結果

問題 No.96 圏外です。
ユーザー 沙耶花沙耶花
提出日時 2021-10-25 23:27:38
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
WA  
実行時間 -
コード長 9,035 bytes
コンパイル時間 4,618 ms
コンパイル使用メモリ 288,756 KB
実行使用メモリ 23,108 KB
最終ジャッジ日時 2024-10-03 22:30:15
合計ジャッジ時間 14,818 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge1
このコードへのチャレンジ
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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 2 ms
5,248 KB
testcase_01 AC 2 ms
5,248 KB
testcase_02 AC 2 ms
5,248 KB
testcase_03 AC 2 ms
5,248 KB
testcase_04 AC 12 ms
5,248 KB
testcase_05 AC 19 ms
5,248 KB
testcase_06 AC 30 ms
5,248 KB
testcase_07 AC 48 ms
5,248 KB
testcase_08 AC 75 ms
5,248 KB
testcase_09 AC 96 ms
5,248 KB
testcase_10 AC 124 ms
5,504 KB
testcase_11 AC 159 ms
6,104 KB
testcase_12 AC 199 ms
6,680 KB
testcase_13 AC 294 ms
6,784 KB
testcase_14 AC 348 ms
7,936 KB
testcase_15 WA -
testcase_16 AC 499 ms
9,728 KB
testcase_17 AC 563 ms
11,648 KB
testcase_18 WA -
testcase_19 AC 650 ms
11,132 KB
testcase_20 AC 676 ms
13,640 KB
testcase_21 AC 521 ms
17,904 KB
testcase_22 AC 733 ms
22,976 KB
testcase_23 AC 697 ms
23,108 KB
testcase_24 AC 2 ms
5,248 KB
testcase_25 AC 390 ms
9,304 KB
testcase_26 AC 521 ms
11,136 KB
testcase_27 AC 433 ms
9,984 KB
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ソースコード

diff # 

#include <stdio.h>
#include <bits/stdc++.h>
#include <atcoder/all>
using namespace atcoder;
using namespace std;
#define rep(i,n) for (int i = 0; i < (n); ++i)
#define Inf 100000000000

const double eps = 1e-10;

template <typename T>
struct vector_2d{
	T x,y,rad,dir;
	
	vector_2d(T a=0.0,T b=0.0){
		x = a;
		y = b;
		fix_rd();
	}
	
	void update_x(T a,T b){
		x = a*x + b;
		fix_rd();
	}
	
	void update_x(T a){
		update_x(0.0,a);
	}
	
	void update_y(T a,T b){
		y = a*y + b;
		fix_rd();
	}
	
	void update_y(T a){
		update_y(0.0,a);
	}
	
	void update_rad(T a,T b){
		rad = a*rad + b;
		fix_xy();
	}
	
	void update_rad(T a){
		update_rad(0.0,a);
	}
	
	void update_dir(T a,T b){
		dir = a*dir + b;
		fix_xy();
	}

	void update_dir(T a){
		update_dir(0.0,a);
	}
	
	void fix_xy(){
		x = rad * cos(dir);
		y = rad * sin(dir);
		fix_rd();
	}
	
	void fix_rd(){
		rad = hypot(x,y);
		if(rad==0.0)dir=0.0;
		else dir = atan2(y,x);
		fix_zero();
	}
	
	void fix_zero(){
		if(abs(x)<eps)x = 0.0;
		if(abs(y)<eps)y = 0.0;
		if(abs(rad)<eps)rad = 0.0;
		if(abs(dir)<eps)dir = 0.0;
	}
	
	void normalize(){
		T s = size();
		update_x(1.0/s,0.0);
		update_y(1.0/s,0.0);
	}
	
	
	T get_dis(vector_2d<T> V){
		return hypot(x-V.x,y-V.y);
	}
	
	T size(){
		return get_dis(vector_2d<T>());
	}
	
	T angle_difference(vector_2d<T> V){
		double ret = dir - V.dir;
		if(ret<-acos(-1.0))ret = acos(-1.0)*2.0+ret;
		if(ret>acos(-1.0))ret=-acos(-1.0)*2.0+ret;
		return ret;
	}
	
