結果
| 問題 |
No.3042 拡大コピー
|
| ユーザー |
 noya2
|
| 提出日時 | 2025-02-28 23:22:21 |
| 言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 390 ms / 2,000 ms |
| コード長 | 17,757 bytes |
| コンパイル時間 | 6,372 ms |
| コンパイル使用メモリ | 559,864 KB |
| 実行使用メモリ | 18,172 KB |
| 最終ジャッジ日時 | 2025-03-01 07:42:20 |
| 合計ジャッジ時間 | 8,313 ms |
|
ジャッジサーバーID （参考情報） |
judge4 / judge1 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 1 |
| other | AC * 24 |
ソースコード
#line 2 "/Users/noya2/Desktop/Noya2_library/template/template.hpp"
using namespace std;
#include<bits/stdc++.h>
#line 1 "/Users/noya2/Desktop/Noya2_library/template/inout_old.hpp"
namespace noya2 {
template <typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &p){
os << p.first << " " << p.second;
return os;
}
template <typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &p){
is >> p.first >> p.second;
return is;
}
template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v){
int s = (int)v.size();
for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];
return os;
}
template <typename T>
istream &operator>>(istream &is, vector<T> &v){
for (auto &x : v) is >> x;
return is;
}
void in() {}
template <typename T, class... U>
void in(T &t, U &...u){
cin >> t;
in(u...);
}
void out() { cout << "\n"; }
template <typename T, class... U, char sep = ' '>
void out(const T &t, const U &...u){
cout << t;
if (sizeof...(u)) cout << sep;
out(u...);
}
template<typename T>
void out(const vector<vector<T>> &vv){
int s = (int)vv.size();
for (int i = 0; i < s; i++) out(vv[i]);
}
struct IoSetup {
IoSetup(){
cin.tie(nullptr);
ios::sync_with_stdio(false);
cout << fixed << setprecision(15);
cerr << fixed << setprecision(7);
}
} iosetup_noya2;
} // namespace noya2
#line 1 "/Users/noya2/Desktop/Noya2_library/template/const.hpp"
namespace noya2{
const int iinf = 1'000'000'007;
const long long linf = 2'000'000'000'000'000'000LL;
const long long mod998 = 998244353;
const long long mod107 = 1000000007;
const long double pi = 3.14159265358979323;
const vector<int> dx = {0,1,0,-1,1,1,-1,-1};
const vector<int> dy = {1,0,-1,0,1,-1,-1,1};
const string ALP = "ABCDEFGHIJKLMNOPQRSTUVWXYZ";
const string alp = "abcdefghijklmnopqrstuvwxyz";
const string NUM = "0123456789";
void yes(){ cout << "Yes\n"; }
void no(){ cout << "No\n"; }
void YES(){ cout << "YES\n"; }
void NO(){ cout << "NO\n"; }
void yn(bool t){ t ? yes() : no(); }
void YN(bool t){ t ? YES() : NO(); }
} // namespace noya2
#line 2 "/Users/noya2/Desktop/Noya2_library/template/utils.hpp"
#line 6 "/Users/noya2/Desktop/Noya2_library/template/utils.hpp"
namespace noya2{
unsigned long long inner_binary_gcd(unsigned long long a, unsigned long long b){
if (a == 0 || b == 0) return a + b;
int n = __builtin_ctzll(a); a >>= n;
int m = __builtin_ctzll(b); b >>= m;
while (a != b) {
int mm = __builtin_ctzll(a - b);
bool f = a > b;
unsigned long long c = f ? a : b;
b = f ? b : a;
a = (c - b) >> mm;
}
return a << std::min(n, m);
}
template<typename T> T gcd_fast(T a, T b){ return static_cast<T>(inner_binary_gcd(std::abs(a),std::abs(b))); }
long long sqrt_fast(long long n) {
if (n <= 0) return 0;
long long x = sqrt(n);
while ((x + 1) * (x + 1) <= n) x++;
while (x * x > n) x--;
return x;
}
template<typename T> T floor_div(const T n, const T d) {
assert(d != 0);
