結果

問題 No.2632 Center of Three Points in Lp Norm
ユーザー AerenAeren
提出日時 2024-02-16 22:19:41
言語 C++23
(gcc 12.3.0 + boost 1.83.0)
結果
WA  
実行時間 -
コード長 8,380 bytes
コンパイル時間 2,442 ms
コンパイル使用メモリ 248,416 KB
実行使用メモリ 6,824 KB
最終ジャッジ日時 2024-09-28 20:54:51
合計ジャッジ時間 5,690 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge5
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 20 ms
6,816 KB
testcase_01 AC 21 ms
6,820 KB
testcase_02 AC 19 ms
6,816 KB
testcase_03 AC 20 ms
6,820 KB
testcase_04 AC 19 ms
6,816 KB
testcase_05 WA -
testcase_06 AC 19 ms
6,820 KB
testcase_07 AC 19 ms
6,816 KB
testcase_08 AC 19 ms
6,816 KB
testcase_09 WA -
testcase_10 WA -
testcase_11 WA -
testcase_12 WA -
testcase_13 AC 19 ms
6,816 KB
testcase_14 AC 19 ms
6,820 KB
testcase_15 AC 19 ms
6,816 KB
testcase_16 WA -
testcase_17 WA -
testcase_18 WA -
testcase_19 WA -
testcase_20 WA -
testcase_21 AC 19 ms
6,820 KB
testcase_22 WA -
testcase_23 WA -
testcase_24 AC 21 ms
6,820 KB
testcase_25 WA -
testcase_26 AC 20 ms
6,820 KB
testcase_27 WA -
testcase_28 AC 20 ms
6,816 KB
testcase_29 AC 19 ms
6,820 KB
testcase_30 AC 20 ms
6,816 KB
testcase_31 AC 19 ms
6,820 KB
testcase_32 WA -
testcase_33 WA -
testcase_34 WA -
testcase_35 WA -
testcase_36 AC 20 ms
6,816 KB
testcase_37 AC 19 ms
6,820 KB
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ソースコード

diff # 

// #pragma GCC optimize("O3,unroll-loops")
#include <bits/stdc++.h>
// #include <x86intrin.h>
using namespace std;
#if __cplusplus >= 202002L
using namespace numbers;
#endif

