// competitive-verifier: LOCALCASE test/cpv_local/_data/bzoj/2731
#include "../../../src/edh/discretization/lib.hpp"
#include "../../../src/math/simpson/lib.hpp"
using namespace tifa_libs;
using std::cin, std::cout;
using data_t = f128;
struct Node {
int x, y, m;
Node(int x = 0, int y = 0, int m = 0) : x(x), y(y), m(m) {}
};
vec<Node> v;
vecpt<data_t> seg;
template <class T>
T f(T pos) {
seg.clear();
for (auto [x, y, m] : v)
if (x < pos && pos < x + m) seg.emplace_back(y, x + y + m - pos);
if (seg.empty()) return 0;
std::ranges::sort(seg);
data_t ans = 0, lst = seg.front().first;
for (auto&& [l, r] : seg)
if (r - lst > 0) {
ans += r - std::max(l, lst);
lst = r;
}
return (T)ans;
}
CEXP data_t EPS = 1e-10l;
int main() {
cout << std::fixed << std::setprecision(1);
u32 n;
cin >> n;
v.clear();
vec<Node> v_(n);
for (auto& [x, y, m] : v_) cin >> y >> x >> m;
std::ranges::sort(v_, [](Node CR l, Node CR r) { return l.m > r.m; });
v.push_back(v_.front());
flt_ (u32, i, 1, n) {
auto&& now = v_[i];
if (now.m == 0) break;
if (std::ranges::none_of(v, [&now](Node CR x) { return now.x >= x.x && now.x + now.m <= x.x + x.m && now.y >= x.y && now.y + now.m <= x.y + x.m && now.x + now.y + now.m <= x.x + x.y + x.m; })) v.push_back(now);
}
seg.reserve(n);
vec<int> pos;
pos.reserve(n * 2);
for (auto&& [x, _, m] : v) {
pos.push_back(x);
pos.push_back(x + m);
}
pos = uniq(pos);
data_t ans = 0;
simpson_impl<f64, f<f64>> integral;
flt_ (u32, i, 1, (u32)pos.size()) ans += integral(f64(pos[i - 1] + EPS), f64(pos[i] - 2 * EPS), (f64)EPS);
cout << ans << '\n';
}
#line 1 "test/cpv_local/math/simpson.bzoj2731.cpp"
// competitive-verifier: LOCALCASE test/cpv_local/_data/bzoj/2731
#line 2 "src/edh/discretization/lib.hpp"
#line 2 "src/fast/rsort32/lib.hpp"
#line 2 "src/util/alias/others/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 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/fast/rsort32/lib.hpp"
namespace tifa_libs {
template <class C>
requires(std::is_array_v<C> && std::integral<decltype(std::declval<C>()[0])> && sizeof(std::declval<C>()[0]) == 4) || (std::contiguous_iterator<TPN C::iterator> && std::integral<TPN C::value_type> && sizeof(TPN C::value_type) == 4)
void rsort32(C& a) NE {
if (a.size() <= 1) return;
if (a.size() <= 200'000) {
std::ranges::sort(a);
return;
}
arr<u32, 256> _0{}, _1{}, _2{}, _3{};
cu32 n = (u32)a.size();
vecu b(n);
u32 *a_ = (u32*)a.data(), *b_ = (u32*)b.data();
for (cu32 *_ = a_ + n, *i = a_; i < _; ++i) ++_0[*i & 255], ++_1[*i >> 8 & 255], ++_2[*i >> 16 & 255], ++_3[*i >> 24 & 255];
flt_ (u32, i, 1, 256) _0[i] += _0[i - 1], _1[i] += _1[i - 1], _2[i] += _2[i - 1], _3[i] += _3[i - 1];
for (u32 CP i = a_ + n; --i >= a_;) b_[--_0[*i & 255]] = *i;
for (u32 CP i = b_ + n; --i >= b_;) a_[--_1[*i >> 8 & 255]] = *i;
for (u32 CP i = a_ + n; --i >= a_;) b_[--_2[*i >> 16 & 255]] = *i;
for (u32 CP i = b_ + n; --i >= b_;) a_[--_3[*i >> 24 & 255]] = *i;
if CEXP (std::is_signed_v<TPN C::value_type>) {
u32 i = n;
while (i && a[i - 1] < 0) --i;
rotate(a_, a_ + n, a_ + i);
}
}
template <class C>
requires(std::is_array_v<C> && std::integral<decltype(std::declval<C>()[0])> && sizeof(std::declval<C>()[0]) == 4) || range<C>
