// competitive-verifier: STANDALONE
#include "../../../src/geo2d/ang_pp/lib.hpp"
#include "../../../src/geo2d/area_triedges/lib.hpp"
#include "../../../src/geo2d/dis/pl/lib.hpp"
#include "../../../src/geo2d/pred/is_in_middle_p/lib.hpp"
#include "../../../src/geo2d/tcenter/e/lib.hpp"
#include "../../../src/geo2d/tcenter/g/lib.hpp"
#include "../../../src/geo2d/tcenter/h/lib.hpp"
#include "../../../src/geo2d/tcenter/i/lib.hpp"
#include "../../../src/geo2d/tcenter/n/lib.hpp"
#include "../../../src/geo2d/tcenter/o/lib.hpp"
#include "../../../src/geo2d/tcenter/x/lib.hpp"
#include "../../../src/util/rand/lib.hpp"
#include "../base.hpp"
using namespace tifa_libs;
template <class T>
void test_e(triangle<T> CR t) {
point<T> ea = center_EA(t), eb = center_EB(t), ec = center_EC(t);
point<T> i = center_I(t);
point<T> he = center_H(triangle<T>(ea, eb, ec));
check(he, i, check_param(t), check_param(ea), check_param(eb), check_param(ec));
}
template <class T>
void test_g(triangle<T> CR t) {
point<T> g = center_G(t);
point<T> mab = mid_point(t.A, t.B), mbc = mid_point(t.B, t.C), mca = mid_point(t.C, t.A);
check_bool(is_in_middle(t.A, g, mbc), check_param(t), check_param(g), check_param(mbc));
check_bool(is_in_middle(t.B, g, mca), check_param(t), check_param(g), check_param(mca));
check_bool(is_in_middle(t.C, g, mab), check_param(t), check_param(g), check_param(mab));
}
template <class T>
void test_h(triangle<T> CR t) {
point<T> h = center_H(t);
point<T> uva = (t.A - h).do_unit(), uvb = (t.B - h).do_unit(), uvc = (t.C - h).do_unit();
point<T> uab = (t.A - t.B).do_unit(), ubc = (t.B - t.C).do_unit(), uca = (t.C - t.A).do_unit();
check_bool(is_zero(uva * ubc), check_param(t), check_param(h), check_param(uva), check_param(ubc));
check_bool(is_zero(uvb * uca), check_param(t), check_param(h), check_param(uva), check_param(uca));
check_bool(is_zero(uvc * uab), check_param(t), check_param(h), check_param(uva), check_param(uab));
line<T> lab(t.A, t.B), lbc(t.B, t.C), lca(t.C, t.A);
T dist_ah = dist_PP(t.A, h), dist_bh = dist_PP(t.B, h), dist_ch = dist_PP(t.C, h);
T dist_hd = dist_PL(h, lbc), dist_he = dist_PL(h, lca), dist_hf = dist_PL(h, lab);
check_bool(is_eq(dist_ah * dist_hd, dist_bh * dist_he) && is_eq(dist_bh * dist_he, dist_ch * dist_hf), check_param(t), check_param(h), check_param(dist_ah), check_param(dist_bh), check_param(dist_ch), check_param(dist_hd), check_param(dist_he), check_param(dist_hf));
}
template <class T>
void test_i(triangle<T> CR t) {
point<T> i = center_I(t);
T dist_ai = dist_PP(t.A, i), dist_bi = dist_PP(t.B, i), dist_ci = dist_PP(t.C, i);
auto [a, b, c] = t.edges();
T R = radius_O(t), r = radius_I(t);
check_bool(is_eq(dist_ai * dist_ai / (b * c) + dist_bi * dist_bi / (c * a) + dist_ci * dist_ci / (a * b), (T)1), check_param(t), check_param(i), check_param(dist_ai), check_param(dist_bi), check_param(dist_ci), check_param(c), check_param(a), check_param(b));
check_bool(is_eq(dist_ai * dist_bi * dist_ci, 4 * R * r * r), check_param(t), check_param(i), check_param(R), check_param(r), check_param(dist_ai), check_param(dist_bi), check_param(dist_ci));
T ang_cai = ang2pi_PP(t.C - t.A, i - t.A), ang_iab = ang2pi_PP(i - t.A, t.B - t.A);
T ang_abi = ang2pi_PP(t.A - t.B, i - t.B), ang_ibc = ang2pi_PP(i - t.B, t.C - t.B);
T ang_bci = ang2pi_PP(t.B - t.C, i - t.C), ang_ica = ang2pi_PP(i - t.C, t.A - t.C);
check_bool(is_eq(ang_cai, ang_iab), check_param(t), check_param(i), check_param(ang_cai), check_param(ang_iab));
check_bool(is_eq(ang_abi, ang_ibc), check_param(t), check_param(i), check_param(ang_abi), check_param(ang_ibc));
check_bool(is_eq(ang_bci, ang_ica), check_param(t), check_param(i), check_param(ang_bci), check_param(ang_ica));
}
template <class T>
void test_o(triangle<T> CR t) {
point<T> o = center_O(t);
T R = radius_O(t), diam = R * 2;
T dist_ao = dist_PP(t.A, o), dist_bo = dist_PP(t.B, o), dist_co = dist_PP(t.C, o);
check_bool(is_eq(R, dist_ao), check_param(t), check_param(R), check_param(dist_ao));
