test/aoj/CGL_4_A.test.cpp

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• Last update: 2023-06-25 16:24:15+09:00
• Problem: https://onlinejudge.u-aizu.ac.jp/problems/CGL_4_A

Depends on

• basic/template.hpp
• math/Geometry.hpp

Code

#define PROBLEM "https://onlinejudge.u-aizu.ac.jp/problems/CGL_4_A"
#include "../../basic/template.hpp"
#include "../../math/Geometry.hpp"
int main() {
	int n;
	std::cin >> n;
	std::vector<Point2D> v(n);
	rep(i, n) std::cin >> v[i];
	auto ans = convex_hull(v);
	std::cout << ans.size() << std::endl;
	int s = 0;
	REP(i, ans.size() - 1) {
		if (ans[s].get_y() > ans[i].get_y() ||
			(ans[s].get_y() == ans[i].get_y() &&
			 ans[s].get_x() > ans[i].get_x()))
			s = i;
	}
	rep(i, ans.size()) std::cout
		<< ans[i + s >= ans.size() ? i + s - ans.size() : i + s] << std::endl;
}

#line 1 "test/aoj/CGL_4_A.test.cpp"
#define PROBLEM "https://onlinejudge.u-aizu.ac.jp/problems/CGL_4_A"
#line 2 "basic/template.hpp"
#define _CRT_SECURE_NO_WARNINGS
#ifndef __clang__
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#endif
#include <string.h>
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cfloat>
#include <chrono>
#include <climits>
#include <cmath>
#include <complex>
#include <ctime>
#include <deque>
#include <fstream>
#include <functional>
#include <iomanip>
#include <iostream>
#include <iterator>
#include <list>
#include <map>
#include <memory>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

#define rep(i, n) for (int i = 0; i < int(n); i++)
#define REP(i, n) for (int i = 1; i <= int(n); i++)
#define all(V) V.begin(), V.end()

using i128 = __int128_t;
using u128 = __uint128_t;
using uint = unsigned int;
using lint = long long;
using ulint = unsigned long long;
using IP = std::pair<int, int>;
using LP = std::pair<lint, lint>;

constexpr int INF = INT_MAX / 2;
constexpr lint LINF = LLONG_MAX / 2;
constexpr double eps = DBL_EPSILON * 10;
constexpr double PI = 3.141592653589793238462643383279;

