#933157 (C++17) No.2555 Intriguing Triangle

• 問題: No.2555 Intriguing Triangle
• ユーザー: tko919
• 提出日時: 2023-12-01 19:56:46
• 言語: C++17 (gcc 13.3.0 + boost 1.87.0)
• 結果: AC
• 実行時間: 6 ms / 2,000 ms
• コード長: 17,110 bytes
• コンパイル時間: 3,077 ms
• コンパイル使用メモリ: 222,452 KB
• 最終ジャッジ日時: 2025-02-18 03:01:10
• ジャッジサーバーID （参考情報）: judge5 / judge3

ファイルパターン	結果
sample	AC * 2
other	AC * 28

ソースコード

#line 1 "library/Template/template.hpp"
#include <bits/stdc++.h>
using namespace std;

#define rep(i,a,b) for(int i=(int)(a);i<(int)(b);i++)
#define ALL(v) (v).begin(),(v).end()
#define UNIQUE(v) sort(ALL(v)),(v).erase(unique(ALL(v)),(v).end())
#define MIN(v) *min_element(ALL(v))
#define MAX(v) *max_element(ALL(v))
#define LB(v,x) lower_bound(ALL(v),(x))-(v).begin()
#define UB(v,x) upper_bound(ALL(v),(x))-(v).begin()

using ll=long long int;
using ull=unsigned long long;
const int inf = 0x3fffffff;
const ll INF = 0x1fffffffffffffff;

template<typename T>inline bool chmax(T& a,T b){if(a<b){a=b;return 1;}return 0;}
template<typename T>inline bool chmin(T& a,T b){if(a>b){a=b;return 1;}return 0;}
template<typename T,typename U>T ceil(T x,U y){assert(y!=0); if(y<0)x=-x,y=-y; return (x>0?(x+y-1)/y:x/y);}
template<typename T,typename U>T floor(T x,U y){assert(y!=0); if(y<0)x=-x,y=-y; return (x>0?x/y:(x-y+1)/y);}
template<typename T>int popcnt(T x){return __builtin_popcountll(x);}
template<typename T>int topbit(T x){return (x==0?-1:63-__builtin_clzll(x));}
template<typename T>int lowbit(T x){return (x==0?-1:__builtin_ctzll(x));}
#line 2 "library/Utility/fastio.hpp"
#include <unistd.h>

