CP-Algorithms Library
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cp-algo/geometry/closest_pair.hpp
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- Last update: 2026-10-16 14:16:08+02:00
- Include:
#include "cp-algo/geometry/closest_pair.hpp"
Depends on
- cp-algo/geometry/point.hpp
- cp-algo/random/rng.hpp
- cp-algo/util/big_alloc.hpp
- cp-algo/util/complex.hpp
- cp-algo/util/simd.hpp
Verified with
Code
#ifndef CP_ALGO_GEOMETRY_CLOSEST_PAIR_HPP
#define CP_ALGO_GEOMETRY_CLOSEST_PAIR_HPP
#include "../random/rng.hpp"
#include "../util/big_alloc.hpp"
#include "point.hpp"
#include <vector>
#include <map>
namespace cp_algo::geometry {
// Rabin & Lipton
auto closest_pair(auto const& r) {
using point = std::decay_t<decltype(r[0])>;
size_t n = size(r);
int64_t md = 1e18;
for(size_t i = 0; i < n / 100; i++) {
auto A = random::rng() % n;
auto B = random::rng() % n;
if(A != B) {
md = std::min(md, norm(r[A] - r[B]));
if(md == 0) {
return std::pair{A, B};
}
}
}
big_map<point, big_vector<size_t>> neigs;
md = (int64_t)ceil(sqrt((double)md));
for(size_t i = 0; i < n; i++) {
neigs[r[i] / md].push_back(i);
}
size_t a = 0, b = 1;
md = norm(r[a] - r[b]);
for(auto &[p, id]: neigs) {
for(int dx: {-1, 0, 1}) {
for(int dy: {-1, 0, 1}) {
auto pp = p + point{dx, dy};
auto it = neigs.find(pp);
if(it == neigs.end()) {
continue;
}
for(size_t i: it->second) {
for(size_t j: id) {
if(j == i) {
break;
}
int64_t cur = norm(r[i] - r[j]);
if(cur < md) {
md = cur;
a = i;
b = j;
}
}
}
}
}
}
return std::pair{a, b};
}
}
#endif // CP_ALGO_GEOMETRY_CLOSEST_PAIR_HPP
#line 1 "cp-algo/geometry/closest_pair.hpp"
#line 1 "cp-algo/random/rng.hpp"
#include <chrono>
#include <random>
namespace cp_algo::random {
std::mt19937_64 gen(
std::chrono::steady_clock::now().time_since_epoch().count()
);
uint64_t rng() {
return gen();
}
}
#line 1 "cp-algo/util/big_alloc.hpp"
#include <set>
#include <map>
#include <deque>
#include <stack>
#include <queue>
#include <vector>
#include <string>
#include <cstddef>
#include <bit>
#include <iostream>
#include <forward_list>
// Single macro to detect POSIX platforms (Linux, Unix, macOS)
#if defined(__linux__) || defined(__unix__) || (defined(__APPLE__) && defined(__MACH__))
#define CP_ALGO_USE_MMAP 1
#include <sys/mman.h>
#else
#define CP_ALGO_USE_MMAP 0
#endif
namespace cp_algo {
template<typename T, size_t Align = 32>
class big_alloc {
static_assert(Align >= alignof(void*), "Align must be at least pointer-size");
static_assert(std::has_single_bit(Align), "Align must be a power of two");
public:
using value_type = T;
template<class U>
struct rebind {
using other = big_alloc<U, Align>;
};
constexpr bool operator==(const big_alloc&) const = default;
big_alloc() noexcept = default;
template<typename U, std::size_t A>
big_alloc(const big_alloc<U, A>&) noexcept {}
[[nodiscard]] T* allocate(std::size_t n) {
std::size_t padded = round_up(n * sizeof(T));
std::size_t align = std::max<std::size_t>(alignof(T), Align);
#if CP_ALGO_USE_MMAP
if(padded >= MEGABYTE) {
void* raw = mmap(nullptr, padded, PROT_READ | PROT_WRITE, MAP_PRIVATE | MAP_ANONYMOUS, -1, 0);
madvise(raw, padded, MADV_HUGEPAGE);
return static_cast<T*>(raw);
}
#endif
return static_cast<T*>(::operator new(padded, std::align_val_t(align)));
}
void deallocate(T* p, std::size_t n) noexcept {
if(!p) {
return;
}
std::size_t padded = round_up(n * sizeof(T));
std::size_t align = std::max<std::size_t>(alignof(T), Align);
#if CP_ALGO_USE_MMAP
if(padded >= MEGABYTE) {
munmap(p, padded);
return;
}
#endif
