結果

問題 No.3154 convex polygon judge
ユーザー MMRZ
提出日時 2025-05-20 21:50:46
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 145 ms / 2,000 ms
コード長 6,012 bytes
コンパイル時間 3,309 ms
コンパイル使用メモリ 290,960 KB
実行使用メモリ 28,392 KB
最終ジャッジ日時 2025-05-20 21:50:52
合計ジャッジ時間 5,311 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge4
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ファイルパターン 結果
sample AC * 3
other AC * 44
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ソースコード

diff # 

# include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ull = unsigned long long;
const double pi = acos(-1);
template<class T>constexpr T inf() { return ::std::numeric_limits<T>::max(); }
template<class T>constexpr T hinf() { return inf<T>() / 2; }
template <typename T_char>T_char TL(T_char cX) { return tolower(cX); }
template <typename T_char>T_char TU(T_char cX) { return toupper(cX); }
template<class T> bool chmin(T& a,T b) { if(a > b){a = b; return true;} return false; }
template<class T> bool chmax(T& a,T b) { if(a < b){a = b; return true;} return false; }
int popcnt(unsigned long long n) { int cnt = 0; for (int i = 0; i < 64; i++)if ((n >> i) & 1)cnt++; return cnt; }
int d_sum(ll n) { int ret = 0; while (n > 0) { ret += n % 10; n /= 10; }return ret; }
int d_cnt(ll n) { int ret = 0; while (n > 0) { ret++; n /= 10; }return ret; }
ll gcd(ll a, ll b) { if (b == 0)return a; return gcd(b, a%b); };
ll lcm(ll a, ll b) { ll g = gcd(a, b); return a / g*b; };
ll MOD(ll x, ll m){return (x%m+m)%m; }
ll FLOOR(ll x, ll m) {ll r = (x%m+m)%m; return (x-r)/m; }
template<class T> using dijk = priority_queue<T, vector<T>, greater<T>>;
# define all(qpqpq)           (qpqpq).begin(),(qpqpq).end()
# define UNIQUE(wpwpw)        (wpwpw).erase(unique(all((wpwpw))),(wpwpw).end())
# define LOWER(epepe)         transform(all((epepe)),(epepe).begin(),TL<char>)
# define UPPER(rprpr)         transform(all((rprpr)),(rprpr).begin(),TU<char>)
# define rep(i,upupu)         for(ll i = 0, i##_len = (upupu);(i) < (i##_len);(i)++)
# define reps(i,opopo)        for(ll i = 1, i##_len = (opopo);(i) <= (i##_len);(i)++)
# define len(x)                ((ll)(x).size())
# define bit(n)               (1LL << (n))
# define pb push_back
# define eb emplace_back
# define exists(c, e)         ((c).find(e) != (c).end())

struct INIT{
	INIT(){
		std::ios::sync_with_stdio(false);
		std::cin.tie(0);
		cout << fixed << setprecision(20);
	}
}INIT;

namespace mmrz {
	void solve();
}

int main(){
	mmrz::solve();
}
#define debug(...) (static_cast<void>(0))

using namespace mmrz;

using DOUBLE = long double;

constexpr DOUBLE EPS = 1e-9;

struct point {
	DOUBLE x, y;

	point(DOUBLE _x = 0, DOUBLE _y = 0): x(_x), y(_y) {}

	point operator+(point p){ return point(x+p.x, y+p.y); };
	point operator-(point p){ return point(x-p.x, y-p.y); };
	point operator*(DOUBLE a) {return point(x*a, y*a); };
	point operator/(DOUBLE a) {return point(x/a, y/a); };

	DOUBLE abs() {return sqrt(norm()); };
	DOUBLE norm() {return x*x + y*y; };

	bool operator<(const point &p) const {
		return (not (fabs(x-p.x) < EPS)? x<p.x : y<p.y);
	}

	bool operator==(const point &p) const {
		return fabs(x-p.x) < EPS && fabs(y-p.y) < EPS;
	}
};


struct segment {point p1, p2; };
typedef segment line;

struct circle {
	point c;
	DOUBLE r;
	circle(point _c = point(), DOUBLE _r = 0.0): c(_c), r(_r) {}
};