	//中点
	vector_2d get_midpoint(vector_2d<T> V){
		V.update_x(0.5,x/2.0);
		V.update_y(0.5,y/2.0);
		return V;
	}
	
	T get_inner_product(vector_2d<T> V){
		return x*V.x+y*V.y;
	}
	
	T get_cross_product(vector_2d<T> V){
		return x*V.y-y*V.x;
	}
	
	vector_2d &operator+=(const vector_2d<T> &another){
		update_x(1,another.x);
		update_y(1,another.y);
		return (*this);
	}
	
	vector_2d &operator-=(const vector_2d<T> &another){
		update_x(1,-another.x);
		update_y(1,-another.y);
		return (*this);
	}
	
	vector_2d operator+(const vector_2d<T> &another)const{
		return (vector_2d(*this)+=another);
	}
	
	vector_2d operator-(const vector_2d<T> &another)const{
		return (vector_2d(*this)-=another);
	}
	
	void show(){
		cout<<x<<','<<y<<endl;
	}
};

//a+tx
template <typename T>
struct line{
	vector_2d<T> a,t;
	
	line(vector_2d<T> V1,vector_2d<T> V2){
		a=V1;
		t=V2-V1;
	}

	T get_signed_dis(vector_2d<T> V){
		vector_2d<double> PA = a-V;
		return PA.get_cross_product(t)/t.size();
	}
	
	T get_dis(vector_2d<T> V){
		return abs(get_signed_dis(V));
	}
	
	vector_2d<T> get_projection(vector_2d<T> P){
		T r = t.get_inner_product(P-a)/t.size();
		vector_2d<T> temp = t;
		temp.update_rad(0.0,r);
		return a+temp;
	}	
	
	vector_2d<T> get_cross_point(line<T> L){
		vector_2d<T> ret(1e20,1e20);
		if(abs(t.get_cross_product(L.t))<eps)return ret;

		T d0 = L.get_signed_dis(a);
		T d1 = L.get_signed_dis(a+t);
		vector_2d<T> temp = t;
		temp.x *= d0/(d1-d0);
		temp.y *= d0/(d1-d0);
		ret = a - temp;
		return ret;
	}
	
};

template <typename T>
struct segment{
	vector_2d<T> V1,V2;
	segment(vector_2d<T> a=vector_2d<T>(),vector_2d<T> b=vector_2d<T>()){
		V1=a;
		V2=b;
	}
	
	T get_dis(vector_2d<T> P){
		T ret = 1e20;
		line<T> L(V1,V2);
		vector_2d<T> Q = L.get_projection(P);
		if(Q.x+eps>min(V1.x,V2.x)&&Q.y+eps>min(V1.y,V2.y)
		&&Q.x<max(V1.x,V2.x)+eps&&Q.y<max(V1.y,V2.y)+eps)ret = min(ret,Q.get_dis(P));
		else{
			ret = min(ret,P.get_dis(V1));
			ret = min(ret,P.get_dis(V2));
		}
		return ret;
	}
	
	T get_dis(segment<T> l){
		if(get_cross_point(l).x<1e20)return 0.0;
		return min({get_dis(l.V1),get_dis(l.V2),l.get_dis(V1),l.get_dis(V2)});
	}
	
	vector_2d<T> get_cross_point(segment<T> l){
		line<T> L1(V1,V2),L2(l.V1,l.V2);
		vector_2d<T> P = L1.get_cross_point(L2);
		if(get_dis(P)<eps&&l.get_dis(P)<eps)return P;
		return vector_2d<T> (1e20,1e20);
	}
};

template <typename T>
struct triangle{
	vector_2d<T> V[3];
	