class FastIO{
    static constexpr int L=1<<16;
    char rdbuf[L];
    int rdLeft=0,rdRight=0;
    inline void reload(){
        int len=rdRight-rdLeft;
        memmove(rdbuf,rdbuf+rdLeft,len);
        rdLeft=0,rdRight=len;
        rdRight+=fread(rdbuf+len,1,L-len,stdin);
    }
    inline bool skip(){
        for(;;){
            while(rdLeft!=rdRight and rdbuf[rdLeft]<=' ')rdLeft++;
            if(rdLeft==rdRight){
                reload();
                if(rdLeft==rdRight)return false;
            }
            else break;
        }
        return true;
    }
    template<typename T,enable_if_t<is_integral<T>::value,int> =0>inline bool _read(T& x){
        if(!skip())return false;
        if(rdLeft+20>=rdRight)reload();
        bool neg=false;
        if(rdbuf[rdLeft]=='-'){
            neg=true;
            rdLeft++;
        }
        x=0;
        while(rdbuf[rdLeft]>='0' and rdLeft<rdRight){
            x=x*10+(neg?-(rdbuf[rdLeft++]^48):(rdbuf[rdLeft++]^48));
        }
        return true;
    }
    inline bool _read(__int128_t& x){
        if(!skip())return false;
        if(rdLeft+40>=rdRight)reload();
        bool neg=false;
        if(rdbuf[rdLeft]=='-'){
            neg=true;
            rdLeft++;
        }
        x=0;
        while(rdbuf[rdLeft]>='0' and rdLeft<rdRight){
            x=x*10+(neg?-(rdbuf[rdLeft++]^48):(rdbuf[rdLeft++]^48));
        }
        return true;
    }
    inline bool _read(__uint128_t& x){
        if(!skip())return false;
        if(rdLeft+40>=rdRight)reload();
        x=0;
        while(rdbuf[rdLeft]>='0' and rdLeft<rdRight){
            x=x*10+(rdbuf[rdLeft++]^48);
        }
        return true;
    }
    template<typename T,enable_if_t<is_floating_point<T>::value,int> =0>inline bool _read(T& x){
        if(!skip())return false;
        if(rdLeft+20>=rdRight)reload();
        bool neg=false;
        if(rdbuf[rdLeft]=='-'){
            neg=true;
            rdLeft++;
        }
        x=0;
        while(rdbuf[rdLeft]>='0' and rdbuf[rdLeft]<='9' and rdLeft<rdRight){
            x=x*10+(rdbuf[rdLeft++]^48);
        }
        if(rdbuf[rdLeft]!='.')return true;
        rdLeft++;
        T base=.1;
        while(rdbuf[rdLeft]>='0' and rdbuf[rdLeft]<='9' and rdLeft<rdRight){
            x+=base*(rdbuf[rdLeft++]^48);
            base*=.1;
        }
        if(neg)x=-x;
        return true;
    }
    inline bool _read(char& x){
        if(!skip())return false;
        if(rdLeft+1>=rdRight)reload();
        x=rdbuf[rdLeft++];
        return true;
    }
    inline bool _read(string& x){
        if(!skip())return false;
        for(;;){
            int pos=rdLeft;
            while(pos<rdRight and rdbuf[pos]>' ')pos++;
            x.append(rdbuf+rdLeft,pos-rdLeft);
            if(rdLeft==pos)break;
            rdLeft=pos;
            if(rdLeft==rdRight)reload();
            else break;
        }
        return true;
    }
    template<typename T>inline bool _read(vector<T>& v){
        for(auto& x:v){
            if(!_read(x))return false;
        }
        return true;
    }

    char wtbuf[L],tmp[50];
    int wtRight=0;
    inline void flush(){
        fwrite(wtbuf,1,wtRight,stdout);
        wtRight=0;
    }
    inline void _write(const char& x){
        if(wtRight>L-32)flush();
        wtbuf[wtRight++]=x;
    }
    inline void _write(const string& x){
        for(auto& c:x)_write(c);
    }
    template<typename T,enable_if_t<is_integral<T>::value,int> =0>inline void _write(T x){
        if(wtRight>L-32)flush();
        if(x==0){
            _write('0');
            return;
        }
        else if(x<0){
            _write('-');
            if (__builtin_expect(x == std::numeric_limits<T>::min(), 0)) {
                switch (sizeof(x)) {
                case 2: _write("32768"); return;
                case 4: _write("2147483648"); return;
                case 8: _write("9223372036854775808"); return;
                }
            }
            x=-x;
        }
        int pos=0;
        while(x!=0){
            tmp[pos++]=char((x%10)|48);
            x/=10;
        }
        rep(i,0,pos)wtbuf[wtRight+i]=tmp[pos-1-i];
        wtRight+=pos;
    }
    inline void _write(__int128_t x){
        if(wtRight>L-40)flush();
        if(x==0){
            _write('0');
            return;
        }
        else if(x<0){
            _write('-');
            x=-x;
        }
        int pos=0;
        while(x!=0){
            tmp[pos++]=char((x%10)|48);
            x/=10;
        }
        rep(i,0,pos)wtbuf[wtRight+i]=tmp[pos-1-i];
        wtRight+=pos;
    }
    inline void _write(__uint128_t x){
        if(wtRight>L-40)flush();
        if(x==0){
            _write('0');
            return;
        }
        int pos=0;
        while(x!=0){
            tmp[pos++]=char((x%10)|48);
            x/=10;
        }
        rep(i,0,pos)wtbuf[wtRight+i]=tmp[pos-1-i];
        wtRight+=pos;
    }
    template<typename T>inline void _write(const vector<T>& v){
        rep(i,0,v.size()){
            if(i)_write(' ');
            _write(v[i]);
        }
    }
public:
    FastIO(){}
    ~FastIO(){flush();}
    inline void read(){}
    template <typename Head, typename... Tail>inline void read(Head& head,Tail&... tail){
        assert(_read(head));
        read(tail...); 
    }
    template<bool ln=true,bool space=false>inline void write(){if(ln)_write('\n');}
    template <bool ln=true,bool space=false,typename Head, typename... Tail>inline void write(const Head& head,const Tail&... tail){
        if(space)_write(' ');
        _write(head);
        write<ln,true>(tail...); 
    }
};