check_bool(is_eq(R, dist_bo), check_param(t), check_param(R), check_param(dist_bo));
check_bool(is_eq(R, dist_co), check_param(t), check_param(R), check_param(dist_co));
auto [a, b, c] = t.edges();
auto [A, B, C] = t.angles();
T das = a / std::sin(A), dbs = b / std::sin(B), dcs = c / std::sin(C);
check_bool(is_eq(diam, das), check_param(t), check_param(diam), check_param(das), check_param(a), check_param(A));
check_bool(is_eq(diam, dbs), check_param(t), check_param(diam), check_param(dbs), check_param(b), check_param(B));
check_bool(is_eq(diam, dcs), check_param(t), check_param(diam), check_param(dcs), check_param(c), check_param(C));
T area = area_T_abc(a, b, c);
T ds = std::sqrt(2 * area / (std::sin(A) * std::sin(B) * std::sin(C)));
T ds2 = a * b * c / (2 * area);
check_bool(is_eq(diam, ds), check_param(t), check_param(diam), check_param(ds), check_param(area), check_param(A), check_param(B), check_param(C));
check_bool(is_eq(diam, ds2), check_param(t), check_param(diam), check_param(ds2), check_param(area), check_param(a), check_param(b), check_param(c));
}
template <class T>
void test_n(triangle<T> CR t) {
point<T> n = center_N(t);
point<T> o = center_O(t), h = center_H(t), g = center_G(t), i = center_I(t);
check(n, mid_point(o, h), check_param(t), check_param(n), check_param(o), check_param(h));
check_bool(is_zero(cross_unit(n, o, g)), check_param(t), check_param(n), check_param(o), check_param(g));
T no = dist_PP(n, o), nh = dist_PP(n, h), ng = dist_PP(n, g);
check_bool(is_eq(no, nh) && is_eq(nh, ng * 3), check_param(t), check_param(n), check_param(o), check_param(h), check_param(g), check_param(no), check_param(nh), check_param(ng));
T R = radius_O(t), r = radius_I(t);
T ni = dist_PP(n, i), oi = dist_PP(o, i);
check_bool(is_eq(ni, R / 2 - r), check_param(t), check_param(n), check_param(i), check_param(ni), check_param(R), check_param(r));
check_bool(is_eq(2 * R * ni, oi * oi), check_param(t), check_param(n), check_param(i), check_param(ni), check_param(oi), check_param(R));
}
template <class T>
void test_x(triangle<T> CR t) {
point<T> x = center_X(t);
point<T> uva = (t.A - x).do_unit(), uvb = (t.B - x).do_unit(), uvc = (t.C - x).do_unit();
T ang_axb = std::abs(ang_PP(uva, uvb)), ang_bxc = std::abs(ang_PP(uvb, uvc)), ang_cxa = std::abs(ang_PP(uvc, uva));
CEXP T _60 = pi_v<T> / 3, _120 = pi_v<T> / 1.5;
check_bool((is_eq(ang_axb, _120) && is_eq(ang_bxc, _120) && is_eq(ang_cxa, _120)) ||
(is_eq(ang_axb, _60) && is_eq(ang_bxc, _60) && is_eq(ang_cxa, _120)) ||
(is_eq(ang_axb, _120) && is_eq(ang_bxc, _60) && is_eq(ang_cxa, _60)) ||
(is_eq(ang_axb, _60) && is_eq(ang_bxc, _120) && is_eq(ang_cxa, _60)),
check_param(t), check_param(x), check_param(uva), check_param(uvb), check_param(uvc), check_param(ang_axb), check_param(ang_bxc), check_param(ang_cxa));
}
template <arithm_c T>
void test(T lim) {
rand_gen<T> g(std::is_signed_v<T> ? -lim : 0, lim);
triangle<T> t(point<T>(g(), g()), point<T>(g(), g()), point<T>(g(), g()));
timer_(test_e(t));
timer_(test_g(t));
timer_(test_h(t));
timer_(test_i(t));
timer_(test_o(t));
timer_(test_n(t));
timer_(test_x(t));
}
int main() {
timer_(test<f64>(1e5));
timer_(test<f128>(1e5));
timer_(test<f64>(1e9));
timer_(test<f128>(1e9));
}
#line 1 "test/cpv_local/geo2d/triangle_centers.cpp"
// competitive-verifier: STANDALONE
#line 2 "src/geo2d/ang_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 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/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/ang_pp/lib.hpp"
namespace tifa_libs {
// clamp angle of two points, result in $(-\pi,\pi]$
template <class FP>
CEXP FP ang_PP(point<FP> CR p1, point<FP> CR p2) NE { return std::atan2(p1 ^ p2, p1 * p2); }
// clamp angle of two points, result in $[0,2\pi)$
template <class FP>
CEXP FP ang2pi_PP(point<FP> CR p1, point<FP> CR p2) NE {
const FP res = ang_PP(p1, p2);
retif_((is_neg(res)), res + 2 * pi_v<FP>, res);
}
} // namespace tifa_libs
#line 2 "src/geo2d/area_triedges/lib.hpp"
#line 4 "src/geo2d/area_triedges/lib.hpp"
namespace tifa_libs {