::operator delete(p, padded, std::align_val_t(align));
}
private:
static constexpr std::size_t MEGABYTE = 1 << 20;
static constexpr std::size_t round_up(std::size_t x) noexcept {
return (x + Align - 1) / Align * Align;
}
};
template<typename T>
using big_vector = std::vector<T, big_alloc<T>>;
template<typename T>
using big_basic_string = std::basic_string<T, std::char_traits<T>, big_alloc<T>>;
template<typename T>
using big_deque = std::deque<T, big_alloc<T>>;
template<typename T>
using big_stack = std::stack<T, big_deque<T>>;
template<typename T>
using big_queue = std::queue<T, big_deque<T>>;
template<typename T>
using big_priority_queue = std::priority_queue<T, big_vector<T>>;
template<typename T>
using big_forward_list = std::forward_list<T, big_alloc<T>>;
using big_string = big_basic_string<char>;
template<typename Key, typename Value, typename Compare = std::less<Key>>
using big_map = std::map<Key, Value, Compare, big_alloc<std::pair<const Key, Value>>>;
template<typename T, typename Compare = std::less<T>>
using big_multiset = std::multiset<T, Compare, big_alloc<T>>;
template<typename T, typename Compare = std::less<T>>
using big_set = std::set<T, Compare, big_alloc<T>>;
}
#line 1 "cp-algo/geometry/point.hpp"
#line 1 "cp-algo/util/complex.hpp"
#line 4 "cp-algo/util/complex.hpp"
#include <cmath>
#include <type_traits>
#line 1 "cp-algo/util/simd.hpp"
#include <experimental/simd>
#include <cstdint>
#line 6 "cp-algo/util/simd.hpp"
#include <memory>
#if defined(__x86_64__) && !defined(CP_ALGO_DISABLE_AVX2)
#define CP_ALGO_SIMD_AVX2_TARGET _Pragma("GCC target(\"avx2,fma\")")
#else
#define CP_ALGO_SIMD_AVX2_TARGET
#endif
#define CP_ALGO_SIMD_PRAGMA_PUSH \
_Pragma("GCC push_options") \
CP_ALGO_SIMD_AVX2_TARGET
CP_ALGO_SIMD_PRAGMA_PUSH
namespace cp_algo {
template<typename T, size_t len>
using simd [[gnu::vector_size(len * sizeof(T))]] = T;
using u64x8 = simd<uint64_t, 8>;
using u32x16 = simd<uint32_t, 16>;
using i64x4 = simd<int64_t, 4>;
using u64x4 = simd<uint64_t, 4>;
using u32x8 = simd<uint32_t, 8>;
using u16x16 = simd<uint16_t, 16>;
using i32x4 = simd<int32_t, 4>;
using u32x4 = simd<uint32_t, 4>;
using u16x8 = simd<uint16_t, 8>;
using u16x4 = simd<uint16_t, 4>;
using i16x4 = simd<int16_t, 4>;
using u8x32 = simd<uint8_t, 32>;
using u8x16 = simd<uint8_t, 16>;
using u8x8 = simd<uint8_t, 8>;
using u8x4 = simd<uint8_t, 4>;
using dx4 = simd<double, 4>;
inline dx4 abs(dx4 a) {
return dx4{
std::abs(a[0]),
std::abs(a[1]),
std::abs(a[2]),
std::abs(a[3])
};
}
// https://stackoverflow.com/a/77376595
// works for ints in (-2^51, 2^51)
static constexpr dx4 magic = dx4() + (3ULL << 51);
inline i64x4 lround(dx4 x) {
return i64x4(x + magic) - i64x4(magic);
}
inline dx4 to_double(i64x4 x) {
return dx4(x + i64x4(magic)) - magic;
}
inline dx4 round(dx4 a) {
return dx4{
std::nearbyint(a[0]),
std::nearbyint(a[1]),
std::nearbyint(a[2]),
std::nearbyint(a[3])
};
}
inline u64x4 low32(u64x4 x) {
return x & uint32_t(-1);
}
inline auto swap_bytes(auto x) {
return decltype(x)(__builtin_shufflevector(u32x8(x), u32x8(x), 1, 0, 3, 2, 5, 4, 7, 6));
}
inline u64x4 montgomery_reduce(u64x4 x, uint32_t mod, uint32_t imod) {
#ifdef __AVX2__
auto x_ninv = u64x4(_mm256_mul_epu32(__m256i(x), __m256i() + imod));
x += u64x4(_mm256_mul_epu32(__m256i(x_ninv), __m256i() + mod));
#else
auto x_ninv = u64x4(u32x8(low32(x)) * imod);
x += x_ninv * uint64_t(mod);
#endif
return swap_bytes(x);
}
// x - mod where x >= mod, for x in [0, 2 mod). Unsigned, so it holds up to mod < 2^31;
// zero upper halves of 64-bit lanes stay zero.