	triangle(vector_2d<T> V1,vector_2d<T> V2,vector_2d<T> V3){
		V[0] = V1;
		V[1] = V2;
		V[2] = V3;
	}
	
	vector_2d<T> get_circumcenter(){
		line<T> L1(V[0],V[1]);
		vector_2d<T> M1 = V[0].get_midpoint(V[1]);
		L1 = line<T>(M1,L1.b,L1.a);

		line<T> L2(V[1],V[2]);
		vector_2d<T> M2 = V[1].get_midpoint(V[2]);
		L2 = line<T>(M2,L2.b,L2.a);
				
		return L1.get_cross_point(L2);
	}
	
	T get_signed_area(){
		return ((V[1].x-V[0].x)*(V[2].y-V[0].y) - (V[2].x-V[0].x)*(V[1].y-V[0].y))/2.0;
	}
	
	T get_area(){
		return abs(get_signed_area());
	}
	
	bool is_inside(vector_2d<T> P){
		T S = triangle<T>(V[0],V[1],P).get_area() + triangle<T>(V[1],V[2],P).get_area() + triangle<T>(V[2],V[0],P).get_area();
		return abs(S - get_area())<eps;
	}
	
	bool is_clockwise(){
		vector_2d<T> X = V[1]-V[0],Y = V[2]-V[1];
		return X.x*Y.y-X.y*Y.x < 0.0;
	}
	
};

template <typename T>
struct polygon{
	vector<vector_2d<T>> V;
	polygon(vector<vector_2d<T>> v){
		V = v;
	}
	
	bool is_convex(){
		bool f = false;
		for(int i=0;i<V.size();i++){
			triangle<T> tri(V[i],V[(i+1)%V.size()],V[(i+2)%V.size()]);
			if(i==0)f = tri.is_clockwise();
			else{
				if(tri.is_clockwise()!=f)return false;
			}
		}
		return true;
	}
	
	T get_signed_area(){
		T ret = 0.0;
		for(int i=1;i<V.size()-1;i++){
			triangle<T> tri(V[0],V[i],V[i+1]);
			ret += tri.get_signed_area();
		}
		return ret;
	}
	
	T get_area(){
		return abs(get_signed_area());
	}
	
	T get_diameter(){
		vector<T> dis(V.size());
		int now = 0;
		for(int i=0;i<V.size();i++){
			while(true){
				int next = (now+1)%V.size();
				if(V[i].get_dis(V[now])<V[i].get_dis(V[next])+eps){
					now = next;
					continue;
				}
				else{
					break;
				}
			}
			dis[i] = V[i].get_dis(V[now]);
		}
		
		T ret = 0.0;
		for(int i=0;i<V.size();i++)ret = max(ret,dis[i]);
		
		return ret;
	}
	
	bool is_on_side(vector_2d<T> P){
		for(int i=0;i<V.size();i++){
			segment<T> l(V[i],V[(i+1)%V.size()]);
			if(l.get_dis(P)<eps)return true;
		}
		return false;
	}
	
	bool is_inside(vector_2d<T> P){
		if(is_on_side(P))return true;
		double R = 0.0;
		for(int i=0;i<V.size();i++){
			vector_2d<T> p1(V[i]-P),p2(V[(i+1)%V.size()]-P);
			R += p1.angle_difference(p2);
		}
		return abs(R)>=eps;
	}
};


template <typename T>
struct circle{
	vector_2d<T> C;
	T R;
	circle(vector_2d<T> c=vector_2d<T>(),T r=0.0){
		C = c;
		R = r;
	}
	
	vector<vector_2d<T>> get_cross_point(circle<T> C2){
		vector<vector_2d<T>> ret;

		T d = C.get_dis(C2.C);
		if(d>R+C2.R+eps)return ret;
		if(d+eps<abs(R-C2.R))return ret;
		T cosine = (pow(R,2.0)+pow(d,2.0)-pow(C2.R,2.0))/(2.0*R*d);
		