// calculate area of triangle by the length of 3 edges
// numerical stability improved
template <class FP>
CEXP FP area_T_abc(FP a, FP b, FP c) NE {
if (a < b) swap(a, b);
if (a < c) swap(a, c);
if (b < c) swap(b, c);
return std::sqrt(a + (b + c)) * std::sqrt(c - (a - b)) * std::sqrt(c + (a - b)) * std::sqrt(a + (b - c)) / 4;
}
} // namespace tifa_libs
#line 2 "src/geo2d/dis/pl/lib.hpp"
#line 2 "src/geo2d/proj/lib.hpp"
#line 2 "src/geo2d/ds/l/lib.hpp"
#line 2 "src/geo2d/cross/lib.hpp"
#line 4 "src/geo2d/cross/lib.hpp"
namespace tifa_libs {
template <class P>
CEXP auto cross(P CR o, P CR a, P CR b) NE { return (a - o) ^ (b - o); }
template <class P>
requires std::floating_point<TPN P::FP_t>
CEXP auto cross_unit(P CR o, P CR a, P CR b) NE { return (a - o).do_unit() ^ (b - o).do_unit(); }
template <class P>
requires std::floating_point<TPN P::FP_t>
CEXP int sgn_cross(P CR o, P CR a, P CR b) NE { return sgn(cross_unit(o, a, b)); }
template <class P>
CEXP int sgn_cross(P CR o, P CR a, P CR b) NE { return sgn(cross(o, a, b)); }
} // namespace tifa_libs
#line 5 "src/geo2d/ds/l/lib.hpp"
namespace tifa_libs {
template <class FP>
struct line {
point<FP> l, r;
CEXP line() = default;
CEXP line(point<FP> CR s, point<FP> CR t) NE : l(s), r(t) {}
CEXP line(point<FP> CR s, FP angle_x) NE : 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) NE {
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) NE : l{s_x, s_y}, r{t_x, t_y} {}
friend std::istream& operator>>(std::istream& is, line& l) NE { return is >> l.l >> l.r; }
friend std::ostream& operator<<(std::ostream& os, line CR l) NE { return os << l.l << ' ' << l.r; }
CEXP point<FP> direction() CNE { return r - l; }
CEXP bool is_parallel(line CR r) CNE { return is_zero(direction() ^ r.direction()); }
friend CEXP bool is_parallel(line CR l, line CR r) NE { return l.is_parallel(r); }
CEXP bool is_same_dir(line CR r) CNE { return is_parallel(r) && is_pos(direction() * r.direction()); }
friend CEXP bool is_same_dir(line CR l, line CR r) NE { return l.is_same_dir(r); }
friend CEXP bool operator==(line CR l, line CR r) NE { return l.l == r.l && l.r == r.r; }
friend CEXP auto operator<=>(line CR l, line CR r) NE {
if (l == r) return 0;
if (l.is_same_dir(r)) {
retif_((r.is_include_strict(l.l)), -1, 1);
} else 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) CNE { return sgn_cross(l, r, p); }
// half plane
CEXP bool is_include_strict(point<FP> CR p) CNE { return toleft(p) > 0; }
// half plane
CEXP bool is_include(point<FP> CR p) CNE { return toleft(p) >= 0; }
// translate @dist along the direction of half plane
CEXP line& do_push(FP dist) NE {
const point delta = direction().do_rot90().do_unit() * dist;
l += delta, r += delta;
return *this;
}
};
} // namespace tifa_libs
#line 4 "src/geo2d/proj/lib.hpp"
namespace tifa_libs {
// projection to a line
template <class FP>
CEXP point<FP> proj(line<FP> CR l, point<FP> CR p) NE {
const point dir = l.direction();
return l.l + dir * (dir * (p - l.l) / dir.norm2());
}
// reflection about a line
template <class FP>
CEXP point<FP> reflect(line<FP> CR l, point<FP> CR p) NE { return proj(l, p) * 2 - p; }
} // namespace tifa_libs
#line 4 "src/geo2d/dis/pl/lib.hpp"
namespace tifa_libs {
// min dist_PP from a point to a line
template <class FP>
CEXP FP dist_PL(point<FP> CR p, line<FP> CR s) NE { retif_((s.l == s.r), dist_PP(s.l, p), dist_PP(p, proj(s, p))); }
} // namespace tifa_libs
#line 2 "src/geo2d/pred/is_in_middle_p/lib.hpp"
#line 4 "src/geo2d/pred/is_in_middle_p/lib.hpp"
namespace tifa_libs {
//! containing endpoints
template <class FP>
CEXP bool is_in_middle(point<FP> CR a, point<FP> CR m, point<FP> CR b) NE { 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
#line 2 "src/geo2d/tcenter/e/lib.hpp"
#line 2 "src/geo2d/ds/t/lib.hpp"
#line 2 "src/geo2d/dis/pp/lib.hpp"
#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 2 "src/geo2d/dot/lib.hpp"
#line 4 "src/geo2d/dot/lib.hpp"
namespace tifa_libs {
template <class P>
CEXP TPN P::FP_t dot(P CR o, P CR a, P CR b) NE { return (a - o) * (b - o); }