return n / d - static_cast<T>((n ^ d) < 0 && n % d != 0);
}
template<typename T> T ceil_div(const T n, const T d) {
assert(d != 0);
return n / d + static_cast<T>((n ^ d) >= 0 && n % d != 0);
}
template<typename T> void uniq(std::vector<T> &v){
std::sort(v.begin(),v.end());
v.erase(unique(v.begin(),v.end()),v.end());
}
template <typename T, typename U> inline bool chmin(T &x, U y) { return (y < x) ? (x = y, true) : false; }
template <typename T, typename U> inline bool chmax(T &x, U y) { return (x < y) ? (x = y, true) : false; }
template<typename T> inline bool range(T l, T x, T r){ return l <= x && x < r; }
} // namespace noya2
#line 8 "/Users/noya2/Desktop/Noya2_library/template/template.hpp"
#define rep(i,n) for (int i = 0; i < (int)(n); i++)
#define repp(i,m,n) for (int i = (m); i < (int)(n); i++)
#define reb(i,n) for (int i = (int)(n-1); i >= 0; i--)
#define all(v) (v).begin(),(v).end()
using ll = long long;
using ld = long double;
using uint = unsigned int;
using ull = unsigned long long;
using pii = pair<int,int>;
using pll = pair<ll,ll>;
using pil = pair<int,ll>;
using pli = pair<ll,int>;
namespace noya2{
/* ~ (. _________ . /) */
}
using namespace noya2;
#line 2 "c.cpp"
#line 2 "/Users/noya2/Desktop/Noya2_library/geometry/float_geometry.hpp"
#include <type_traits>
#include <concepts>
#include <compare>
#line 12 "/Users/noya2/Desktop/Noya2_library/geometry/float_geometry.hpp"
#include <ranges>
#if __has_include(<boost/multiprecision/cpp_bin_float.hpp>)
#include<boost/multiprecision/cpp_bin_float.hpp>
#endif
namespace float_geometry {
template<class T>
struct is_floating_point_number : std::bool_constant<false> {};
template<std::floating_point F>
struct is_floating_point_number<F> : std::bool_constant<true> {};
#if __has_include(<boost/multiprecision/cpp_bin_float.hpp>)
template<unsigned D>
struct is_floating_point_number<boost::multiprecision::number<boost::multiprecision::backends::cpp_bin_float<D>>> : std::bool_constant<true> {};
template<unsigned D>
struct is_floating_point_number<boost::multiprecision::number<boost::multiprecision::backends::cpp_dec_float<D>>> : std::bool_constant<true> {};
#endif
template<class F>
concept FloatingPoint = is_floating_point_number<F>::value;
template<FloatingPoint Float>
constexpr Float EPS = Float{1e-6};
template<FloatingPoint Float>
constexpr int sign(const Float &x, Float eps = EPS<Float>){
return (x < -eps ? -1 : x > eps ? 1 : 0);
}
template<FloatingPoint Float>
struct point {
Float x, y;
point () {}
point (Float _x, Float _y) : x(_x), y(_y) {}
point &operator+=(const point &r){
x += r.x;
y += r.y;
return *this;
}
point &operator-=(const point &r){
x -= r.x;
y -= r.y;
return *this;
}
point operator+() const {
return *this;
}
point operator-() const {
x = -x;
y = -y;
return *this;
}
point &operator*=(const Float &a){
x *= a;
y *= a;
return *this;
}
point &operator/=(const Float &a){
x /= a;
y /= a;
return *this;
}
friend point operator+(const point& lhs, const point& rhs){
return point(lhs) += rhs;
}
friend point operator-(const point& lhs, const point& rhs){
return point(lhs) -= rhs;
}
friend point operator*(const point& lhs, const Float& a){
return point(lhs) *= a;
}
friend point operator*(const Float& a, const point& rhs){
return point(rhs) *= a;