template<class T>
struct point{
	T x{}, y{};
	point(){ }
	template<class U> point(const point<U> &otr): x(otr.x), y(otr.y){ }
	template<class U, class V> point(U x, V y): x(x), y(y){ }
	template<class U> point(const array<U, 2> &p): x(p[0]), y(p[1]){ }
	friend istream &operator>>(istream &in, point &p){
		return in >> p.x >> p.y;
	}
	friend ostream &operator<<(ostream &out, const point &p){
		return out << "{" << p.x << ", " << p.y << "}";
	}
	template<class U> operator array<U, 2>() const{
		return {x, y};
	}
	T operator*(const point &otr) const{
		return x * otr.x + y * otr.y;
	}
	T operator^(const point &otr) const{
		return x * otr.y - y * otr.x;
	}
	point operator+(const point &otr) const{
		return {x + otr.x, y + otr.y};
	}
	point &operator+=(const point &otr){
		return *this = *this + otr;
	}
	point operator-(const point &otr) const{
		return {x - otr.x, y - otr.y};
	}
	point &operator-=(const point &otr){
		return *this = *this - otr;
	}
	point operator-() const{
		return {-x, -y};
	}
#define scalarop_l(op) friend point operator op(const T &c, const point &p){ return {c op p.x, c op p.y}; }
	scalarop_l(+) scalarop_l(-) scalarop_l(*) scalarop_l(/)
#define scalarop_r(op) point operator op(const T &c) const{ return {x op c, y op c}; }
	scalarop_r(+) scalarop_r(-) scalarop_r(*) scalarop_r(/)
#define scalarapply(applyop, op) point &operator applyop(const T &c){ return *this = *this op c; }
	scalarapply(+=, +) scalarapply(-=, -) scalarapply(*=, *) scalarapply(/=, /)
#define compareop(op) bool operator op(const point &otr) const{ return pair<T, T>(x, y) op pair<T, T>(otr.x, otr.y); }
	compareop(>) compareop(<) compareop(>=) compareop(<=) compareop(==) compareop(!=)
#undef scalarop_l
#undef scalarop_r
#undef scalarapply
#undef compareop
	double norm() const{
		return sqrt(x * x + y * y);
	}
	long double norm_l() const{
		return sqrtl(x * x + y * y);
	}
	T squared_norm() const{
		return x * x + y * y;
	}
	// [0, 2 * pi]
	double angle() const{
		auto a = atan2(y, x);
		if(a < 0) a += 2 * acos(-1);
		return a;
	}
	// [0, 2 * pi]
	long double angle_l() const{
		auto a = atan2(y, x);
		if(a < 0) a += 2 * acosl(-1);
		return a;
	}
	point<double> unit() const{
		return point<double>(x, y) / norm();
	}
	point<long double> unit_l() const{
		return point<long double>(x, y) / norm_l();
	}
	point perp() const{
		return {-y, x};
	}
	point<double> normal() const{
		return perp().unit();
	}
	point<long double> normal_l() const{
		return perp().unit_l();
	}
	point<double> rotate(double theta) const{
		return {x * cos(theta) - y * sin(theta), x * sin(theta) + y * cos(theta)};
	}
	point<long double> rotate_l(double theta) const{
		return {x * cosl(theta) - y * sinl(theta), x * sinl(theta) + y * cosl(theta)};
	}
	point reflect_x() const{
		return {x, -y};
	}
	point reflect_y() const{
		return {-x, y};
	}
	point reflect(const point &o = {}) const{
		return {2 * o.x - x, 2 * o.y - y};
	}
	bool parallel_to(const point &q) const{
		if constexpr(is_floating_point_v<T>) return abs(*this ^ q) <= 1e-9;
		else return abs(*this ^ q) == 0;
	}
};
template<class T, class U>
point<double> lerp(const point<T> &p, const point<U> &q, double t){
	return point<double>(p) * (1 - t) + point<double>(q) * t;
}
template<class T, class U>
point<long double> lerp_l(const point<T> &p, const point<U> &q, long double t){
	return point<long double>(p) * (1 - t) + point<long double>(q) * t;
}
template<class T>
double distance(const point<T> &p, const point<T> &q){
	return (p - q).norm();
}
template<class T>
long double distance_l(const point<T> &p, const point<T> &q){
	return (p - q).norm_l();
}
template<class T>
T squared_distance(const point<T> &p, const point<T> &q){
	return (p - q).squared_norm();
}
template<class T>
T doubled_signed_area(const point<T> &p, const point<T> &q, const point<T> &r){
	return q - p ^ r - p;
}
template<class T>
T doubled_signed_area(const vector<point<T>> &a){
	if(a.empty()) return 0;
	T res = a.back() ^ a.front();
	for(auto i = 1; i < (int)a.size(); ++ i) res += a[i - 1] ^ a[i];
	return res;
}
// [-pi, pi]
template<class T>
double angle(const point<T> &p, const point<T> &q){
	return atan2(p ^ q, p * q);
}
// [-pi, pi]
template<class T>
long double angle_l(const point<T> &p, const point<T> &q){
	return atan2l(p ^ q, p * q);
}
// Check if p->q->r is sorted by angle with respect to the origin
template<class T>
bool is_sorted_by_angle(const point<T> &origin, const point<T> &p, const point<T> &q, const point<T> &r){
	T x = p - origin ^ q - origin;
	T y = q - origin ^ r - origin;
	if(x >= 0 && y >= 0) return true;
	if(x < 0 && y < 0) return false;
	return (p - origin ^ r - origin) < 0;
}
// Check if a is sorted by angle with respect to the origin
template<class T>
bool is_sorted_by_angle(const point<T> &origin, const vector<point<T>> &a){
	for(auto i = 0; i < (int)a.size() - 2; ++ i) if(!is_sorted_by_angle(origin, a[i], a[i + 1], a[i + 2])) return false;
	return true;
}
template<class T>
bool counterclockwise(const point<T> &p, const point<T> &q, const point<T> &r){
	return doubled_signed_area(p, q, r) > 0;
}
template<class T>
bool clockwise(const point<T> &p, const point<T> &q, const point<T> &r){
	return doubled_signed_area(p, q, r) < 0;
}
template<class T>
bool colinear(const point<T> &p, const point<T> &q, const point<T> &r){
	return doubled_signed_area(p, q, r) == 0;
}
template<class T>
bool colinear(const vector<point<T>> &a){
	int i = 1;
	while(i < (int)a.size() && a[0] == a[i]) ++ i;
	if(i == (int)a.size()) return true;
	for(auto j = i + 1; j < (int)a.size(); ++ j) if(!colinear(a[0], a[i], a[j])) return false;
	return true;
}
point<double> polar(double x, double theta){
	assert(x >= 0);
	return {x * cos(theta), x * sin(theta)};
}
point<long double> polar_l(long double x, long double theta){
	assert(x >= 0);
	return {x * cosl(theta), x * sinl(theta)};
}
// T must be able to hold the fourth power of max coordinate
// returns [a, b, c, and d lies in a circle]
template<class T>
bool concircular(point<T> a, point<T> b, point<T> c, const point<T> &d){
		a -= d, b -= d, c -= d;
	return a.squared_norm() * (b ^ c) + b.squared_norm() * (c ^ a) + c.squared_norm() * (a ^ b) == 0;
}
// T must be able to hold the fourth power of max coordinate
// returns [d lies in the interior of the circle defined by a, b, c]
template<class T>
bool inside_of_circle(point<T> a, point<T> b, point<T> c, const point<T> &d){
		a -= d, b -= d, c -= d;
	return (a.squared_norm() * (b ^ c) + b.squared_norm() * (c ^ a) + c.squared_norm() * (a ^ b)) * (doubled_signed_area(a, b, c) > 0 ? 1 : -1) > 0;
}
// T must be able to hold the fourth power of max coordinate
// returns [d lies in the exterior of the circle defined by a, b, c]
template<class T>
bool outside_of_circle(point<T> a, point<T> b, point<T> c, const point<T> &d){
		a -= d, b -= d, c -= d;
	return (a.squared_norm() * (b ^ c) + b.squared_norm() * (c ^ a) + c.squared_norm() * (a ^ b)) * (doubled_signed_area(a, b, c) > 0 ? -1 : 1) > 0;
}