template <class P>
CEXP int sgn_dot(P CR o, P CR a, P CR b) NE { return sgn(dot(o, a, b)); }
} // namespace tifa_libs
#line 7 "src/geo2d/ds/t/lib.hpp"
namespace tifa_libs {
template <class FP>
struct triangle {
point<FP> A, B, C;
CEXP triangle() = default;
CEXP triangle(point<FP> CR a, point<FP> CR b, point<FP> CR c) NE : A(a), B(b), C(c) {}
CEXP triangle(FP a_x, FP a_y, FP b_x, FP b_y, FP c_x, FP c_y) NE : A(a_x, a_y), B(b_x, b_y), C(c_x, c_y) {}
friend auto& operator>>(istream_c auto& is, triangle& t) NE { return is >> t.A >> t.B >> t.C; }
friend auto& operator<<(ostream_c auto& os, triangle CR t) NE { return os << t.A << ' ' << t.B << ' ' << t.C; }
friend CEXP bool operator==(triangle CR l, triangle CR r) NE { return l.A == r.A && l.B == r.B && l.C == r.C; }
// (a, b, c)
CEXP pt3<FP> edges() CNE { return {dist_PP(B, C), dist_PP(C, A), dist_PP(A, B)}; }
// (A, B, C)
CEXP pt3<FP> angles() CNE { return {abs(ang_PP(C - A, B - A)), abs(ang_PP(A - B, C - B)), abs(ang_PP(A - C, B - C))}; }
CEXP point<FP> trilinears(FP x, FP y, FP z) CNE {
auto [a, b, c] = edges();
x *= a, y *= b, z *= c;
return (A * x + B * y + C * z) / (x + y + z);
}
CEXP point<FP> barycentrics(FP u, FP v, FP w) CNE { return (A * u + B * v + C * w) / (u + v + w); }
CEXP FP area() CNE { return abs(cross(A, B, C)) / 2; }
ND CEXP bool is_acute() CNE { return is_pos(dot(A, B, C)) && is_pos(dot(B, C, A)) && is_pos(dot(C, A, B)); }
ND CEXP bool is_right() CNE { return is_zero(dot(A, B, C)) || is_zero(dot(B, C, A)) || is_zero(dot(C, A, B)); }
ND CEXP bool is_obtuse() CNE { return is_neg(dot(A, B, C)) || is_neg(dot(B, C, A)) || is_neg(dot(C, A, B)); }
};
} // namespace tifa_libs
#line 4 "src/geo2d/tcenter/e/lib.hpp"
namespace tifa_libs {
// excenter of A
template <class FP>
CEXP point<FP> center_EA(triangle<FP> CR t) NE { return t.trilinears(-1, 1, 1); }
// excenter of B
template <class FP>
CEXP point<FP> center_EB(triangle<FP> CR t) NE { return t.trilinears(1, -1, 1); }
// excenter of C
template <class FP>
CEXP point<FP> center_EC(triangle<FP> CR t) NE { return t.trilinears(1, 1, -1); }
} // namespace tifa_libs
#line 2 "src/geo2d/tcenter/g/lib.hpp"
#line 4 "src/geo2d/tcenter/g/lib.hpp"
namespace tifa_libs {
// centroid (X2)
template <class FP>
CEXP point<FP> center_G(triangle<FP> CR t) NE { return t.barycentrics(1, 1, 1); }
} // namespace tifa_libs
#line 2 "src/geo2d/tcenter/h/lib.hpp"
#line 4 "src/geo2d/tcenter/h/lib.hpp"
namespace tifa_libs {
// orthocenter (X4)
template <class FP>
CEXP point<FP> center_H(triangle<FP> CR t) NE {
auto [A, B, C] = t.angles();
return t.trilinears(1 / std::cos(A), 1 / std::cos(B), 1 / std::cos(C));
}
} // namespace tifa_libs
#line 2 "src/geo2d/tcenter/i/lib.hpp"
#line 4 "src/geo2d/tcenter/i/lib.hpp"
namespace tifa_libs {
// radius of inscribed circle
template <class FP>
CEXP FP radius_I(triangle<FP> CR t) NE {
auto [a, b, c] = t.edges();
return 2 * t.area() / (a + b + c);
}
// incenter (X1)
template <class FP>
CEXP point<FP> center_I(triangle<FP> CR t) NE { return t.trilinears(1, 1, 1); }
} // namespace tifa_libs
#line 2 "src/geo2d/tcenter/n/lib.hpp"
#line 4 "src/geo2d/tcenter/n/lib.hpp"
namespace tifa_libs {
// 9-point center (X5)
template <class FP>
CEXP point<FP> center_N(triangle<FP> CR t) NE {
auto [A, B, C] = t.angles();
return t.trilinears(std::cos(B - C), std::cos(C - A), std::cos(A - B));
}
} // namespace tifa_libs
#line 2 "src/geo2d/tcenter/o/lib.hpp"
#line 2 "src/geo2d/ins/ll/lib.hpp"
#line 4 "src/geo2d/ins/ll/lib.hpp"
namespace tifa_libs {
// judge if two lines are intersected or not
template <class FP>
CEXP bool is_ins_LL(line<FP> CR l1, line<FP> CR l2) NE { return !is_zero(cross(l2.l, l2.r, l1.l) - cross(l2.l, l2.r, l1.r)); }
// intersection point of two lines
template <class FP>
CEXP point<FP> ins_LL(line<FP> CR l1, line<FP> CR l2) NE {
const FP a1 = cross(l2.l, l2.r, l1.l), a2 = -cross(l2.l, l2.r, l1.r);
return (l1.l * a2 + l1.r * a1) / (a1 + a2);
}
template <class FP>
CEXP point<FP> ins_LL(line<FP> CR l, FP a, FP b, FP c) NE {