template <class T>
class prique : public std::priority_queue<T, std::vector<T>, std::greater<T>> {};
int popcount(uint x) {
#if __cplusplus >= 202002L
	return std::popcount(x);
#else
#ifndef __clang__
	return __builtin_popcount(x);
#endif
#endif
	x = (x & 0x55555555) + (x >> 1 & 0x55555555);
	x = (x & 0x33333333) + (x >> 2 & 0x33333333);
	x = (x & 0x0f0f0f0f) + (x >> 4 & 0x0f0f0f0f);
	x = (x & 0x00ff00ff) + (x >> 8 & 0x00ff00ff);
	return (x & 0x0000ffff) + (x >> 16 & 0x0000ffff);
}
template <class F>
inline constexpr decltype(auto) lambda_fix(F&& f) {
	return [f = std::forward<F>(f)](auto&&... args) {
		return f(f, std::forward<decltype(args)>(args)...);
	};
}
template <class T>
constexpr std::vector<T> make_vec(size_t n) {
	return std::vector<T>(n);
}
template <class T, class... Args>
constexpr auto make_vec(size_t n, Args&&... args) {
	return std::vector<decltype(make_vec<T>(args...))>(n, make_vec<T>(std::forward<Args>(args)...));
}
template <class T, class U, class Stream>
Stream& operator>>(Stream& ist, std::pair<T, U>& x) {
	return ist >> x.first >> x.second;
}
template <class T, class U, class Stream>
Stream& operator<<(Stream& ost, const std::pair<T, U>& x) {
	return ost << x.first << " " << x.second;
}
template <class Container,
		  std::enable_if_t<!std::is_same<Container, std::string>::value, std::nullptr_t> = nullptr>
auto operator>>(std::istream& ist, Container& cont)
	-> decltype(typename Container::iterator(), std::cin)& {
	Container tmp;
	while (true) {
		typename Container::value_type t;
		ist >> t;
		tmp.emplace_back(t);
		if (getchar() == '\n') break;
	}
	cont = Container(std::move(tmp));
	return ist;
}
template <class Container, class Stream,
		  std::enable_if_t<!std::is_same<Container, std::string>::value, std::nullptr_t> = nullptr>
auto operator<<(Stream& ost, const Container& cont)
	-> decltype(typename Container::iterator(), ost)& {
	for (auto it = cont.begin(); it != cont.end(); it++) {
		if (it != cont.begin()) ost << ' ';
		ost << *it;
	}
	return ost;
}
template <class Container>
auto sum(const Container& cont) -> decltype(typename Container::iterator(), 0LL) {
	lint res = 0;
	for (auto it = cont.begin(); it != cont.end(); it++) res += *it;
	return res;
}
template <class T, class U>
constexpr inline bool chmax(T& lhs, const U& rhs) noexcept {
	if (lhs < rhs) {
		lhs = rhs;
		return true;
	}
	return false;
}
template <class T, class U>
constexpr inline bool chmin(T& lhs, const U& rhs) noexcept {
	if (lhs > rhs) {
		lhs = rhs;
		return true;
	}
	return false;
}
constexpr inline lint gcd(lint a, lint b) noexcept {
	while (b) {
		lint c = a;
		a = b;
		b = c % b;
	}
	return a;
}
inline lint lcm(lint a, lint b) noexcept { return a / gcd(a, b) * b; }
constexpr bool isprime(lint n) noexcept {
	if (n == 1) return false;
	for (int i = 2; i * i <= n; i++) {
		if (n % i == 0) return false;
	}
	return true;
}
template <class T>
constexpr T mypow(T a, lint b) noexcept {
	T res(1);
	while (true) {
		if (b & 1) res *= a;
		b >>= 1;
		if (!b) break;
		a *= a;
	}
	return res;
}
constexpr lint modpow(lint a, lint b, lint m) noexcept {
	a %= m;
	lint res(1);
	while (b) {
		if (b & 1) res *= a, res %= m;
		a *= a, a %= m, b >>= 1;
	}
	return res;
}
LP extGcd(lint a, lint b) noexcept {
	if (b == 0) return {1, 0};
	LP s = extGcd(b, a % b);
	std::swap(s.first, s.second);
	s.second -= a / b * s.first;
	return s;
}
LP ChineseRem(const lint& b1, const lint& m1, const lint& b2, const lint& m2) noexcept {
	auto p = extGcd(m1, m2);
	lint g = gcd(m1, m2), l = m1 / g * m2;
	lint tmp = (b2 - b1) / g * p.first % (m2 / g);
	lint r = (b1 + m1 * tmp + l) % l;
	return {r, l};
}
int LCS(const std::string& a, const std::string& b) {
	auto dp = make_vec<int>(a.size() + 1, b.size() + 1);
	rep(i, a.size()) {
		rep(j, b.size()) {
			chmax(dp[i + 1][j], dp[i][j]);
			chmax(dp[i][j + 1], dp[i][j]);
			if (a[i] == b[j]) chmax(dp[i + 1][j + 1], dp[i][j] + 1);
		}
		chmax(dp[i + 1][b.size()], dp[i][b.size()]);
	}
	rep(j, b.size()) chmax(dp[a.size()][j + 1], dp[a.size()][j]);
	return dp[a.size()][b.size()];
}
template <class T, std::enable_if_t<std::is_convertible<int, T>::value, std::nullptr_t> = nullptr>
void compress(std::vector<T>& vec) {
	auto tmp = vec;
	std::sort(all(tmp));
	tmp.erase(std::unique(all(tmp)), tmp.end());
	for (T& i : vec) i = std::lower_bound(all(tmp), i) - tmp.begin();
}
template <class T>
void compress(T* l, T* r) {
	std::vector<T> tmp(l, r);
	std::sort(all(tmp));
	tmp.erase(std::unique(all(tmp)), tmp.end());
	for (auto i = l; i < r; i++) {
		*i = std::lower_bound(all(tmp), *i) - tmp.begin();
	}
}
template <class InputIter>
void compress(InputIter l, InputIter r) {
	std::vector<typename InputIter::value_type> tmp(l, r);
	std::sort(all(tmp));
	tmp.erase(std::unique(all(tmp)), tmp.end());
	for (auto i = l; i < r; i++) {
		*i = std::lower_bound(all(tmp), *i) - tmp.begin();
	}
}
template <class InputIter,
		  std::enable_if_t<std::is_same<typename InputIter::value_type, std::pair<IP, int>>::value,
						   std::nullptr_t> = nullptr>
void mo_sort(InputIter l, InputIter r, int N) {
	const int M = std::max(1.0, std::sqrt(lint(N) * N / std::distance(l, r)));
	std::sort(l, r, [M](const auto& lhs, const auto& rhs) {
		if (lhs.first.first / M < rhs.first.first / M) return true;
		if (lhs.first.first / M == rhs.first.first / M) return lhs.first.second < rhs.first.second;
		return false;
	});
	int before = -1, cnt = 0;
	bool f = false;
	for (InputIter i = l; i != r; i++) {
		if (before != i->first.first / M) {
			if (f) std::reverse(i - cnt, i);
			f ^= true, before = i->first.first / M, cnt = 1;
		} else
			cnt++;
	}
	if (f) std::reverse(r - cnt, r);
}
template <class T>
std::vector<T> xor_bases(const std::vector<T>& vec) {
	std::vector<T> res;
	for (T i : vec) {
		for (T j : res) {
			chmin(i, i ^ j);
		}
		if (i) res.emplace_back(i);
	}
	return res;
}
#line 2 "math/Geometry.hpp"
static bool equal(double lhs, double rhs) { return std::abs(lhs - rhs) < eps; }