inline u32x8 reduce_once(u32x8 x, uint32_t mod) {
auto y = x - mod;
return x < y ? x : y;
}
inline u64x4 reduce_once(u64x4 x, uint32_t mod) {
return u64x4(reduce_once(u32x8(x), mod));
}
inline u64x4 montgomery_mul(u64x4 x, u64x4 y, uint32_t mod, uint32_t imod) {
#ifdef __AVX2__
return montgomery_reduce(u64x4(_mm256_mul_epu32(__m256i(x), __m256i(y))), mod, imod);
#else
return montgomery_reduce(x * y, mod, imod);
#endif
}
inline u32x8 montgomery_mul(u32x8 x, u32x8 y, uint32_t mod, uint32_t imod) {
return u32x8(montgomery_mul(u64x4(x), u64x4(y), mod, imod)) |
u32x8(swap_bytes(montgomery_mul(u64x4(swap_bytes(x)), u64x4(swap_bytes(y)), mod, imod)));
}
inline dx4 rotate_right(dx4 x) {
static constexpr u64x4 shuffler = {3, 0, 1, 2};
return __builtin_shuffle(x, shuffler);
}
template<std::size_t Align = 32>
inline bool is_aligned(const auto *p) noexcept {
return (reinterpret_cast<std::uintptr_t>(p) % Align) == 0;
}
template<class Target>
inline Target& vector_cast(auto &&p) {
return *reinterpret_cast<Target*>(std::assume_aligned<alignof(Target)>(&p));
}
}
#pragma GCC pop_options
#line 7 "cp-algo/util/complex.hpp"
CP_ALGO_SIMD_PRAGMA_PUSH
namespace cp_algo {
// Custom implementation, since std::complex is UB on non-floating types
template<typename T>
struct complex {
using value_type = T;
T x, y;
inline constexpr complex(): x(), y() {}
inline constexpr complex(T const& x): x(x), y() {}
inline constexpr complex(T const& x, T const& y): x(x), y(y) {}
inline complex& operator *= (T const& t) {x *= t; y *= t; return *this;}
inline complex& operator /= (T const& t) {x /= t; y /= t; return *this;}
inline complex operator * (T const& t) const {return complex(*this) *= t;}
inline complex operator / (T const& t) const {return complex(*this) /= t;}
inline complex& operator += (complex const& t) {x += t.x; y += t.y; return *this;}
inline complex& operator -= (complex const& t) {x -= t.x; y -= t.y; return *this;}
inline complex operator * (complex const& t) const {return {x * t.x - y * t.y, x * t.y + y * t.x};}
inline complex operator / (complex const& t) const {return *this * t.conj() / t.norm();}
inline complex operator + (complex const& t) const {return complex(*this) += t;}
inline complex operator - (complex const& t) const {return complex(*this) -= t;}
inline complex& operator *= (complex const& t) {return *this = *this * t;}
inline complex& operator /= (complex const& t) {return *this = *this / t;}
inline complex operator - () const {return {-x, -y};}
inline complex conj() const {return {x, -y};}
inline T norm() const {return x * x + y * y;}
inline T abs() const {return std::sqrt(norm());}
inline T const real() const {return x;}
inline T const imag() const {return y;}
inline T& real() {return x;}
inline T& imag() {return y;}
inline static constexpr complex polar(T r, T theta) {return {T(r * cos(theta)), T(r * sin(theta))};}
inline auto operator <=> (complex const& t) const = default;
};
template<typename T> inline complex<T> conj(complex<T> const& x) {return x.conj();}
template<typename T> inline T norm(complex<T> const& x) {return x.norm();}
template<typename T> inline T abs(complex<T> const& x) {return x.abs();}
template<typename T> inline T& real(complex<T> &x) {return x.real();}
template<typename T> inline T& imag(complex<T> &x) {return x.imag();}
template<typename T> inline T const real(complex<T> const& x) {return x.real();}