const FP a1 = abs(a * l.l.x + b * l.l.y + c), a2 = abs(a * l.r.x + b * l.r.y + c);
return (l.l * a2 + l.r * a1) / (a1 + a2);
}
} // namespace tifa_libs
#line 5 "src/geo2d/tcenter/o/lib.hpp"
namespace tifa_libs {
// radius of circumscribed circle
template <class FP>
CEXP FP radius_O(triangle<FP> CR t) NE { return dist_PP(t.B, t.C) / std::sin(abs(ang_PP(t.B - t.A, t.C - t.A))) / 2; }
// circumcenter (X3)
template <class FP>
CEXP point<FP> center_O(triangle<FP> CR t) NE {
// auto [A, B, C] = t.angles();
// return t.trilinears(std::cos(A), std::cos(B), std::cos(C));
const point<FP> p1 = mid_point(t.B, t.C), p2 = mid_point(t.C, t.A);
return ins_LL<FP>({p1, p1 + (t.B - t.C).do_rot90()}, {p2, p2 + (t.C - t.A).do_rot90()});
}
} // namespace tifa_libs
#line 2 "src/geo2d/tcenter/x/lib.hpp"
#line 4 "src/geo2d/tcenter/x/lib.hpp"
namespace tifa_libs {
// fermat center (X13)
template <class FP>
CEXP point<FP> center_X(triangle<FP> CR t) NE {
auto [A, B, C] = t.angles();
return t.trilinears(1 / std::sin(A + pi_v<FP> / 3), 1 / std::sin(B + pi_v<FP> / 3), 1 / std::sin(C + pi_v<FP> / 3));
}
} // namespace tifa_libs
#line 2 "src/util/rand/lib.hpp"
#line 5 "src/util/rand/lib.hpp"
namespace tifa_libs {
template <class T>
requires std::is_arithmetic_v<T>
class rand_gen {
using res_t = std::conditional_t<sizeof(T) <= 4, u32, u64>;
using res_wt = std::conditional_t<sizeof(T) <= 4, u64, u128>;
// clang-format off
struct mt19937_param { static CEXP u32 w = 32, n = 624, m = 397, r = 31, a = 0x9908b0df, u = 11, d = 0xffffffff, s = 7, b = 0x9d2c5680, t = 15, c = 0xefc60000, l = 18, f = 1812433253; };
struct mt19937_64_param { static CEXP u64 w = 64, n = 312, m = 156, r = 31, a = 0xb5026f5aa96619e9, u = 29, d = 0x5555555555555555, s = 17, b = 0x71d67fffeda60000, t = 37, c = 0xfff7eee000000000, l = 43, f = 6364136223846793005; };
using pm = std::conditional_t<std::is_same_v<res_t, u32>, mt19937_param, mt19937_64_param>;
// clang-format on
T a_, b_;
arr<res_t, pm::n> x_;
u32 p_;
CEXP void gen_() NE {
CEXP res_t um = (~res_t()) << pm::r, lm = ~um;
res_t _;
flt_ (res_t, i, p_ = 0, pm::n - pm::m) _ = ((x_[i] & um) | (x_[i + 1] & lm)), x_[i] = (x_[i + pm::m] ^ (_ >> 1) ^ ((_ & 1) ? pm::a : 0));
flt_ (res_t, i, pm::n - pm::m, pm::n - 1) _ = ((x_[i] & um) | (x_[i + 1] & lm)), x_[i] = (x_[i + (pm::m - pm::n)] ^ (_ >> 1) ^ ((_ & 1) ? pm::a : 0));
_ = ((x_[pm::n - 1] & um) | (x_[0] & lm)), x_[pm::n - 1] = (x_[pm::m - 1] ^ (_ >> 1) ^ ((_ & 1) ? pm::a : 0));
}
public:
CEXPE rand_gen(T a = std::numeric_limits<T>::min(), T b = std::numeric_limits<T>::max(), res_t sd = (res_t)TIME) NE : a_(a), b_(b) { assert(a < b || (std::is_integral_v<T> && a == b)), seed(sd); }
CEXP void range(T min, T max) NE { assert(min < max || (std::is_integral_v<T> && min == max)), a_ = min, b_ = max; }
void seed() NE { seed((res_t)std::chrono::duration_cast<std::chrono::nanoseconds>(std::chrono::high_resolution_clock::now().time_since_epoch()).count()); }
CEXP void seed(res_t sd) NE {
x_[0] = sd & gen_max();
flt_ (res_t, i, 1, p_ = pm::n) x_[i] = ((x_[i - 1] ^ (x_[i - 1] >> (pm::w - 2))) * pm::f + i % pm::n) & gen_max();
}
ND CEXP res_t gen_min() CNE { return 0; }
ND CEXP res_t gen_max() CNE {
if CEXP (sizeof(res_t) * 8 == pm::w) return ~res_t();
else return ((res_t)1 << pm::w) - 1;
}
CEXP res_t next() NE {
if (p_ >= pm::n) gen_();
res_t _ = x_[p_++];
_ ^= (_ >> pm::u) & pm::d, _ ^= (_ << pm::s) & pm::b, _ ^= (_ << pm::t) & pm::c, _ ^= (_ >> pm::l);
return _;
}
CEXP T operator()() NE {
if CEXP (std::integral<T>) {
const res_wt r = (res_wt)b_ - (res_wt)a_ + 1;
res_wt p = r * next();
if (auto l = (res_t)p, _ = res_t(res_wt(-(res_t)r) % r); l < r)
while (l < _) l = res_t(p = r * next());
return T((res_t)(p >> pm::w) + (res_t)a_);
} else return T(next() / (f128)((u128)gen_max() + 1) * (b_ - a_) + a_);
}
};
} // namespace tifa_libs
#line 2 "test/cpv_local/base.hpp"
#line 2 "src/io/container/lib.hpp"
#line 4 "src/io/container/lib.hpp"
namespace tifa_libs {