void sort(C& a) NE {
if CEXP (std::is_array_v<C> || (std::contiguous_iterator<TPN C::iterator> && std::integral<TPN C::value_type> && sizeof(TPN C::value_type) == 4)) rsort32(a);
else std::ranges::sort(a);
}
} // namespace tifa_libs
#line 4 "src/edh/discretization/lib.hpp"
namespace tifa_libs {
template <common_range T>
CEXP T uniq(T v) NE {
tifa_libs::sort(v);
auto r = unique(begin(v), end(v));
return {begin(v), begin(r)};
}
template <common_range T>
CEXP std::pair<T, vecu> gen_id(T CR v) NE {
const T _ = uniq(v);
vecu _1;
_1.reserve(v.size());
flt_ (u32, i, 0, (u32)v.size()) _1.push_back(u32(lower_bound(_, v[i]) - begin(_)));
return {_, _1};
}
} // namespace tifa_libs
#line 2 "src/math/simpson/lib.hpp"
#line 4 "src/math/simpson/lib.hpp"
namespace tifa_libs {
template <std::floating_point FP, FP (*f)(FP)>
class simpson_impl {
static CEXP FP sps(FP l, FP r, FP fl, FP fmid, FP fr) NE { return (fl + 4 * fmid + fr) * (r - l) / 6; }
CEXP FP asr(FP l, FP r, FP area, FP eps, i64 dep) CNE {
const FP mid = r - (r - l) * .5, lmid = mid - (mid - l) * .5, rmid = r - (r - mid) * .5;
const FP fl = f(l), flmid = f(lmid), fmid = f(mid), frmid = f(rmid), fr = f(r);
const FP ls = sps(l, mid, fl, flmid, fmid), rs = sps(mid, r, fmid, frmid, fr);
if (abs(ls + rs - area) <= 15 * eps && dep <= 0) return ls + rs + (ls + rs - area) / 15;
return asr(l, mid, ls, eps * .5, dep - 1) + asr(mid, r, rs, eps * .5, dep - 1);
}
public:
CEXP FP operator()(FP l, FP r, FP eps = eps_v<FP>, i64 min_dep = -1) CNE { return asr(l, r, sps(l, r, f(l), f(r - (r - l) * .5), f(r)), eps, min_dep); }
};
} // namespace tifa_libs
#line 5 "test/cpv_local/math/simpson.bzoj2731.cpp"
using namespace tifa_libs;
using std::cin, std::cout;
using data_t = f128;
struct Node {
int x, y, m;
Node(int x = 0, int y = 0, int m = 0) : x(x), y(y), m(m) {}
};
vec<Node> v;
vecpt<data_t> seg;
template <class T>
T f(T pos) {
seg.clear();
for (auto [x, y, m] : v)
if (x < pos && pos < x + m) seg.emplace_back(y, x + y + m - pos);
if (seg.empty()) return 0;
std::ranges::sort(seg);
data_t ans = 0, lst = seg.front().first;
for (auto&& [l, r] : seg)
if (r - lst > 0) {
ans += r - std::max(l, lst);
lst = r;
}
return (T)ans;
}
CEXP data_t EPS = 1e-10l;
int main() {
cout << std::fixed << std::setprecision(1);
u32 n;
cin >> n;
v.clear();
vec<Node> v_(n);
for (auto& [x, y, m] : v_) cin >> y >> x >> m;
std::ranges::sort(v_, [](Node CR l, Node CR r) { return l.m > r.m; });
v.push_back(v_.front());
flt_ (u32, i, 1, n) {
auto&& now = v_[i];
if (now.m == 0) break;
if (std::ranges::none_of(v, [&now](Node CR x) { return now.x >= x.x && now.x + now.m <= x.x + x.m && now.y >= x.y && now.y + now.m <= x.y + x.m && now.x + now.y + now.m <= x.x + x.y + x.m; })) v.push_back(now);
}
seg.reserve(n);
vec<int> pos;
pos.reserve(n * 2);
for (auto&& [x, _, m] : v) {
pos.push_back(x);
pos.push_back(x + m);
}
pos = uniq(pos);
data_t ans = 0;
simpson_impl<f64, f<f64>> integral;
flt_ (u32, i, 1, (u32)pos.size()) ans += integral(f64(pos[i - 1] + EPS), f64(pos[i] - 2 * EPS), (f64)EPS);
cout << ans << '\n';
}
test/cpv_local/math/simpson.bzoj2731.cpp