template<typename T> inline T const imag(complex<T> const& x) {return x.imag();}
template<typename T>
inline constexpr complex<T> polar(T r, T theta) {
return complex<T>::polar(r, theta);
}
template<typename T>
inline std::ostream& operator << (std::ostream &out, complex<T> const& x) {
return out << x.real() << ' ' << x.imag();
}
}
#pragma GCC pop_options
#line 5 "cp-algo/geometry/point.hpp"
namespace cp_algo::geometry {
template<typename ftype>
struct point_t: complex<ftype> {
using Base = complex<ftype>;
using Base::Base;
point_t(Base const& t): Base(t) {}
auto operator <=> (point_t const& t) const {
return std::pair{y(), -x()} <=> std::pair{t.y(), -t.x()};
}
ftype x() const {return Base::real();}
ftype y() const {return Base::imag();}
point_t cmul(point_t const& t) const {return conj(*this) * t;}
ftype dot(point_t const& t) const {return cmul(t).x();}
ftype cross(point_t const& t) const {return cmul(t).y();}
static constexpr point_t O = {0, 0};
int half() const {
return *this < O ? -1 : *this == O ? 0 : 1;
}
static bool ccw(point_t const& a, point_t const& b) {
return a.cross(b) > 0;
}
static bool ccw_abs(point_t const& a, point_t const & b) {
return std::tuple{a.half(), (ftype)0, norm(a)} <
std::tuple{b.half(), a.cross(b), norm(b)};
}
void read() {
ftype _x, _y;
std::cin >> _x >> _y;
*this = {_x, _y};
}
void print() const {
std::cout << x() << ' ' << y() << "\n";
}
};
}
#line 8 "cp-algo/geometry/closest_pair.hpp"
namespace cp_algo::geometry {
// Rabin & Lipton
auto closest_pair(auto const& r) {
using point = std::decay_t<decltype(r[0])>;
size_t n = size(r);
int64_t md = 1e18;
for(size_t i = 0; i < n / 100; i++) {
auto A = random::rng() % n;
auto B = random::rng() % n;
if(A != B) {
md = std::min(md, norm(r[A] - r[B]));
if(md == 0) {
return std::pair{A, B};
}
}
}
big_map<point, big_vector<size_t>> neigs;
md = (int64_t)ceil(sqrt((double)md));
for(size_t i = 0; i < n; i++) {
neigs[r[i] / md].push_back(i);
}
size_t a = 0, b = 1;
md = norm(r[a] - r[b]);
for(auto &[p, id]: neigs) {
for(int dx: {-1, 0, 1}) {
for(int dy: {-1, 0, 1}) {
auto pp = p + point{dx, dy};
auto it = neigs.find(pp);
if(it == neigs.end()) {
continue;
}
for(size_t i: it->second) {
for(size_t j: id) {
if(j == i) {
break;
}
int64_t cur = norm(r[i] - r[j]);
if(cur < md) {
md = cur;
a = i;
b = j;
}
}
}
}
}
}
return std::pair{a, b};
}
}
#ifndef CP_ALGO_GEOMETRY_CLOSEST_PAIR_HPP
#define CP_ALGO_GEOMETRY_CLOSEST_PAIR_HPP
#include "../random/rng.hpp"
#include "../util/big_alloc.hpp"
#include "point.hpp"
#include <vector>
#include <map>
namespace cp_algo::geometry{ auto closest_pair(auto const&r){ using point=std::decay_t<decltype(r[0])>; size_t n=size(r); int64_t md=1e18; for(size_t i=0;i<n/100;i++){ auto A=random::rng()%n; auto B=random::rng()%n; if(A!=B){ md=std::min(md,norm(r[A] -r[B])); if(md==0){ return std::pair{A,B}; } } } big_map<point,big_vector<size_t>>neigs; md=(int64_t)ceil(sqrt((double)md)); for(size_t i=0;i<n;i++){ neigs[r[i] /md].push_back(i); } size_t a=0,b=1; md=norm(r[a] -r[b]); for(auto&[p,id]:neigs){ for(int dx:{-1,0,1}){ for(int dy:{-1,0,1}){ auto pp=p+point{dx,dy}; auto it=neigs.find(pp); if(it==neigs.end()){ continue; } for(size_t i:it->second){ for(size_t j:id){ if(j==i){ break; } int64_t cur=norm(r[i] -r[j]); if(cur<md){ md=cur; a=i; b=j; } } } } } } return std::pair{a,b}; } }
#endif
#line 1 "cp-algo/geometry/closest_pair.hpp"