auto& operator>>(tifa_libs::istream_c auto& is, tifa_libs::container_c auto& x) NE {
for (auto& i : x) is >> i;
return is;
}
auto& operator<<(tifa_libs::ostream_c auto& os, tifa_libs::container_c auto CR x) NE {
if (begin(x) == end(x)) [[unlikely]]
return os;
auto it = begin(x);
for (os << *it++; it != end(x); ++it) os << ' ' << *it;
return os;
}
} // namespace tifa_libs
#line 2 "src/io/i128/lib.hpp"
#line 5 "src/io/i128/lib.hpp"
namespace tifa_libs {
namespace ios128_impl_ {
auto& read(tifa_libs::istream_c auto& is, tifa_libs::u128_c auto& n) {
static strn int_buf;
int_buf.reserve(43), n = 0, is >> int_buf;
for (u32 i = 0; i + 1 < int_buf.size(); i += 2) (n *= 100) += STR2U16[*(u16*)(int_buf.data() + i)];
if (int_buf.size() & 1) (n *= 10) += int_buf.back() & 15;
return is;
}
} // namespace ios128_impl_
auto& operator>>(tifa_libs::istream_c auto& is, tifa_libs::s128_c auto& n) NE {
bool neg = false;
if CEXP (requires { is.skip_nnegdigit(); }) neg = (is.skip_nnegdigit().peek() == '-' && is.get_unchk());
else
while (!neg && !isdigit(is.peek())) {
if (is.peek() == '-') neg = true;
is.get();
}
u128 n_ = 0;
if (ios128_impl_::read(is, n_); neg) n_ = -n_;
n = (i128)n_;
return is;
}
auto& operator>>(tifa_libs::istream_c auto& is, tifa_libs::u128_c auto& n) NE {
if CEXP (requires { is.skip_ndigit(); }) is.skip_ndigit();
else
while (!isdigit(is.peek())) is.get();
return ios128_impl_::read(is, n);
}
auto& operator<<(tifa_libs::ostream_c auto& os, tifa_libs::u128_c auto n) NE {
static strn int_buf(40, '\0');
auto it = end(int_buf);
do *(--(it)) = chr(n % 10) | '0';
while (n /= 10);
return os << int_buf.substr(usz(it - begin(int_buf)));
}
auto& operator<<(tifa_libs::ostream_c auto& os, tifa_libs::s128_c auto n) NE {
if (n < 0) return os << '-' << -(u128)n;
return os << (u128)n;
}
} // namespace tifa_libs
#line 2 "src/io/pair/lib.hpp"
#line 4 "src/io/pair/lib.hpp"
namespace tifa_libs {
template <class T, class U>
auto& operator>>(tifa_libs::istream_c auto& is, std::pair<T, U>& p) NE { return is >> p.first >> p.second; }
template <class T, class U>
auto& operator<<(tifa_libs::ostream_c auto& os, std::pair<T, U> CR p) NE { return os << p.first << ' ' << p.second; }
} // namespace tifa_libs
#line 2 "src/io/tuple/lib.hpp"
#line 4 "src/io/tuple/lib.hpp"
namespace tifa_libs {
template <class... Ts>
auto& operator>>(tifa_libs::istream_c auto& is, std::tuple<Ts...>& p) NE {
std::apply([&](Ts&... ts) NE { (is >> ... >> ts); }, p);
return is;
}
template <class... Ts>
auto& operator<<(tifa_libs::ostream_c auto& os, std::tuple<Ts...> CR p) NE {
std::apply([&, n = 0](Ts const&... ts) mutable NE { ((os << ts << (++n != sizeof...(Ts) ? " " : "")), ...); }, p);
return os;
}
} // namespace tifa_libs
#line 7 "test/cpv_local/base.hpp"
namespace tifa_libs {
namespace detail__ {
template <class T>
strn to_str(T CR x) NE {
std::stringstream ss;
ss << std::fixed << std::setprecision(12) << x;
auto str = ss.str();
retif_((str.length() <= 1024), str, std::format("{}... (length = {})", str.substr(0, 1024), std::to_string(str.length())));
}
template <class T, class... Ts>
void check_(strnv pretty_func, strnv got_str, T CR got, strnv want_str, T CR want, Ts... param) {
if CEXP (sizeof...(param) == 0) {
if (got != want) throw std::runtime_error(std::format("{}: got \"{}\" = {}, want \"{}\" = {}", pretty_func, got_str, to_str(got), want_str, to_str(want)));
} else {
if (got != want) throw std::runtime_error(std::format("{}: got \"{}\" = {}, want \"{}\" = {} with", pretty_func, got_str, to_str(got), want_str, to_str(want)) + (std::format(" {} = {};", param.first, ::tifa_libs::detail__::to_str(param.second)) + ...));
}
}
template <class... Ts>
void check_bool_(strnv pretty_func, strnv expression, bool res, Ts... param) {
if CEXP (sizeof...(param) == 0) {
if (!res) throw std::runtime_error(std::format("{} :\"{}\" failed", pretty_func, expression));
} else {
if (!res) throw std::runtime_error(std::format("{} :\"{}\" failed with", pretty_func, expression) + (std::format(" {} = {};", param.first, ::tifa_libs::detail__::to_str(param.second)) + ...));