class Point2D : public std::complex<double> {
	using C = std::complex<double>;

  public:
	Point2D() = default;
	Point2D(double x, double y) : C(x, y) {}
	Point2D(const std::complex<double>& c) : C(c) {}
	Point2D(std::complex<double>&& c) : C(c) {}

	double get_x() const { return real(); }
	double get_y() const { return imag(); }

	double abs() const { return std::abs(*this); }
	bool equals(const Point2D& x) {
		return equal(real(), x.real()) && equal(imag(), x.imag());
	}

	Point2D unit() const { return Point2D(*this / abs()); }
	Point2D normal() const { return *this * std::complex<double>(0, 1); }

	friend double dot(const Point2D& lhs, const Point2D& rhs);
	friend double cross(const Point2D& lhs, const Point2D& rhs);
	friend Point2D rotate(const Point2D& p, double theta);
};

double dot(const Point2D& lhs, const Point2D& rhs) {
	return lhs.real() * rhs.real() + lhs.imag() * rhs.imag();
}
double cross(const Point2D& lhs, const Point2D& rhs) {
	return lhs.real() * rhs.imag() - lhs.imag() * rhs.real();
}
Point2D rotate(const Point2D& p, double theta) {
	return Point2D(p * std::polar(1.0, theta));
}

class Line2D {
  protected:
	Point2D s, t;

  public:
	Line2D() = default;
	Line2D(const Point2D& s_, const Point2D& t_) : s(s_), t(t_) {}
	Line2D(double A, double B, double C) {
		if (equal(A, 0))
			s = Point2D(0, C / B), t = Point2D(1, C / B);
		else if (equal(B, 0))
			s = Point2D(C / A, 0), t = Point2D(C / A, 1);
		else
			s = Point2D(0, C / B), t = Point2D(C / A, 0);
	}

	friend Point2D projection(const Line2D& l, const Point2D& p);
	friend bool is_orthogonal(const Line2D& a, const Line2D& b);
	friend bool is_parallel(const Line2D& a, const Line2D& b);
	friend Point2D cross_point(const Line2D& a, const Line2D& b);
};

class Segment2D : public Line2D {
  public:
	Segment2D() = default;
	Segment2D(const Point2D& s, const Point2D& t) : Line2D(s, t) {}

	friend bool is_intersect(const Segment2D& a, const Segment2D& b);
	friend double distance(const Segment2D& l, const Point2D& p);
	friend double distance(const Segment2D& a, const Segment2D& b);
};

class Circle2D {
	Point2D p;
	double r;

  public:
	Circle2D() = default;
	Circle2D(const Point2D& p_, double r_) : p(p_), r(r_) {}
};

Point2D projection(const Line2D& l, const Point2D& p) {
	double t = dot(p - l.s, l.s - l.t) / std::norm(l.s - l.t);
	return l.s + (l.s - l.t) * t;
}

Point2D reflection(const Line2D& l, const Point2D& p) {
	return p + (projection(l, p) - p) * 2.0;
}

// 1: COUNTER_CLOCKWISE
// -1: CLOCKWISE
// 2: ONLine2D_BACK
// -2: ONLine2D_FRONT
// 0: ON_Segment2D
int counter_clockwise(const Point2D& a, Point2D b, Point2D c) {
	b -= a, c -= a;
	if (cross(b, c) > eps) return 1;
	if (cross(b, c) < -eps) return -1;
	if (dot(b, c) < 0) return 2;
	if (std::norm(b) < std::norm(c)) return -2;
	return 0;
}

bool is_orthogonal(const Line2D& a, const Line2D& b) {
	return equal(dot(a.t - a.s, b.t - b.s), 0);
}

bool is_parallel(const Line2D& a, const Line2D& b) {
	return equal(cross(a.t - a.s, b.t - b.s), 0);
}

bool is_intersect(const Segment2D& a, const Segment2D& b) {
	return counter_clockwise(a.s, a.t, b.s) *
				   counter_clockwise(a.s, a.t, b.t) <=
			   0 &&
		   counter_clockwise(b.s, b.t, a.s) *
				   counter_clockwise(b.s, b.t, a.t) <=
			   0;
}