#line 1 "cp-algo/random/rng.hpp"
#include <chrono>
#include <random>
namespace cp_algo::random{ std::mt19937_64 gen( std::chrono::steady_clock::now().time_since_epoch().count() ); uint64_t rng(){ return gen(); } }
#line 1 "cp-algo/util/big_alloc.hpp"
#include <set>
#include <map>
#include <deque>
#include <stack>
#include <queue>
#include <vector>
#include <string>
#include <cstddef>
#include <bit>
#include <iostream>
#include <forward_list>
#if defined(__linux__) || defined(__unix__) || (defined(__APPLE__) && defined(__MACH__))
#define CP_ALGO_USE_MMAP 1
#include <sys/mman.h>
#else
#define CP_ALGO_USE_MMAP 0
#endif
namespace cp_algo{ template<typename T,size_t Align=32> class big_alloc{ static_assert(Align>=alignof(void*),"Align must be at least pointer-size"); static_assert(std::has_single_bit(Align),"Align must be a power of two"); public: using value_type=T; template<class U> struct rebind{ using other=big_alloc<U,Align>; }; constexpr bool operator==(const big_alloc&)const=default; big_alloc()noexcept=default; template<typename U,std::size_t A> big_alloc(const big_alloc<U,A>&)noexcept{} [[nodiscard]]T*allocate(std::size_t n){ std::size_t padded=round_up(n*sizeof(T)); std::size_t align=std::max<std::size_t>(alignof(T),Align);
#if CP_ALGO_USE_MMAP
if(padded>=MEGABYTE){ void*raw=mmap(nullptr,padded,PROT_READ|PROT_WRITE,MAP_PRIVATE|MAP_ANONYMOUS,-1,0); madvise(raw,padded,MADV_HUGEPAGE); return static_cast<T*>(raw); }
#endif
return static_cast<T*>(::operator new(padded,std::align_val_t(align))); } void deallocate(T*p,std::size_t n)noexcept{ if(!p){ return; } std::size_t padded=round_up(n*sizeof(T)); std::size_t align=std::max<std::size_t>(alignof(T),Align);
#if CP_ALGO_USE_MMAP
if(padded>=MEGABYTE){ munmap(p,padded); return; }
#endif
::operator delete(p,padded,std::align_val_t(align)); } private: static constexpr std::size_t MEGABYTE=1<<20; static constexpr std::size_t round_up(std::size_t x)noexcept{ return(x+Align-1)/Align*Align; } }; template<typename T> using big_vector=std::vector<T,big_alloc<T>>; template<typename T> using big_basic_string=std::basic_string<T,std::char_traits<T>,big_alloc<T>>; template<typename T> using big_deque=std::deque<T,big_alloc<T>>; template<typename T> using big_stack=std::stack<T,big_deque<T>>; template<typename T> using big_queue=std::queue<T,big_deque<T>>; template<typename T> using big_priority_queue=std::priority_queue<T,big_vector<T>>; template<typename T> using big_forward_list=std::forward_list<T,big_alloc<T>>; using big_string=big_basic_string<char>; template<typename Key,typename Value,typename Compare=std::less<Key>> using big_map=std::map<Key,Value,Compare,big_alloc<std::pair<const Key,Value>>>; template<typename T,typename Compare=std::less<T>> using big_multiset=std::multiset<T,Compare,big_alloc<T>>; template<typename T,typename Compare=std::less<T>> using big_set=std::set<T,Compare,big_alloc<T>>; }
#line 1 "cp-algo/geometry/point.hpp"
#line 1 "cp-algo/util/complex.hpp"
#line 4 "cp-algo/util/complex.hpp"
#include <cmath>
#include <type_traits>
#line 1 "cp-algo/util/simd.hpp"
#include <experimental/simd>
#include <cstdint>
#line 6 "cp-algo/util/simd.hpp"
#include <memory>
#if defined(__x86_64__) && !defined(CP_ALGO_DISABLE_AVX2)
#define CP_ALGO_SIMD_AVX2_TARGET _Pragma("GCC target(\"avx2,fma\")")
#else
#define CP_ALGO_SIMD_AVX2_TARGET
#endif