/**
 * @brief Fast IO
 */
#line 3 "sol.cpp"

#line 2 "library/Geometry/geometry.hpp"

using T=double;
const T eps=1e-12;
using Point=complex<T>;
using Poly=vector<Point>;
#define X real()
#define Y imag()
inline bool eq(const T& a,const T& b){
    return fabs(a-b)<eps;
}
bool cmp(const Point& a,const Point& b){
    auto sub=[&](Point a){return (a.Y<0?-1:(a.Y==0&&a.X>=0?0:1));};
    if(sub(a)!=sub(b))return sub(a)<sub(b);
    return a.Y*b.X<a.X*b.Y;
}
struct Line{
    Point a,b;
    Line(){}
    Line(Point _a,Point _b):a(_a),b(_b){}
    Line(T A,T B,T C){
        if(eq(A,.0)){
            a=Point(0,C/B),b=Point(1/C/B);
        }
        else if(eq(B,.0)){
            a=Point(C/A,0),b=Point(C/A,1);
        }
        else{
            a=Point(0,C/B),b=Point(C/A,0);
        }
    }
};
struct Segment:Line{
    Segment(){}
    Segment(Point _a,Point _b):Line(_a,_b){}
};
struct Circle{
    Point p; T r;
    Circle(){}
    Circle(Point _p,T _r):p(_p),r(_r){}
};

istream& operator>>(istream& is,Point& p){
    T x,y; is>>x>>y; p=Point(x,y);
    return is;
}
ostream& operator<<(ostream& os,Point& p){
    os<<fixed<<setprecision(12)<<p.X<<' '<<p.Y;
    return os;
}
Point unit(const Point& a){return a/abs(a);}
T dot(const Point& a,const Point& b){
    return a.X*b.X+a.Y*b.Y;
}
T cross(const Point& a,const Point& b){
    return a.X*b.Y-a.Y*b.X;
}
Point rot(const Point& a,const T& theta){
    return Point(cos(theta)*a.X-sin(theta)*a.Y,
        sin(theta)*a.X+cos(theta)*a.Y);
}
T arg(const Point& a,const Point& b,const Point& c){
    return acos(dot(a-b,c-b)/abs(a-b)/abs(c-b));
}