using pointint = point<int>;
using pointll = point<long long>;
using pointlll = point<__int128_t>;
using pointd = point<double>;
using pointld = point<long double>;



int main(){
	cin.tie(0)->sync_with_stdio(0);
	cin.exceptions(ios::badbit | ios::failbit);
	cout << fixed << setprecision(15);
	double k;
	pointd a, b, c;
	cin >> k >> a >> b >> c;
	pointd dx = (b - a).unit();
	pointd dy = dx.normal();
	if(dy * c < 0){
		dy = -dy;
	}
	auto dist = [&](pointd p, pointd q)->double{
		return pow(abs(p.x - q.x), k) + pow(abs(p.y - q.y), k);
	};
	auto search_x = [&](double y)->double{
		double low = -1e18, high = 1e18;
		for(auto rep = 400; rep; -- rep){
			double mid = (low + high) / 2;
			dist(a, dx * mid + dy * y) > dist(b, dx * mid + dy * y) ? high = mid : low = mid;
		}
		return (low + high) / 2;
	};
	auto search_y = [&]()->double{
		double low = -1e18, high = 1e18;
		for(auto rep = 400; rep; -- rep){
			double mid = (low + high) / 2;
			double x = search_x(mid);
			dist(a, dx * x + dy * mid) > dist(c, dx * x + dy * mid) ? high = mid : low = mid;
		}
		return (low + high) / 2;
	};
	double y = search_y();
	double x = search_x(y);
	auto res = dx * x + dy * y;
	cout << res.x << " " << res.y << "\n";
	return 0;
}

/*

*/
0