flt_ (u32, i, 48, 58) flt_ (u32, j, 48, 58) table[i << 8 | j] = (j & 15) * 10 + (i & 15); return table; }();
inline const auto fn_0 = [](auto&&...) NE {};
inline const auto fn_is0 = [](auto x) NE { return x == 0; };
} // namespace tifa_libs
// clang-format on
#line 2 "src/util/traits/math/lib.hpp"
// clang-format off
#line 4 "src/util/traits/math/lib.hpp"
namespace tifa_libs {
template <class T> concept char_c = std::same_as<T, char> || std::same_as<T, signed char> || std::same_as<T, unsigned char>;
#pragma GCC diagnostic ignored "-Wpedantic"
template <class T> concept s128_c = std::same_as<T, __int128_t> || std::same_as<T, __int128>;
template <class T> concept u128_c = std::same_as<T, __uint128_t> || std::same_as<T, unsigned __int128>;
template <class T> concept i128_c = s128_c<T> || u128_c<T>;
#pragma GCC diagnostic warning "-Wpedantic"
template <class T> concept imost64_c = std::integral<T> && sizeof(T) * __CHAR_BIT__ <= 64;
template <class T> concept smost64_c = imost64_c<T> && std::signed_integral<T>;
template <class T> concept umost64_c = imost64_c<T> && std::unsigned_integral<T>;
template <class T> concept int_c = i128_c<T> || imost64_c<T>;
template <class T> concept sint_c = s128_c<T> || smost64_c<T>;
template <class T> concept uint_c = u128_c<T> || umost64_c<T>;
template <class T> concept arithm_c = std::is_arithmetic_v<T> || int_c<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, std::vector<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> struct to_sint : std::make_signed<T> {};
template <> struct to_sint<u128> { using type = i128; };
template <> struct to_sint<i128> { using type = i128; };
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;
template <arithm_c T> struct to_bigger : std::make_unsigned<T> {};
#define _(w,ww) template <> struct to_bigger<w> { using type = ww; }
#define _2(w,ww) _(i##w,i##ww); _(u##w,u##ww);
_2(8, 16); _2(16, 32); _2(32, 64); _2(64, 128); _(f32, f64); _(f64, f128);
#undef _2
#undef _
template <class T> using to_bigger_t = TPN to_bigger<T>::type;
template <arithm_c T> CEXP T inf_v = [] {
if CEXP(sint_c<T>) return T(to_uint_t<T>(-1) / 4 - 1);
else if CEXP(uint_c<T>) return T(-1) / 2 - 1;
else return std::numeric_limits<T>::max() / 2 - 1;
}();
} // namespace tifa_libs
// clang-format on
#line 5 "src/util/func_fp/lib.hpp"
namespace tifa_libs {
template <sint_c T>
CEXP int sgn(T x) NE { return (!!x) | (x >> (sizeof(T) * 8 - 1)); }
CEXP int sgn(uint_c auto x) NE { return !!x; }
template <std::floating_point FP>
CEXP int sgn(FP x) NE { return (x > eps_v<FP>)-(x < -eps_v<FP>); }
template <class FP>
CEXP bool is_neg(FP x) NE { return sgn(x) < 0; }
template <class FP>
CEXP bool is_zero(FP x) NE { return !sgn(x); }
template <class FP>
CEXP bool is_pos(FP x) NE { return sgn(x) > 0; }
CEXP int comp(sint_c auto l, sint_c auto r) NE { return sgn(l - r); }
CEXP int comp(uint_c auto l, uint_c auto r) NE { return (!!(l - r)) | -(l < r); }
template <std::floating_point FP>
CEXP int comp(FP l, FP r) NE { return sgn((l - r) / max({abs(l), abs(r), FP(1)})); }
template <class FP>
CEXP bool is_lt(FP l, FP r) NE { return comp(l, r) < 0; }
template <class FP>
CEXP bool is_eq(FP l, FP r) NE { return !comp(l, r); }
template <class FP>
CEXP bool is_gt(FP l, FP r) NE { return comp(l, r) > 0; }
//! containing endpoints
CEXP bool is_in_middle(arithm_c auto l, arithm_c auto mid, arithm_c auto r) NE { return is_eq(l, mid) || is_eq(r, mid) || ((l < mid) ^ (r < mid)); }
//! containing endpoints
template <class FP>
CEXP bool is_intersect(FP l1, FP r1, FP l2, FP r2) NE {
if (l1 > r1) swap(l1, r1);