Point Projection(const Line&l,const Point& p){
    T t=dot(p-l.a,l.a-l.b)/norm(l.a-l.b);
    return l.a+(l.a-l.b)*t;
}
Point Projection(const Segment&l,const Point& p){
    T t=dot(p-l.a,l.a-l.b)/norm(l.a-l.b);
    return l.a+(l.a-l.b)*t;
}
Point Reflection(const Line& l,const Point& p){
    return p+(Projection(l,p)-p)*2.;
}
int ccw(const Point& a,Point b,Point c){
    b-=a; c-=a;
    if(cross(b,c)>eps)return 1; //ccw
    if(cross(b,c)<-eps)return -1; //cw
    if(dot(b,c)<0)return 2; //c,a,b
    if(norm(b)<norm(c))return -2; //a,b,c
    return 0; //a,c,b
}
bool isOrthogonal(const Line& a,const Line& b){
    return eq(dot(a.b-a.a,b.b-b.a),.0);
}
bool isParallel(const Line& a,const Line& b){
    return eq(cross(a.b-a.a,b.b-b.a),.0);
}
bool isIntersect(const Segment& a,const Segment& b){
    return ccw(a.a,a.b,b.a)*ccw(a.a,a.b,b.b)<=0 and
        ccw(b.a,b.b,a.a)*ccw(b.a,b.b,a.b)<=0;
}
int isIntersect(const Circle& a,const Circle& b){
    T d=abs(a.p-b.p);
    if(d>a.r+b.r+eps)return 4;
    if(eq(d,a.r+b.r))return 3;
    if(eq(d,abs(a.r-b.r)))return 1;
    if(d<abs(a.r-b.r)-eps)return 0;
    return 2;
}
T Dist(const Line& a,const Point& b){
    Point c=Projection(a,b);
    return abs(c-b);
}
T Dist(const Segment& a,const Point& b){
    if(dot(a.b-a.a,b-a.a)<eps)return abs(b-a.a);
    if(dot(a.a-a.b,b-a.b)<eps)return abs(b-a.b);
    return abs(cross(a.b-a.a,b-a.a))/abs(a.b-a.a);
}
T Dist(const Segment& a,const Segment& b){
    if(isIntersect(a,b))return .0;
    T res=min({Dist(a,b.a),Dist(a,b.b),Dist(b,a.a),Dist(b,a.b)});
    return res;
}
Point Intersection(const Line& a,const Line& b){
    T d1=cross(a.b-a.a,b.b-b.a);
    T d2=cross(a.b-a.a,a.b-b.a);
    if(eq(d1,0) and eq(d2,0))return b.a;
    return b.a+(b.b-b.a)*(d2/d1);
}
Poly Intersection(const Circle& a,const Line& b){
    Poly res;
    T d=Dist(b,a.p);
    if(d>a.r+eps)return res;
    Point h=Projection(b,a.p);
    if(eq(d,a.r)){
        res.push_back(h);
        return res;
    }
    Point e=unit(b.b-b.a);
    T ph=sqrt(a.r*a.r-d*d);
    res.push_back(h-e*ph);
    res.push_back(h+e*ph);
    return res;
}
Poly Intersection(const Circle& a,const Segment& b){
    Line c(b.a,b.b);
    Poly sub=Intersection(a,c);
    double xmi=min(b.a.X,b.b.X),xma=max(b.a.X,b.b.X);
    double ymi=min(b.a.Y,b.b.Y),yma=max(b.a.Y,b.b.Y);
    Poly res;
    rep(i,0,sub.size()){
        if(xmi<=sub[i].X+eps and sub[i].X-eps<=xma and
            ymi<=sub[i].Y+eps and sub[i].Y-eps<=yma){
            res.push_back(sub[i]);
        }
    }
    return res;
}
Poly Intersection(const Circle& a,const Circle& b){
    Poly res;
    int mode=isIntersect(a,b);
    T d=abs(a.p-b.p);
    if(mode==4 or mode==0)return res;
    if(mode==3){
        T t=a.r/(a.r+b.r);
        res.push_back(a.p+(b.p-a.p)*t);
        return res;
    }
    if(mode==1){
        if(b.r<a.r-eps){
            res.push_back(a.p+(b.p-a.p)*(a.r/d));
        }
        else{
            res.push_back(b.p+(a.p-b.p)*(b.r/d));
        }
        return res;
    }
    T rc=(a.r*a.r+d*d-b.r*b.r)/d/2.;
    T rs=sqrt(a.r*a.r-rc*rc);