}
friend point operator/(const point& lhs, const Float& a){
return point(lhs) /= a;
}
auto operator<=>(const point&) const = default;
friend std::ostream &operator<<(std::ostream &os, const point& p){
return os << p.x << ' ' << p.y;
}
friend std::istream &operator>>(std::istream &is, point &a){
Float _x, _y; is >> _x >> _y;
a = point(_x, _y);
return (is);
}
friend Float norm(const point &a) {
return a.x*a.x + a.y*a.y;
}
friend Float dot(const point &a, const point &b){
return a.x*b.x + a.y*b.y;
}
friend Float cross(const point &a, const point &b){
return a.x*b.y - a.y*b.x;
}
friend point rot90(const point &a){
return point(-a.y, a.x);
}
friend point rot(const point &a, const Float rad){
using std::cos, std::sin;
Float cosrad = cos(rad);
Float sinrad = sin(rad);
return point(a.x * cosrad - a.y * sinrad, a.x * sinrad + a.y * cosrad);
}
friend Float abs(const point &a){
using std::sqrt;
return sqrt(norm(a));
}
friend int quadrant_atan2(const point &a){
// not origin point
// ceil ( atan2(y,x) / (pi/2) )
int signx = sign(a.x);
int signy = sign(a.y);
if (signx <= 0 && signy < 0) return -1;
if (signx > 0 && signy <= 0) return 0;
if (signx >= 0 && signy > 0) return 1;
if (signx < 0 && signy >= 0) return 2;
// origin point x == 0 && y == 0
return 0;
}
friend int sign_cross(const point &a, const point &b){
using std::abs;
return sign(cross(a, b), EPS<Float> * (abs(a.x) + abs(a.y) + abs(b.x) + abs(b.y)));
}
friend int sign_dot(const point &a, const point &b){
using std::abs;
return sign(dot(a, b), EPS<Float> * (abs(a.x) + abs(a.y) + abs(b.x) + abs(b.y)));
}
friend int ccw(const point &a, point b, point c){
b -= a;
c -= a;
int signcr = sign_cross(b, c);
if (signcr > 0){
// ccw
// c
// a --> b
return 1;
}
if (signcr < 0){
// cw
// a --> b
// c
return -1;
}
if (sign_dot(b, c) < 0){
// c a --> b
return 2;
}
if (norm(b) < norm(c)){
// a --> b c
return -2;
}
// a - c -> b
return 0;
}
friend bool has_common_point(const point &a, const point &b){
return sign(a.x - b.x) == 0 && sign(a.y - b.y) == 0;
}
};
template<FloatingPoint Float>
struct arg_less {
constexpr bool operator()(const point<Float> &l, const point<Float> &r){
using std::atan2;
return atan2(l.y, l.x) < atan2(r.y, r.x);
}
};
template<FloatingPoint Float>
void arg_sort(std::vector<point<Float>> &a){
std::sort(a.begin(), a.end(), arg_less<Float>{});
}
template<FloatingPoint Point>
std::vector<int> upper_convex_hull_index(const std::vector<Point> &a){
if (a.empty()) return {};
std::vector<int> ids(a.size());
std::iota(ids.begin(), ids.end(), 0);
std::sort(ids.begin(), ids.end(), [&](int l, int r){
return a[l] < a[r];
});
std::vector<int> st(a.size());
int ptr = 0;
for (int i : ids){
if (ptr >= 1 && a[st[ptr-1]].x == a[i].x) ptr--;
while (ptr >= 2){
int c = st[ptr-1];
int p = st[ptr-2];
if (sign_cross(a[i] - a[c], a[c] - a[p]) > 0){
break;
}
ptr--;
}
st[ptr++] = i;
}
st.resize(ptr);
return st;
}
template<FloatingPoint Float>
std::vector<int> lower_convex_hull_index(const std::vector<point<Float>> &a){
if (a.empty()) return {};
std::vector<int> ids(a.size());
std::iota(ids.begin(), ids.end(), 0);
std::sort(ids.begin(), ids.end(), [&](int l, int r){
return a[l] < a[r];
});
std::vector<int> st(a.size());
int ptr = 0;
for (int i : ids){