}
}
} // namespace detail__
template <class clock_t = std::chrono::high_resolution_clock, class duration_t = std::chrono::microseconds>
requires specialized_from_v<duration_t, std::chrono::duration>
struct timer {
void tic(int line_num) NE {
s_line_num = line_num;
const std::lock_guard<std::mutex> lock(s_clock_mutex);
s_clock_start = clock_t::now();
}
void tac() NE {
const std::lock_guard<std::mutex> lock(s_clock_mutex);
s_clock_end = clock_t::now();
}
auto passed() CNE { return std::chrono::duration_cast<duration_t>(s_clock_end - s_clock_start); }
operator strn() { return std::format("{} passed in line {}", passed(), s_line_num); }
private:
std::mutex s_clock_mutex;
std::chrono::time_point<clock_t> s_clock_start, s_clock_end;
int s_line_num;
};
inline timer default_timer;
#define timer_(...) \
::tifa_libs::default_timer.tic(__LINE__); \
__VA_ARGS__; \
::tifa_libs::default_timer.tac(); \
std::cerr << (strn)::tifa_libs::default_timer << '\n'
#define check(got, want, ...) ::tifa_libs::detail__::check_(__PRETTY_FUNCTION__, #got, got, #want, want __VA_OPT__(, ) __VA_ARGS__)
#define check_bool(expression, ...) ::tifa_libs::detail__::check_bool_(__PRETTY_FUNCTION__, #expression, expression __VA_OPT__(, ) __VA_ARGS__)
#define check_param(x) \
std::pair<std::string, decltype(x)> { #x, x }
} // namespace tifa_libs
#line 16 "test/cpv_local/geo2d/triangle_centers.cpp"
using namespace tifa_libs;
template <class T>
void test_e(triangle<T> CR t) {
point<T> ea = center_EA(t), eb = center_EB(t), ec = center_EC(t);
point<T> i = center_I(t);
point<T> he = center_H(triangle<T>(ea, eb, ec));
check(he, i, check_param(t), check_param(ea), check_param(eb), check_param(ec));
}
template <class T>
void test_g(triangle<T> CR t) {
point<T> g = center_G(t);
point<T> mab = mid_point(t.A, t.B), mbc = mid_point(t.B, t.C), mca = mid_point(t.C, t.A);
check_bool(is_in_middle(t.A, g, mbc), check_param(t), check_param(g), check_param(mbc));
check_bool(is_in_middle(t.B, g, mca), check_param(t), check_param(g), check_param(mca));
check_bool(is_in_middle(t.C, g, mab), check_param(t), check_param(g), check_param(mab));
}
template <class T>
void test_h(triangle<T> CR t) {
point<T> h = center_H(t);
point<T> uva = (t.A - h).do_unit(), uvb = (t.B - h).do_unit(), uvc = (t.C - h).do_unit();
point<T> uab = (t.A - t.B).do_unit(), ubc = (t.B - t.C).do_unit(), uca = (t.C - t.A).do_unit();
check_bool(is_zero(uva * ubc), check_param(t), check_param(h), check_param(uva), check_param(ubc));
check_bool(is_zero(uvb * uca), check_param(t), check_param(h), check_param(uva), check_param(uca));
check_bool(is_zero(uvc * uab), check_param(t), check_param(h), check_param(uva), check_param(uab));
line<T> lab(t.A, t.B), lbc(t.B, t.C), lca(t.C, t.A);
T dist_ah = dist_PP(t.A, h), dist_bh = dist_PP(t.B, h), dist_ch = dist_PP(t.C, h);
T dist_hd = dist_PL(h, lbc), dist_he = dist_PL(h, lca), dist_hf = dist_PL(h, lab);
check_bool(is_eq(dist_ah * dist_hd, dist_bh * dist_he) && is_eq(dist_bh * dist_he, dist_ch * dist_hf), check_param(t), check_param(h), check_param(dist_ah), check_param(dist_bh), check_param(dist_ch), check_param(dist_hd), check_param(dist_he), check_param(dist_hf));
}
template <class T>
void test_i(triangle<T> CR t) {
point<T> i = center_I(t);
T dist_ai = dist_PP(t.A, i), dist_bi = dist_PP(t.B, i), dist_ci = dist_PP(t.C, i);
auto [a, b, c] = t.edges();
T R = radius_O(t), r = radius_I(t);
check_bool(is_eq(dist_ai * dist_ai / (b * c) + dist_bi * dist_bi / (c * a) + dist_ci * dist_ci / (a * b), (T)1), check_param(t), check_param(i), check_param(dist_ai), check_param(dist_bi), check_param(dist_ci), check_param(c), check_param(a), check_param(b));
check_bool(is_eq(dist_ai * dist_bi * dist_ci, 4 * R * r * r), check_param(t), check_param(i), check_param(R), check_param(r), check_param(dist_ai), check_param(dist_bi), check_param(dist_ci));
T ang_cai = ang2pi_PP(t.C - t.A, i - t.A), ang_iab = ang2pi_PP(i - t.A, t.B - t.A);