    if(a.r-abs(rc)<eps)rs=0;
    Point e=unit(b.p-a.p);
    res.push_back(a.p+rc*e+rs*e*Point(0,1));
    res.push_back(a.p+rc*e+rs*e*Point(0,-1));
    return res;
}
T Area(const Poly& a){
    T res=0;
    int n=a.size();
    rep(i,0,n)res+=cross(a[i],a[(i+1)%n]);
    return fabs(res/2.);
}
T Area(const Poly& a,const Circle& b){
    int n=a.size();
    if(n<3)return .0;
    auto rec=[&](auto self,const Circle& c,const Point& p1,const Point& p2){
        Point va=c.p-p1,vb=c.p-p2;
        T f=cross(va,vb),res=.0;
        if(eq(f,.0))return res;
        if(max(abs(va),abs(vb))<c.r+eps)return f;
        if(Dist(Segment(p1,p2),c.p)>c.r-eps)return c.r*c.r*arg(vb*conj(va));
        auto u=Intersection(c,Segment(p1,p2));
        Poly sub;
        sub.push_back(p1);
        for(auto& x:u)sub.push_back(x);
        sub.push_back(p2);
        rep(i,0,sub.size()-1)res+=self(self,c,sub[i],sub[i+1]);
        return res;
    };
    T res=.0;
    rep(i,0,n)res+=rec(rec,b,a[i],a[(i+1)%n]);
    return fabs(res/2.);
}
T Area(const Circle& a,const Circle& b){
    T d=abs(a.p-b.p);
    if(d>=a.r+b.r-eps)return .0;
    if(d<=abs(a.r-b.r)+eps){
        T r=min(a.r,b.r);
        return M_PI*r*r;
    }
    T ath=acos((a.r*a.r+d*d-b.r*b.r)/d/a.r/2.);
    T res=a.r*a.r*(ath-sin(ath*2)/2.);
    T bth=acos((b.r*b.r+d*d-a.r*a.r)/d/b.r/2.);
    res+=b.r*b.r*(bth-sin(bth*2)/2.);
    return fabs(res);
}
bool isConvex(const Poly& a){
    int n=a.size();
    int cur,pre,nxt;
    rep(i,0,n){
        pre=(i-1+n)%n;
        nxt=(i+1)%n;
        cur=i;
        if(ccw(a[pre],a[cur],a[nxt])==-1)return 0;
    }
    return 1;
}
int isContained(const Poly& a,const Point& b){ // 0:not contain,1:on edge,2:contain
    bool res=0;
    int n=a.size();
    rep(i,0,n){
        Point p=a[i]-b,q=a[(i+1)%n]-b;
        if(p.Y>q.Y)swap(p,q);
        if(p.Y<eps and eps<q.Y and cross(p,q)>eps)res^=1;
        if(eq(cross(p,q),.0) and dot(p,q)<eps)return 1;
    }
    return (res?2:0);
}
Poly ConvexHull(Poly& a){
    int n=a.size(),k=0;
    sort(ALL(a),[](const Point& p,const Point& q){
        return (eq(p.Y,q.Y)?p.X<q.X:p.Y<q.Y);
    });
    Poly res(n*2);
    for(int i=0;i<n;res[k++]=a[i++]){
        while(k>=2 and cross(res[k-1]-res[k-2],a[i]-res[k-1])<-eps)k--;
    }
    for(int i=n-2,t=k+1;i>=0;res[k++]=a[i--]){
        while(k>=t and cross(res[k-1]-res[k-2],a[i]-res[k-1])<-eps)k--;
    }
    res.resize(k-1); return res;
}
T Diam(const Poly& a){
    int n=a.size();
    int x=0,y=0;
    rep(i,1,n){
        if(a[i].Y>a[x].Y)x=i;
        if(a[i].Y<a[y].Y)y=i;
    }
    T res=abs(a[x]-a[y]);
    int i=x,j=y;
    do{
        if(cross(a[(i+1)%n]-a[i],a[(j+1)%n]-a[j])<0)i=(i+1)%n;
        else j=(j+1)%n;
        chmax(res,abs(a[i]-a[j]));
    }while(i!=x or j!=y);
    return res;
}
Poly Cut(const Poly& a,const Line& l){
    int n=a.size(); Poly res;
    rep(i,0,n){
        Point p=a[i],q=a[(i+1)%n];
        if(ccw(l.a,l.b,p)!=-1)res.push_back(p);
        if(ccw(l.a,l.b,p)*ccw(l.a,l.b,q)<0)res.push_back(Intersection(Line(p,q),l));
    }
    return res;
}