#define CP_ALGO_SIMD_PRAGMA_PUSH _Pragma("GCC push_options") CP_ALGO_SIMD_AVX2_TARGET
CP_ALGO_SIMD_PRAGMA_PUSH
namespace cp_algo{ template<typename T,size_t len> using simd[[gnu::vector_size(len*sizeof(T))]] =T; using u64x8=simd<uint64_t,8>; using u32x16=simd<uint32_t,16>; using i64x4=simd<int64_t,4>; using u64x4=simd<uint64_t,4>; using u32x8=simd<uint32_t,8>; using u16x16=simd<uint16_t,16>; using i32x4=simd<int32_t,4>; using u32x4=simd<uint32_t,4>; using u16x8=simd<uint16_t,8>; using u16x4=simd<uint16_t,4>; using i16x4=simd<int16_t,4>; using u8x32=simd<uint8_t,32>; using u8x16=simd<uint8_t,16>; using u8x8=simd<uint8_t,8>; using u8x4=simd<uint8_t,4>; using dx4=simd<double,4>; inline dx4 abs(dx4 a){ return dx4{ std::abs(a[0]), std::abs(a[1]), std::abs(a[2]), std::abs(a[3]) }; } static constexpr dx4 magic=dx4()+(3ULL<<51); inline i64x4 lround(dx4 x){ return i64x4(x+magic)-i64x4(magic); } inline dx4 to_double(i64x4 x){ return dx4(x+i64x4(magic))-magic; } inline dx4 round(dx4 a){ return dx4{ std::nearbyint(a[0]), std::nearbyint(a[1]), std::nearbyint(a[2]), std::nearbyint(a[3]) }; } inline u64x4 low32(u64x4 x){ return x&uint32_t(-1); } inline auto swap_bytes(auto x){ return decltype(x)(__builtin_shufflevector(u32x8(x),u32x8(x),1,0,3,2,5,4,7,6)); } inline u64x4 montgomery_reduce(u64x4 x,uint32_t mod,uint32_t imod){
#ifdef __AVX2__
auto x_ninv=u64x4(_mm256_mul_epu32(__m256i(x),__m256i()+imod)); x+=u64x4(_mm256_mul_epu32(__m256i(x_ninv),__m256i()+mod));
#else
auto x_ninv=u64x4(u32x8(low32(x))*imod); x+=x_ninv*uint64_t(mod);
#endif
return swap_bytes(x); } inline u32x8 reduce_once(u32x8 x,uint32_t mod){ auto y=x-mod; return x<y?x:y; } inline u64x4 reduce_once(u64x4 x,uint32_t mod){ return u64x4(reduce_once(u32x8(x),mod)); } inline u64x4 montgomery_mul(u64x4 x,u64x4 y,uint32_t mod,uint32_t imod){
#ifdef __AVX2__
return montgomery_reduce(u64x4(_mm256_mul_epu32(__m256i(x),__m256i(y))),mod,imod);
#else
return montgomery_reduce(x*y,mod,imod);
#endif
} inline u32x8 montgomery_mul(u32x8 x,u32x8 y,uint32_t mod,uint32_t imod){ return u32x8(montgomery_mul(u64x4(x),u64x4(y),mod,imod))| u32x8(swap_bytes(montgomery_mul(u64x4(swap_bytes(x)),u64x4(swap_bytes(y)),mod,imod))); } inline dx4 rotate_right(dx4 x){ static constexpr u64x4 shuffler={3,0,1,2}; return __builtin_shuffle(x,shuffler); } template<std::size_t Align=32> inline bool is_aligned(const auto*p)noexcept{ return(reinterpret_cast<std::uintptr_t>(p)%Align)==0; } template<class Target> inline Target&vector_cast(auto&&p){ return*reinterpret_cast<Target*>(std::assume_aligned<alignof(Target)>(&p)); } }
#pragma GCC pop_options
#line 7 "cp-algo/util/complex.hpp"
CP_ALGO_SIMD_PRAGMA_PUSH
namespace cp_algo{ template<typename T> struct complex{ using value_type=T; T x,y; inline constexpr complex():x(),y(){} inline constexpr complex(T const&x):x(x),y(){} inline constexpr complex(T const&x,T const&y):x(x),y(y){} inline complex&operator*=(T const&t){x*=t;y*=t;return*this;} inline complex&operator/=(T const&t){x/=t;y/=t;return*this;} inline complex operator*(T const&t)const{return complex(*this)*=t;} inline complex operator/(T const&t)const{return complex(*this)/=t;} inline complex&operator+=(complex const&t){x+=t.x;y+=t.y;return*this;} inline complex&operator-=(complex const&t){x-=t.x;y-=t.y;return*this;} inline complex operator*(complex const&t)const{return{x*t.x-y*t.y,x*t.y+y*t.x};} inline