if (l2 > r2) swap(l2, r2);
return !(is_lt(r1, l2) || is_lt(r2, l1));
}
} // namespace tifa_libs
#line 2 "src/util/traits/others/lib.hpp"
// clang-format off
#line 2 "src/util/alias/others/lib.hpp"
#line 4 "src/util/alias/others/lib.hpp"
namespace tifa_libs {
template <class T>
struct chash {
CEXP static u64 C = u64(pi_v<f128> * 2e18) | 71;
CEXP u64 operator()(T x) CNE { return __builtin_bswap64(((u64)x ^ TIME) * C); }
};
// clang-format off
#define mk_(w, t) using w = t; using c##w = const t;
mk_(strn, std::string) mk_(strnv, std::string_view)
#undef mk_
template <class T> struct edge_t { T w; u32 u, v; CEXP auto operator<=>(edge_t CR) const = default; }; template <class T> using cedge_t = const edge_t<T>;
template <class T> struct pt3 { T _0, _1, _2; CEXP auto operator<=>(pt3 CR) const = default; }; template <class T> using cpt3 = const pt3<T>;
template <class T> struct pt4 { T _0, _1, _2, _3; CEXP auto operator<=>(pt4 CR) const = default; }; template <class T> using cpt4 = const pt4<T>;
#define mkT_(w, t, ...) template <class T> using w = t __VA_OPT__(, ) __VA_ARGS__; template <class T> using c##w = const t __VA_OPT__(, ) __VA_ARGS__;
mkT_(ptt, std::pair<T, T>) mkT_(alc, std::pmr::polymorphic_allocator<T>) mkT_(vec, std::vector<T>) mkT_(vvec, vec<vec<T>>) mkT_(v3ec, vvec<vec<T>>) mkT_(vecpt, vec<ptt<T>>) mkT_(vvecpt, vvec<ptt<T>>) mkT_(ptvec, ptt<vec<T>>) mkT_(ptvvec, ptt<vvec<T>>)
#undef mkT_
template <class T> using itl = std ::initializer_list<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 T, usz N> using carr = std::array<const 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 U, class T> using vvecp = vvec<std::pair<U, T>>; template <class U, class T> using vvvecp = vvec<vvec<std::pair<U, T>>>;
#ifdef PB_DS_ASSOC_CNTNR_HPP
template <class T, class C = std::less<T>> using set = __gnu_pbds::tree<T, __gnu_pbds::null_type, C>;
template <class K, class V, class C = std::less<K>> using map = __gnu_pbds::tree<K, V, C>;
// hset<u64> s({}, {}, {}, {}, {1<<16});
template <class T, class HF = chash<T>> using hset = __gnu_pbds::gp_hash_table<T, __gnu_pbds::null_type, HF>;
// hmap<u64, int> s({}, {}, {}, {}, {1<<16});
template <class K, class V, class HF = chash<K>> using hmap = __gnu_pbds::gp_hash_table<K, V, HF>;
#else
using std::set, std::map;
template <class T, class HF = chash<T>> using hset = std::unordered_set<T, HF>;
template <class K, class V, class HF = chash<K>> using hmap = std::unordered_map<K, V, HF>;
#endif
#ifdef PB_DS_PRIORITY_QUEUE_HPP
template <class T, class C = std::less<T>> using pq = __gnu_pbds::priority_queue<T, C>;
#else
template <class T, class C = std::less<T>> using pq = std::priority_queue<T, vec<T>, C>;
#endif
template <class T> using pqg = pq<T, std::greater<T>>;
// clang-format on
#define mk1_(V, A, T) using V##A = V<T>;
#define mk_(V, A, T) mk1_(V, A, T) mk1_(c##V, A, 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) mk1_(spn, A, T) mk1_(itl, A, T)
mk(b, bool) mk(c, chr) mk(i, i32) mk(u, u32) mk(ii, i64) mk(uu, u64) mk(t, isz) mk(z, usz) mk(f, f32) mk(d, f64) mk(s, strn);
#undef mk
#undef mk_
#undef mk1_
} // namespace tifa_libs
#line 4 "src/util/traits/others/lib.hpp"
namespace tifa_libs {
//! only for template without non-type argument
template <class, template <class...> class> CEXP bool specialized_from_v = false;
template <template <class...> class T, class... Args> CEXP bool specialized_from_v<T<Args...>, T> = true;
static_assert(specialized_from_v<vecu, std::vector>);
