#1047782 (C++23) No.3042 拡大コピー

提出ソース
結果

問題	No.3042 拡大コピー
コンテスト
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
このコードへのチャレンジ
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ファイルパターン	結果
sample	AC * 1
other	AC * 24
権限があれば一括ダウンロードができます
ソースコード

raw source code
#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(); }
}
yukicoder

結果

ソースコード