		T Rc = R*cosine;
		T Rs = sqrt(pow(R,2.0)-pow(Rc,2.0));
		
		vector_2d<T> e1 = (C2.C-C);
		e1.update_rad(1.0/d,0.0);
		vector_2d<T> e2 = e1;
		e2.update_dir(1.0,acos(-1.0)/2.0);
		e1.update_rad(Rc,0.0);
		e2.update_rad(Rs,0.0);
		ret.push_back(C + e1+e2);
		e2.update_dir(1.0,-acos(-1.0));
		ret.push_back(C+e1+e2);
		return ret;
	}
};

vector<int> get_CH(vector<vector_2d<double>> &v){
	vector<pair<vector_2d<double>,int>> V(v.size());
	for(int i=0;i<v.size();i++){
		V[i].first=v[i];
		V[i].second=i;
	}
	
	sort(V.begin(),V.end(),[](auto &a,auto &b){
		if(abs(a.first.y-b.first.y)>eps)return a.first.y<b.first.y;
		return a.first.x<b.first.x;
	});
	
	vector<int> ret;
	
	for(int i=0;i<V.size();i++){
		if(ret.size()<2){
			ret.push_back(i);
		}
		else{
			vector_2d<double> v1 = V[ret[ret.size()-2]].first,v2 = V[ret[ret.size()-1]].first,v3 = V[i].first;
			v3 -= v2;
			v2 -= v1;
			if(v2.get_cross_product(v3)>-eps){
				ret.push_back(i);
			}
			else{
				ret.pop_back();
				i--;
				continue;
			}
		}
	}

	for(int i=(int)V.size()-2;i>=0;i--){
		if(ret.size()<2){
			ret.push_back(i);
		}
		else{
			vector_2d<double> v1 = V[ret[ret.size()-2]].first,v2 = V[ret[ret.size()-1]].first,v3 = V[i].first;
			v3 -= v2;
			v2 -= v1;
			if(v2.get_cross_product(v3)>-eps){
				ret.push_back(i);
			}
			else{
				ret.pop_back();
				i++;
				continue;
			}
		}
	}
	ret.pop_back();
	for(int i=0;i<ret.size();i++)ret[i] = V[ret[i]].second;
	set<int> S;
	{
		vector<int> ret2;
		for(int i=0;i<ret.size();i++){
			if(S.count(ret[i]))continue;
			ret2.push_back(ret[i]);
			S.insert(ret[i]);
		}
		ret = ret2;
	}
	return ret;
	
}

int main(){
	int N;
	cin>>N;
	
	vector<pair<int,int>> xy(N);
	rep(i,N){
		cin>>xy[i].first>>xy[i].second;
	}
	
	sort(xy.begin(),xy.end());
	
	dsu D(N);
	
	rep(i,N){
		int x = xy[i].first,y = xy[i].second;
		rep(j,11){
			for(int k=-10;k<=10;k++){
				if(j*j + k*k <= 100){
					int d = distance(xy.begin(),lower_bound(xy.begin(),xy.end(),make_pair(x+j,y+k)));
					if(d!=N && xy[d]==make_pair(x+j,y+k))D.merge(d,i);
				}
			}
		}
		
	}
	
	double ans = 1.0;
	
	auto g = D.groups();
	
	rep(i,g.size()){
		if(g[i].size()==1){
			ans = max(ans,2.0);
			continue;
		}
		
		vector<vector_2d<double>> temp;
		rep(j,g[i].size()){
			temp.push_back(vector_2d<double>(xy[g[i][j]].first,xy[g[i][j]].second));
		}
		auto ret = get_CH(temp);
		vector<vector_2d<double>> temp2;
		rep(j,ret.size()){
			temp2.push_back(temp[ret[j]]);
		}
		polygon<double> P(temp);
		ans = max(ans,P.get_diameter()+2.0);
		
	}
	
	cout<<fixed<<setprecision(10)<<ans<<endl;
	
	
	return 0;
}
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