template <class T> concept container_c = common_range<T> && !std::is_array_v<std::remove_cvref_t<T>> && !std::same_as<std::remove_cvref_t<T>, strn> && !std::same_as<std::remove_cvref_t<T>, strnv>;
template <class T> concept istream_c = std::derived_from<T, std::istream> || std::derived_from<T, std::wistream> || requires(T is) { is.peek(); };
template <class T> concept ostream_c = std::derived_from<T, std::ostream> || std::derived_from<T, std::wostream> || requires(T os) { os.flush(); };
} // namespace tifa_libs
// clang-format on
#line 5 "src/geo2d/ds/p/lib.hpp"
namespace tifa_libs {
template <class FP>
struct point {
using FP_t = FP;
FP x, y;
CEXP point() = default;
CEXP point(FP x, FP y) NE : x{x}, y{y} {}
friend auto& operator>>(istream_c auto& is, point& p) NE { return is >> p.x >> p.y; }
friend auto& operator<<(ostream_c auto& os, point CR p) NE { return os << p.x << ' ' << p.y; }
// s + (t - s) * r
template <std::floating_point T>
friend CEXP point lerp(point CR s, point CR t, T r) NE { return s + (t - s) * r; }
friend CEXP point mid_point(point CR s, point CR t) NE { return lerp(s, t, .5); }
CEXP point& operator+=(arithm_c auto n) NE {
this->x += n, this->y += n;
return *this;
}
CEXP point& operator-=(arithm_c auto n) NE {
this->x -= n, this->y -= n;
return *this;
}
CEXP point& operator*=(arithm_c auto n) NE {
this->x *= n, this->y *= n;
return *this;
}
CEXP point& operator/=(arithm_c auto n) NE {
this->x /= n, this->y /= n;
return *this;
}
friend CEXP point operator+(point x, arithm_c auto n) NE { return x += n; }
friend CEXP point operator+(arithm_c auto n, point x) NE { return x += n; }
friend CEXP point operator-(point x, arithm_c auto n) NE { return x -= n; }
friend CEXP point operator-(arithm_c auto n, point x) NE { return x -= n; }
friend CEXP point operator*(point x, arithm_c auto n) NE { return x *= n; }
friend CEXP point operator*(arithm_c auto n, point x) NE { return x *= n; }
friend CEXP point operator/(point x, arithm_c auto n) NE { return x /= n; }
friend CEXP point operator/(arithm_c auto n, point x) NE { return x /= n; }
CEXP point& operator+=(point CR p) NE {
this->x += p.x, this->y += p.y;
return *this;
}
CEXP point& operator-=(point CR p) NE {
this->x -= p.x, this->y -= p.y;
return *this;
}
CEXP point operator+(point CR p) CNE { return point(*this) += p; }
CEXP point operator-(point CR p) CNE { return point(*this) -= p; }
CEXP point operator-() CNE { return point{-x, -y}; }
CEXP auto operator<=>(point CR p) CNE {
if (auto CR c = comp(x, p.x); c) return c;
return comp(y, p.y);
}
CEXP bool operator==(point CR p) CNE { return (*this <=> p) == 0; }
CEXP FP operator*(point CR p) CNE { return x * p.x + y * p.y; }
CEXP FP operator^(point CR p) CNE { return x * p.y - y * p.x; }
CEXP FP arg() CNE {
static_assert(std::is_floating_point_v<FP>);
return std::atan2(y, x);
}
CEXP FP arg_2pi() CNE {
FP res = arg();
retif_((is_neg(res)), res + 2 * pi_v<FP>, res);
}
CEXP FP norm2() CNE { return x * x + y * y; }
CEXP FP norm() CNE {
static_assert(std::is_floating_point_v<FP>);
return std::hypot(x, y);
}
CEXP point& do_unit() NE {
static_assert(std::is_floating_point_v<FP>);
return *this /= norm();
}
static CEXP arr<u32, 9> QUAD__{6, 7, 8, 5, 0, 1, 4, 3, 2};
// 4 3 2
// 5 0 1
// 6 7 8
ND CEXP u32 quad() CNE { return QUAD__[(sgn(y) + 1) * 3 + sgn(x) + 1]; }
CEXP int toleft(point CR p) CNE { return sgn(*this ^ p); }
CEXP point& do_rot(FP theta) NE {
const FP x0 = x, y0 = y, ct = std::cos(theta), st = std::sin(theta);
x = x0 * ct - y0 * st, y = x0 * st + y0 * ct;
return *this;
}
friend CEXP point rot(point p, FP theta) NE { return p.do_rot(theta); }
CEXP point& do_rot90() NE {
const FP _ = x;