T ang_abi = ang2pi_PP(t.A - t.B, i - t.B), ang_ibc = ang2pi_PP(i - t.B, t.C - t.B);
T ang_bci = ang2pi_PP(t.B - t.C, i - t.C), ang_ica = ang2pi_PP(i - t.C, t.A - t.C);
check_bool(is_eq(ang_cai, ang_iab), check_param(t), check_param(i), check_param(ang_cai), check_param(ang_iab));
check_bool(is_eq(ang_abi, ang_ibc), check_param(t), check_param(i), check_param(ang_abi), check_param(ang_ibc));
check_bool(is_eq(ang_bci, ang_ica), check_param(t), check_param(i), check_param(ang_bci), check_param(ang_ica));
}
template <class T>
void test_o(triangle<T> CR t) {
point<T> o = center_O(t);
T R = radius_O(t), diam = R * 2;
T dist_ao = dist_PP(t.A, o), dist_bo = dist_PP(t.B, o), dist_co = dist_PP(t.C, o);
check_bool(is_eq(R, dist_ao), check_param(t), check_param(R), check_param(dist_ao));
check_bool(is_eq(R, dist_bo), check_param(t), check_param(R), check_param(dist_bo));
check_bool(is_eq(R, dist_co), check_param(t), check_param(R), check_param(dist_co));
auto [a, b, c] = t.edges();
auto [A, B, C] = t.angles();
T das = a / std::sin(A), dbs = b / std::sin(B), dcs = c / std::sin(C);
check_bool(is_eq(diam, das), check_param(t), check_param(diam), check_param(das), check_param(a), check_param(A));
check_bool(is_eq(diam, dbs), check_param(t), check_param(diam), check_param(dbs), check_param(b), check_param(B));
check_bool(is_eq(diam, dcs), check_param(t), check_param(diam), check_param(dcs), check_param(c), check_param(C));
T area = area_T_abc(a, b, c);
T ds = std::sqrt(2 * area / (std::sin(A) * std::sin(B) * std::sin(C)));
T ds2 = a * b * c / (2 * area);
check_bool(is_eq(diam, ds), check_param(t), check_param(diam), check_param(ds), check_param(area), check_param(A), check_param(B), check_param(C));
check_bool(is_eq(diam, ds2), check_param(t), check_param(diam), check_param(ds2), check_param(area), check_param(a), check_param(b), check_param(c));
}
template <class T>
void test_n(triangle<T> CR t) {
point<T> n = center_N(t);
point<T> o = center_O(t), h = center_H(t), g = center_G(t), i = center_I(t);
check(n, mid_point(o, h), check_param(t), check_param(n), check_param(o), check_param(h));
check_bool(is_zero(cross_unit(n, o, g)), check_param(t), check_param(n), check_param(o), check_param(g));
T no = dist_PP(n, o), nh = dist_PP(n, h), ng = dist_PP(n, g);
check_bool(is_eq(no, nh) && is_eq(nh, ng * 3), check_param(t), check_param(n), check_param(o), check_param(h), check_param(g), check_param(no), check_param(nh), check_param(ng));
T R = radius_O(t), r = radius_I(t);
T ni = dist_PP(n, i), oi = dist_PP(o, i);
check_bool(is_eq(ni, R / 2 - r), check_param(t), check_param(n), check_param(i), check_param(ni), check_param(R), check_param(r));
check_bool(is_eq(2 * R * ni, oi * oi), check_param(t), check_param(n), check_param(i), check_param(ni), check_param(oi), check_param(R));
}
template <class T>
void test_x(triangle<T> CR t) {
point<T> x = center_X(t);
point<T> uva = (t.A - x).do_unit(), uvb = (t.B - x).do_unit(), uvc = (t.C - x).do_unit();
T ang_axb = std::abs(ang_PP(uva, uvb)), ang_bxc = std::abs(ang_PP(uvb, uvc)), ang_cxa = std::abs(ang_PP(uvc, uva));
CEXP T _60 = pi_v<T> / 3, _120 = pi_v<T> / 1.5;
check_bool((is_eq(ang_axb, _120) && is_eq(ang_bxc, _120) && is_eq(ang_cxa, _120)) ||
(is_eq(ang_axb, _60) && is_eq(ang_bxc, _60) && is_eq(ang_cxa, _120)) ||
(is_eq(ang_axb, _120) && is_eq(ang_bxc, _60) && is_eq(ang_cxa, _60)) ||
(is_eq(ang_axb, _60) && is_eq(ang_bxc, _120) && is_eq(ang_cxa, _60)),
check_param(t), check_param(x), check_param(uva), check_param(uvb), check_param(uvc), check_param(ang_axb), check_param(ang_bxc), check_param(ang_cxa));
}
template <arithm_c T>
void test(T lim) {
rand_gen<T> g(std::is_signed_v<T> ? -lim : 0, lim);
triangle<T> t(point<T>(g(), g()), point<T>(g(), g()), point<T>(g(), g()));
timer_(test_e(t));
timer_(test_g(t));
timer_(test_h(t));
timer_(test_i(t));
timer_(test_o(t));
timer_(test_n(t));
timer_(test_x(t));
}
int main() {
timer_(test<f64>(1e5));
timer_(test<f128>(1e5));
timer_(test<f64>(1e9));
timer_(test<f128>(1e9));
}
test/cpv_local/geo2d/triangle_centers.cpp