if (ptr >= 1 && a[st[ptr-1]].x == a[i].x) continue;
while (ptr >= 2){
int c = st[ptr-1];
int p = st[ptr-2];
if (sign_cross(a[c] - a[p], a[i] - a[c]) > 0){
break;
}
ptr--;
}
st[ptr++] = i;
}
st.resize(ptr);
return st;
}
template<FloatingPoint Point>
std::vector<int> convex_hull_index(const std::vector<Point> &a){
if (a.empty()) return {};
auto upper = upper_convex_hull_index(a);
auto lower = lower_convex_hull_index(a);
if (upper.size() == 1u){
// lower.size() == 1u
if (a[upper.front()] == a[lower.front()]){
return {upper.front()};
}
return {lower.front(), upper.front()};
}
if (a[upper.back()] == a[lower.back()]){
lower.pop_back();
}
lower.insert(lower.end(), upper.rbegin(), upper.rend());
if (a[upper.front()] == a[lower.front()]) lower.pop_back();
return lower;
}
template<FloatingPoint Float>
struct line {
point<Float> end0, end1;
line () {}
line (const point<Float> &_end0, const point<Float> &_end1) : end0(_end0), end1(_end1) {
assert(end0 != end1);
}
auto operator<=>(const line &) const = default;
point<Float> direction() const {
return end1 - end0;
}
friend bool is_parallel(const line &a, const line &b){
return sign_cross(a.direction(), b.direction()) == 0;
}
friend bool is_orthgonal(const line &a, const line &b){
return sign_dot(a.direction(), b.direction()) == 0;
}
friend bool has_common_point(const line &a, const point<Float> &b){
return sign(cross(a.direction(), b - a.end0)) == 0;
}
friend bool has_common_point(const line &a, const line &b){
return !is_parallel(a, b) || has_common_point(a, b.end0);
}
friend point<Float> common_point(const line &a, const line &b){
// assert(has_common_point(a, b));
if (is_parallel(a, b)){
return a.end0;
}
return a.end0 + a.direction() * cross(b.end0 - a.end0, b.end1 - b.end0) / cross(a.direction(), b.direction());
}
friend point<Float> projection(const line &a, const point<Float> &b){
auto dir = a.direction();
return a.end0 + dir * (dot(dir, b - a.end0) / norm(dir));
}
friend point<Float> reflection(const line &a, const point<Float> &b){
auto prj = projection(a, b);
return prj + prj - b;
}
friend line<Float> perpendicular_bisector(const point<Float> &p1, const point<Float> &p2){
auto ctr = (p1 + p2) / Float{2};
auto dir = rot90(p2 - p1);
return line<Float>(ctr, ctr + dir);
}
};
template<FloatingPoint Float>
line<Float> perpendicular_bisector(const point<Float> &p1, const point<Float> &p2){
auto ctr = (p1 + p2) / Float{2};
auto dir = rot90(p2 - p1);
return line<Float>(ctr, ctr + dir);
}
template<FloatingPoint Float>
struct segment {
point<Float> end0, end1;
segment () {}
segment (const point<Float> &_end0, const point<Float> &_end1) : end0(_end0), end1(_end1) {
assert(end0 != end1);
}
auto operator<=>(const segment &) const = default;
point<Float> direction() const {
return end1 - end0;
}
friend bool is_parallel(const segment &a, const segment &b){
return sign_cross(a.direction(), b.direction()) == 0;
}
friend bool is_orthgonal(const segment &a, const segment &b){
return sign_dot(a.direction(), b.direction()) == 0;
}
friend bool has_common_point(const segment &a, const segment &b){
return ccw(a.end0, a.end1, b.end0) * ccw(a.end0, a.end1, b.end1) <= 0
&& ccw(b.end0, b.end1, a.end0) * ccw(b.end0, b.end1, a.end1) <= 0;
}
friend bool has_common_point(const segment &a, const point<Float> &b){