Point2D cross_point(const Line2D& a, const Line2D& b) {
	double d1 = cross(a.t - a.s, b.t - b.s);
	double d2 = cross(a.t - a.s, a.t - b.s);
	if (equal(std::abs(d1), 0) && equal(std::abs(d2), 0)) return a.s;
	return b.s + (b.t - b.s) * (d2 / d1);
}

double distance(const Point2D& x, const Point2D& y) { return std::abs(x - y); }

double distance(const Segment2D& l, const Point2D& p) {
	if (dot(l.t - l.s, p - l.s) < eps) return std::abs(p - l.s);
	if (dot(l.s - l.t, p - l.t) < eps) return std::abs(p - l.t);
	return std::abs(cross(l.t - l.s, p - l.s) / (l.t - l.s));
}

double distance(const Segment2D& a, const Segment2D& b) {
	if (is_intersect(a, b)) return 0;
	double ans = distance(a, b.s);
	chmin(ans, distance(a, b.t));
	chmin(ans, distance(b, a.s));
	chmin(ans, distance(b, a.t));
	return ans;
}

double polygon_area(const std::vector<Point2D>& v) {
	double res = cross(v.back(), v[0]);
	rep(i, v.size() - 1) res += cross(v[i], v[i + 1]);
	return res * 0.5;
}

bool is_convex(const std::vector<Point2D>& v) {
	const int n = v.size();
	if (counter_clockwise(v[n - 1], v[0], v[1]) == -1) return false;
	if (counter_clockwise(v[n - 2], v[n - 1], v[0]) == -1) return false;
	rep(i, n - 2) {
		if (counter_clockwise(v[i], v[i + 1], v[i + 2]) == -1) return false;
	}
	return true;
}

int is_contained(const std::vector<Point2D>& v, const Point2D& p) {
	bool in = false;
	rep(i, v.size()) {
		Point2D a = v[i] - p, b = v[i == v.size() - 1 ? 0 : i + 1] - p;
		if (a.get_y() > b.get_y()) std::swap(a, b);
		if (a.get_y() < eps && eps < b.get_y() && cross(a, b) < -eps)
			in ^= true;
		if (cross(a, b) == 0 && dot(a, b) <= 0) return 1;
	}
	return in ? 2 : 0;
}

std::vector<Point2D> convex_hull(std::vector<Point2D> p) {
	int n = p.size(), k = 0;
	std::sort(all(p), [](const Point2D& a, const Point2D& b) {
		return a.get_x() != b.get_x() ? a.get_x() < b.get_x()
									  : a.get_y() < b.get_y();
	});
	std::vector<Point2D> res(2 * n);
	for (int i = 0; i < n; res[k++] = p[i++]) {
		while (k >= 2 &&
			   cross(res[k - 1] - res[k - 2], p[i] - res[k - 1]) < -eps)
			k--;
	}
	for (int i = n - 2, t = k + 1; i >= 0; res[k++] = p[i--]) {
		while (k >= t &&
			   cross(res[k - 1] - res[k - 2], p[i] - res[k - 1]) < -eps)
			k--;
	}
	res.resize(k - 1);
	return res;
}

double convex_polygon_diameter(const std::vector<Point2D>& p) {
	int cur = 0;
	double res = 0;
	rep(i, p.size()) {
		double cur_dist = distance(p[i], p[cur]), nxt_dist;
		while (true) {
			nxt_dist = distance(p[i], p[cur + 1 == p.size() ? 0 : cur + 1]);
			if (cur_dist > nxt_dist) break;
			cur_dist = nxt_dist;
			cur = cur + 1 == p.size() ? 0 : cur + 1;
		}
		chmax(res, cur_dist);
	}
	return res;
}

std::istream& operator>>(std::istream& ist, Point2D& p) {
	double x, y;
	ist >> x >> y;
	p = Point2D(x, y);
	return ist;
}

std::ostream& operator<<(std::ostream& ost, const Point2D& p) {
	ost << p.get_x() << ' ' << p.get_y();
	return ost;
}
#line 4 "test/aoj/CGL_4_A.test.cpp"
int main() {
	int n;
	std::cin >> n;
	std::vector<Point2D> v(n);
	rep(i, n) std::cin >> v[i];
	auto ans = convex_hull(v);
	std::cout << ans.size() << std::endl;
	int s = 0;
	REP(i, ans.size() - 1) {
		if (ans[s].get_y() > ans[i].get_y() ||
			(ans[s].get_y() == ans[i].get_y() &&
			 ans[s].get_x() > ans[i].get_x()))
			s = i;
	}
	rep(i, ans.size()) std::cout
		<< ans[i + s >= ans.size() ? i + s - ans.size() : i + s] << std::endl;
}

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