x = -y, y = _;
return *this;
}
friend CEXP point rot90(point p) NE { return p.do_rot90(); }
CEXP point& do_rot270() NE {
const FP _ = y;
y = -x, x = _;
return *this;
}
friend CEXP point rot270(point p) NE { return p.do_rot270(); }
};
} // namespace tifa_libs
#line 4 "src/geo2d/dis/pp/lib.hpp"
namespace tifa_libs {
// distance of two points
// @return $(|x_1-x_2|^p + |y_1-y_2|^p)^{1/p}$, p = 0 means $\infty$
template <class FP, u32 p = 2>
CEXP FP dist_PP(point<FP> CR p1, point<FP> CR p2) NE {
static_assert(p < 2 || std::floating_point<FP>);
if CEXP (p == 0) return max(abs(p1.x - p2.x), abs(p1.y - p2.y)); // Chebyshev
else if CEXP (p == 1) return abs(p1.x - p2.x) + abs(p1.y - p2.y); // Manhattan
else if CEXP (p == 2) return (p1 - p2).norm(); // Euclidian
else return std::pow(std::pow(abs(p1.x - p2.x), p) + std::pow(abs(p1.y - p2.y), p), FP{1} / p);
}
} // namespace tifa_libs
#line 5 "src/geo2d/dis/pp_p/lib.hpp"
namespace tifa_libs {
// distance of two points
// @return Chebyshev dis if p = 0, otherwise $(|x_1-x_2|^p + |y_1-y_2|^p)$
template <class FP, u32 p = 2>
CEXP FP distp_PP(point<FP> CR p1, point<FP> CR p2) NE {
if CEXP (p == 0) return max(abs(p1.x - p2.x), abs(p1.y - p2.y)); // Chebyshev
else if CEXP (p == 1) return abs(p1.x - p2.x) + abs(p1.y - p2.y); // Manhattan
else if CEXP (p == 2) return (p1 - p2).norm2(); // Euclidian
else return qpow(abs(p1.x - p2.x), p) + qpow(abs(p1.y - p2.y), p);
}
template <class FP, u32 p = 2>
CEXP auto comp_distp(point<FP> CR p1, point<FP> CR p2, FP r) NE {
if CEXP (std::floating_point<FP>) return comp(dist_PP<FP, p>(p1, p2), r);
else return comp(distp_PP<FP, p>(p1, p2), qpow(r, p ? p : 1));
}
template <class FP, u32 p = 2>
CEXP auto comp_distp(point<FP> CR p1, point<FP> CR p2, point<FP> CR q1, point<FP> CR q2) NE {
if CEXP (std::floating_point<FP>) return comp(dist_PP<FP, p>(p1, p2), dist_PP<FP, p>(q1, q2));
else return comp(distp_PP<FP, p>(p1, p2), distp_PP<FP, p>(q1, q2));
}
} // namespace tifa_libs
#line 2 "src/geo2d/ds/c/lib.hpp"
#line 4 "src/geo2d/ds/c/lib.hpp"
namespace tifa_libs {
template <class FP>
struct circle {
point<FP> o;
FP r;
CEXP circle() = default;
CEXP circle(point<FP> CR c, FP r) NE : o(c), r(r) {}
CEXP circle(FP c_x, FP c_y, FP r_) NE : o(c_x, c_y), r(r_) {}
friend auto& operator>>(istream_c auto& is, circle& c) NE { return is >> c.o >> c.r; }
friend auto& operator<<(ostream_c auto& os, circle CR c) NE { return os << c.o << ' ' << c.r; }
friend CEXP bool operator==(circle CR l, circle CR r) NE { return l.o == r.o && l.r == r.r; }
friend CEXP auto operator<=>(circle CR l, circle CR r) NE {
if (auto c = l.o <=> r.o; c) return c;
return comp(l.r, r.r);
}
CEXP FP area(FP angle = pi_v<FP> * 2) CNE { return angle * r * r / 2; }
CEXP FP crown_area(FP angle = pi_v<FP> * 2) CNE { return (angle - std::sin(angle)) * r * r / 2; }
CEXP FP arc(FP angle = pi_v<FP> * 2) CNE { return angle * r; }
};
} // namespace tifa_libs
#line 5 "src/geo2d/rel/cc/lib.hpp"
namespace tifa_libs {
// relation between circle and circle
// clang-format off
enum class RELCC : u8 { lyingin, touchin, intersect, touchex, lyingout };
// clang-format on
template <class FP>
CEXP RELCC relation_CC(circle<FP> CR c1, circle<FP> CR c2) NE {
if (const auto d1 = comp_distp(c1.o, c2.o, c1.r + c2.r); d1 > 0) return RELCC::lyingout;
else if (d1 == 0) return RELCC::touchex;
if (const auto d2 = comp_distp(c1.o, c2.o, abs(c1.r - c2.r)); d2 > 0) return RELCC::intersect;
else if (d2 == 0) return RELCC::touchin;
return RELCC::lyingin;
}
} // namespace tifa_libs
src/geo2d/rel/cc/lib.hpp
src/geo2d/make_c/pcc_ex/lib.hpp