return ccw(a.end0, a.end1, b) == 0;
}
friend point<Float> common_point(const segment &a, const segment &b){
// assert(has_common_point(a, b));
if (is_parallel(a, b)){
if (has_common_point(a, b.end0)){
return b.end0;
}
if (has_common_point(a, b.end1)){
return b.end1;
}
return a.end0;
}
return a.end0 + a.direction() * cross(b.end0 - a.end0, b.end1 - b.end0) / cross(a.direction(), b.direction());
}
line<Float> as_line() const {
return line<Float>(end0, end1);
}
};
template<FloatingPoint Float>
struct circle {
point<Float> center;
Float radius;
circle () {}
circle (const point<Float> &_center, const Float &_radius) : center(_center), radius(_radius) {
assert(sign(radius) >= 0);
if (radius < Float{}){
radius = Float{};
}
}
friend int num_of_common_tangents(const circle &a, const circle &b){
if (has_common_point(a.center, b.center) && sign(a.radius - b.radius) == 0){
return 5; // infty
}
Float d = abs(a.center - b.center);
Float r1 = a.radius, r2 = b.radius;
int sumsign = sign(d - (r1 + r2));
if (sumsign >= 0) return sumsign + 3;
using std::abs;
int diffsign = sign(d - abs(r1 - r2));
return diffsign + 1;
}
friend bool has_common_point(const circle &a, const circle &b){
int cnt = num_of_common_tangents(a, b);
return cnt == 1 || cnt == 2 || cnt == 3 || cnt == 5;
}
friend bool has_common_point(const circle &c, const line<Float> &l){
point<Float> p = reflection(l, c.center);
Float d = abs(c.center, p);
return sign(c.radius - d) >= 0;
}
friend bool has_common_point(const circle &c, const segment<Float> &s){
return std::ranges::any_of(common_points(c, s.as_line()), [&](auto p){
return has_common_point(s, p);
});
}
friend bool has_common_point(const circle &c, const point<Float> &p){
return sign(abs(p - c.center) - c.radius) == 0;
}
friend std::vector<point<Float>> common_points(const circle &a, const circle &b){
int cnt = num_of_common_tangents(a, b);
assert(cnt != 5); // cannot be same circle
if (cnt == 0 || cnt == 4){
return {};
}
Float d = abs(a.center - b.center);
Float x = (d*d + a.radius*a.radius - b.radius*b.radius) / (d + d);
point<Float> p = a.center + (b.center - a.center) * x / d;
if (cnt == 1 || cnt == 3 || sign(a.radius - x) <= 0){
return {p};
}
point<Float> v = rot90(b.center - a.center);
using std::sqrt;
v *= sqrt(a.radius*a.radius - x*x) / abs(v);
return {p + v, p - v};
}
friend std::vector<point<Float>> common_points(const circle &c, const line<Float> &l) {
point<Float> p = reflection(l, c.center);
Float d = abs(c.center, p);
int cnt = sign(c.radius - d) + 1;
if (cnt == 0){
return {};
}
if (cnt == 1 || sign(c.radius - d) <= 0){
return {p};
}
point<Float> v = l.direction();
using std::sqrt;
v *= sqrt(c.radius*c.radius - d*d) / abs(v);
return {p + v, p - v};
}
};
} // float_geometry
#line 4 "c.cpp"
using namespace float_geometry;
using vec = point<ld>;
vec center(const vector<vec> &a){
vec sum(0,0);
int n = a.size();
rep(i,n){
sum += a[i];
}
sum /= a.size();
return sum;
}
ld farest(const vector<vec> &a, vec c){
ld d = 0;
for (auto v : a){
chmax(d,abs(v-c));
}
return d;
}
void solve(){
int n; in(n);
vector<vec> a(n), b(n); in(a,b);
vec ca = center(a), cb = center(b);
ld ans = farest(b,cb) / farest(a,ca);
out(ans);
}
int main(){
int t = 1; //in(t);
while (t--) { solve(); }
}