DOUBLE dot(point a, point b) {
	return a.x*b.x + a.y*b.y;
}

DOUBLE cross(point a, point b) {
	return a.x*b.y - a.y*b.x;
}

constexpr int COUNTER_CLOCKWISE = 1;
constexpr int CLOCKWISE = -1;
constexpr int ONLINE_BACK = 2;
constexpr int ONLINE_FRONT = -2;
constexpr int ON_SEGMENT = 0;

int ccw(point p0, point p1, point p2) {
	point a = p1 - p0;
	point b = p2 - p0;

	if(p0 == p1)return ON_SEGMENT;
	if(p0 == p2)return ON_SEGMENT;
	if(p1 == p2)return ON_SEGMENT;

	if(cross(a, b) > EPS)return COUNTER_CLOCKWISE;
	if(cross(a, b) < -EPS)return CLOCKWISE;
	if(dot(a, b) < -EPS)return ONLINE_BACK;
	if(a.norm() < b.norm())return ONLINE_FRONT;

	return ON_SEGMENT;
}

bool intersect(point p1, point p2, point p3, point p4) {
	return (ccw(p1, p2, p3)*ccw(p1, p2, p4) <= 0 && ccw(p3, p4, p1)*ccw(p3, p4, p2) <= 0);
}

bool intersect(segment s1, segment s2) {
	return intersect(s1.p1, s1.p2, s2.p1, s2.p2);
}

point project(line &s, point &p) {
	point base = s.p2 - s.p1;
	DOUBLE r = dot(p-s.p1, base) / base.norm();
	return s.p1 + base*r;
}

DOUBLE get_distance(point &a, point &b){
	return (a-b).abs();
}

// line, point
DOUBLE get_distance_lp(line &l, point &p){
	return abs(cross(l.p2-l.p1, p-l.p1) / (l.p2-l.p1).abs());
}
// segment, point
DOUBLE get_distance_sp(segment &s, point &p){
	if(dot(s.p2-s.p1, p-s.p1) < 0.0)return (p-s.p1).abs();
	if(dot(s.p1-s.p2, p-s.p2) < 0.0)return (p-s.p2).abs();
	return get_distance_lp(s, p);
}

DOUBLE get_distance(segment &s1, segment &s2){
	if(intersect(s1, s2))return 0.0;
	return min({get_distance_sp(s1, s2.p1), get_distance_sp(s1, s2.p2), get_distance_sp(s2, s1.p1), get_distance_sp(s2, s1.p2)});
}

pair<point, point> get_crosspoints(circle &c, line &l){
	point pr = project(l, c.c);
	point e = (l.p2-l.p1)/(l.p2-l.p1).abs();
	DOUBLE base = sqrt(max<DOUBLE>(0.0, c.r*c.r - (pr-c.c).norm()));
	return {pr+e*base, pr-e*base};
}

point polar (DOUBLE a, DOUBLE r){
	return point(cos(r)*a, sin(r)*a);
}

pair<point, point> get_crosspoints(circle &c1, circle &c2){
	DOUBLE d = (c1.c-c2.c).abs();
	DOUBLE a = acos((c1.r*c1.r + d*d - c2.r*c2.r) / (2*c1.r*d));
	DOUBLE t = atan2((c2.c-c1.c).y, (c2.c-c1.c).x);
	return {c1.c+polar(c1.r, t+a), c1.c+polar(c1.r, t-a)};
}

DOUBLE deg_to_rad(const DOUBLE &deg) {return deg*pi / 180.0; };

vector<point> convex_hull(vector<point> ps, bool _ON_SEGMENT){
	int n = (int)ps.size();
	sort(ps.begin(), ps.end());
	int k = 0;
	vector<point> qs(n*2);
	for(int i = 0;i < n;i++){
		if(_ON_SEGMENT)while(k > 1 && cross(qs[k-1]-qs[k-2], ps[i]-qs[k-1]) <  0.0)k--;
		else           while(k > 1 && cross(qs[k-1]-qs[k-2], ps[i]-qs[k-1]) <= 0.0)k--;
		qs[k++] = ps[i];
	}
	for(int i = n-2, t=k;i >= 0;i--){
		if(_ON_SEGMENT)while(k > t && cross(qs[k-1]-qs[k-2], ps[i]-qs[k-1]) <  0.0)k--;
		else           while(k > t && cross(qs[k-1]-qs[k-2], ps[i]-qs[k-1]) <= 0.0)k--;
		qs[k++] = ps[i];
	}
	qs.resize(k-1);
	return qs;
}

void SOLVE(){
	int n;
	cin >> n;
	vector<point> ps(n);
	rep(i, n){
		cin >> ps[i].x >> ps[i].y;
	}
	auto qs = convex_hull(ps, false);
	cout << (len(qs) == n ? "Yes\n" : "No\n");
}

void mmrz::solve(){
	int t = 1;
	//cin >> t;
	while(t--)SOLVE();
}
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