結果

問題 No.96 圏外です。
ユーザー 沙耶花
提出日時 2021-10-25 23:39:48
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 881 ms / 5,000 ms
コード長 8,328 bytes
コンパイル時間 5,293 ms
コンパイル使用メモリ 276,044 KB
最終ジャッジ日時 2025-01-25 06:56:17
ジャッジサーバーID
（参考情報） 		judge2 / judge2
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ファイルパターン 結果
other AC * 28
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ソースコード

diff #
プレゼンテーションモードにする

#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;
    }
};
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(temp2);
        ans = max(ans,P.get_diameter()+2.0);
        
    }
    
    cout<<fixed<<setprecision(10)<<ans<<endl;
    
    
    return 0;
}
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