T Closest(Poly& a){
    int n=a.size();
    if(n<=1)return 0;
    sort(ALL(a),[&](Point a,Point b){return (eq(a.X,b.X)?a.Y<b.Y:a.X<b.X);});
    Poly buf(n);
    auto rec=[&](auto self,int lb,int rb)->T{
        if(rb-lb<=1)return (T)INF;
        int mid=(lb+rb)>>1;
        auto x=a[mid].X;
        T res=min(self(self,lb,mid),self(self,mid,rb));
        inplace_merge(a.begin()+lb,a.begin()+mid,a.begin()+rb,
            [&](auto p,auto q){return p.Y<q.Y;});
        int ptr=0;
        rep(i,lb,rb){
            if(abs(a[i].X-x)>=res)continue;
            rep(j,0,ptr){
            auto sub=a[i]-buf[ptr-1-j];
            if(sub.Y>=res)break;
            chmin(res,abs(sub));
            }
            buf[ptr++]=a[i];
        }
        return res;
    };
    return rec(rec,0,n);
}

Circle Incircle(const Point& a,const Point& b,const Point& c){
    T A=abs(b-c),B=abs(c-a),C=abs(a-b);
    Point p(A*a.X+B*b.X+C*c.X,A*a.Y+B*b.Y+C*c.Y);
    p/=(A+B+C);
    T r=Dist(Line(a,b),p);
    return Circle(p,r);
}
Circle Circumcircle(const Point& a,const Point& b,const Point& c){
    Line l1((a+b)/2.,(a+b)/2.+(b-a)*Point(0,1));
    Line l2((b+c)/2.,(b+c)/2.+(c-b)*Point(0,1));
    Point p=Intersection(l1,l2);
    return Circle(p,abs(p-a));
}
Poly tangent(const Point& a,const Circle& b){
    return Intersection(b,Circle(a,sqrt(norm(b.p-a)-b.r*b.r)));
}
vector<Line> tangent(const Circle& a,const Circle& b){
    vector<Line> res;
    T d=abs(a.p-b.p);
    if(eq(d,0))return res;
    Point u=unit(b.p-a.p);
    Point v=u*Point(0,1);
    for(int t:{-1,1}){
        T h=(a.r+b.r*t)/d;
        if(eq(h*h,1)){
            res.push_back(Line(a.p+(h>0?u:-u)*a.r,
            a.p+(h>0?u:-u)*a.r+v));
        }
        else if(1>h*h){
            Point U=u*h,V=v*sqrt(1-h*h);
            res.push_back(Line(a.p+(U+V)*a.r,b.p-(U+V)*(b.r*t)));
            res.push_back(Line(a.p+(U-V)*a.r,b.p-(U-V)*(b.r*t)));
        }
    }
    return res;
}

/**
 * @brief Geometry
 */
#line 5 "sol.cpp"

FastIO io;
int main(){
    int a,b,c;
    io.read(a,b,c);

    Point A(0,0),B(b,0);
    rep(x,1,b+c)rep(y,1,b+c){
        double cosa=double(b*b+c*c-(x+y+a)*(x+y+a))*1./(2*b*c);
        if(cosa>1.-eps or fabs(cosa)<eps)continue;
        if(b+c==x+a+y)continue;
        Point C=rot(Point(c,0),acos(cosa));
        Point D=C*(double(x)/(x+y+a))+B*(double(a+y)/(x+y+a));
        Point E=B*(double(y)/(x+y+a))+C*(double(a+x)/(x+y+a));
        double diff=fabs(arg(C,A,E)-arg(D,A,B));
        if(diff<eps){
            io.write("Yes");
            cerr<<x<<' '<<y<<'\n';
            return 0;
        }
    }
    io.write("No");
    return 0;
}