complex operator/(complex const&t)const{return*this*t.conj()/t.norm();} inline complex operator+(complex const&t)const{return complex(*this)+=t;} inline complex operator-(complex const&t)const{return complex(*this)-=t;} inline complex&operator*=(complex const&t){return*this= *this*t;} inline complex&operator/=(complex const&t){return*this= *this/t;} inline complex operator-()const{return{-x,-y};} inline complex conj()const{return{x,-y};} inline T norm()const{return x*x+y*y;} inline T abs()const{return std::sqrt(norm());} inline T const real()const{return x;} inline T const imag()const{return y;} inline T&real(){return x;} inline T&imag(){return y;} inline static constexpr complex polar(T r,T theta){return{T(r*cos(theta)),T(r*sin(theta))};} inline auto operator<=>(complex const&t)const=default; }; template<typename T>inline complex<T>conj(complex<T>const&x){return x.conj();} template<typename T>inline T norm(complex<T>const&x){return x.norm();} template<typename T>inline T abs(complex<T>const&x){return x.abs();} template<typename T>inline T&real(complex<T> &x){return x.real();} template<typename T>inline T&imag(complex<T> &x){return x.imag();} template<typename T>inline T const real(complex<T>const&x){return x.real();} template<typename T>inline T const imag(complex<T>const&x){return x.imag();} template<typename T> inline constexpr complex<T>polar(T r,T theta){ return complex<T>::polar(r,theta); } template<typename T> inline std::ostream&operator<<(std::ostream&out,complex<T>const&x){ return out<<x.real()<<' '<<x.imag(); } }
#pragma GCC pop_options
#line 5 "cp-algo/geometry/point.hpp"
namespace cp_algo::geometry{ template<typename ftype> struct point_t:complex<ftype>{ using Base=complex<ftype>; using Base::Base; point_t(Base const&t):Base(t){} auto operator<=>(point_t const&t)const{ return std::pair{y(),-x()}<=>std::pair{t.y(),-t.x()}; } ftype x()const{return Base::real();} ftype y()const{return Base::imag();} point_t cmul(point_t const&t)const{return conj(*this)*t;} ftype dot(point_t const&t)const{return cmul(t).x();} ftype cross(point_t const&t)const{return cmul(t).y();} static constexpr point_t O={0,0}; int half()const{ return*this<O?-1: *this==O?0:1; } static bool ccw(point_t const&a,point_t const&b){ return a.cross(b)>0; } static bool ccw_abs(point_t const&a,point_t const&b){ return std::tuple{a.half(),(ftype)0,norm(a)}< std::tuple{b.half(),a.cross(b),norm(b)}; } void read(){ ftype _x,_y; std::cin>>_x>>_y; *this={_x,_y}; } void print()const{ std::cout<<x()<<' '<<y()<<"\n"; } }; }
#line 8 "cp-algo/geometry/closest_pair.hpp"
namespace cp_algo::geometry{ auto closest_pair(auto const&r){ using point=std::decay_t<decltype(r[0])>; size_t n=size(r); int64_t md=1e18; for(size_t i=0;i<n/100;i++){ auto A=random::rng()%n; auto B=random::rng()%n; if(A!=B){ md=std::min(md,norm(r[A] -r[B])); if(md==0){ return std::pair{A,B}; } } } big_map<point,big_vector<size_t>>neigs; md=(int64_t)ceil(sqrt((double)md)); for(size_t i=0;i<n;i++){ neigs[r[i] /md].push_back(i); } size_t a=0,b=1; md=norm(r[a] -r[b]); for(auto&[p,id]:neigs){ for(int dx:{-1,0,1}){ for(int dy:{-1,0,1}){ auto pp=p+point{dx,dy}; auto it=neigs.find(pp); if(it==neigs.end()){ continue; } for(size_t i:it->second){ for(size_t j:id){ if(j==i){ break; } int64_t cur=norm(r[i] -r[j]); if(cur<md){ md=cur; a=i; b=j; } } } } } } return std::pair{a,b}; } }