結果

問題 No.3005 トレミーの問題
ユーザー GOTKAKO
提出日時 2025-01-17 22:32:29
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 2 ms / 2,000 ms
コード長 5,081 bytes
コンパイル時間 2,785 ms
コンパイル使用メモリ 201,596 KB
実行使用メモリ 5,248 KB
最終ジャッジ日時 2025-01-17 22:34:37
合計ジャッジ時間 3,619 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge4
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 30
権限があれば一括ダウンロードができます

ソースコード

diff # 

#include <bits/stdc++.h>
using namespace std;

struct frac{ //最終的に分子分母64bitに収まる計算のみ.
    public:
    long long n,d;
    frac() : n(0),d(1){}
    frac(long long v) : n(v),d(1) {}
    frac(__int128_t a,__int128_t b,bool redu = true){
        assert(b != 0);
        if(redu) reduce(a,b);
        n = a,d = b; 
    }
    private:
    __int128_t gcd(__int128_t a,__int128_t b){
        if(a%b == 0) return b;
        return gcd(b,a%b);
    } 
    __int128_t gcd128(__int128_t a,__int128_t b){ //絶対値gcd128.
        if(b == 0) return abs(a);
        return gcd(abs(a),abs(b));
    }
    void reduce(__int128_t &a,__int128_t &b){ //約分.
        if(b < 0) a = -a,b = -b;
        __int128_t div = gcd128(a,b);
        a /= div; b /= div;
    }
    public:
    //計算量 O(logmax(d,b.d)).
    friend frac operator+(const frac &b){return b;}
    friend frac operator-(const frac &b){return frac(-b.n,b.d,false);}
    friend frac operator+(const frac &a,const frac &b){
        return frac((__int128_t)a.n*b.d+(__int128_t)b.n*a.d,(__int128_t)a.d*b.d);
    } 
    friend frac operator-(const frac &a,const frac &b){
        return frac((__int128_t)a.n*b.d-(__int128_t)b.n*a.d,(__int128_t)a.d*b.d);
    }
    friend frac operator*(const frac &a,const frac &b){
        long long g1 = std::gcd(a.n,b.d),g2 = std::gcd(a.d,b.n);
        return frac((a.n/g1)*(b.n/g2),(a.d/g2)*(b.d/g1),false);
    }
    friend frac operator/(const frac &a,const frac &b){
        assert(b.n != 0);
        long long g1 = std::gcd(a.n,b.n),g2 = std::gcd(a.d,b.d);
        if(b.n < 0) return frac((-a.n/g1)*(b.d/g2),(a.d/g2)*(-b.n/g1));
        else return frac((a.n/g1)*(b.d/g2),(a.d/g2)*(b.n/g1));
    }
    friend bool operator==(const frac &a,const frac &b){return a.n==b.n && a.d==b.d;}
    friend bool operator!=(const frac &a,const frac &b){return a.n!=b.n || a.d!=b.d;}
    friend bool operator>(const frac &a,const frac &b){return (__int128_t)a.n*b.d > (__int128_t)b.n*a.d;}
    friend bool operator>=(const frac &a,const frac &b){return (__int128_t)a.n*b.d >= (__int128_t)b.n*a.d;}
    friend bool operator<(const frac &a,const frac &b){return (__int128_t)a.n*b.d < (__int128_t)b.n*a.d;}
    friend bool operator<=(const frac &a,const frac &b){return (__int128_t)a.n*b.d <= (__int128_t)b.n*a.d;}
 
    frac &operator=(const frac &b) = default;
    frac operator+=(const frac &b){return *this=*this+b;}
    frac operator-=(const frac &b){return *this=*this-b;}
    frac operator*=(const frac &b){return *this=*this*b;}
    frac operator/=(const frac &b){return *this=*this/b;}
    frac operator++(int){*this += frac(1); return *this;}
    frac operator--(int){*this -= frac(1); return *this;}
 
    double decimal(){return (n+0.0)/d;}
    long double decimall(){return ((long double)n)/d;}
    long long num(){return n;} long long den(){return d;}
    long long floor(){return n<0?(n+1)/d-1:n/d;}
    long long ceil(){return n>0?(n-1)/d+1:n/d;}
    frac inv(){return frac(n>=0?d:-d,n>=0?n:-n,false);}
};
struct Point{
    frac x,y;
    Point() : x(0),y(0) {}
    Point(long long a,long long b) : x(frac(a)),y(frac(b)) {}
    Point(frac a,frac b) : x(a),y(b) {}
    Point operator+(const Point &b){return Point(x+b.x,y+b.y);}
    Point operator-(const Point &b){return Point(x-b.x,y-b.y);}
    Point operator+=(const Point &b){return *this=*this+b;}
    Point operator-=(const Point &b){return *this=*this-b;}
    bool operator==(const Point &b){return x==b.x && y==b.y;}
    bool operator!=(const Point &b){return x!=b.x || y!=b.y;}

    friend frac dist(const Point &a,const Point &b){
        return (a.x-b.x)*(a.x-b.x)+(a.y-b.y)*(a.y-b.y);
    }
};
long long INF = 8e18;
frac cross(Point &a,Point &b){return a.x*b.y-a.y*b.x;}
Point findInt/*ersecton*/(Point &a,Point &b,Point &c,Point &d){//線分abと線分cdの交点.
    Point NG(INF,INF);
    Point ba = b-a,dc = d-c,ca = c-a,ac = a-c;
    frac div = cross(ba,dc);
    if(div == 0) return NG;
    frac s = cross(ca,dc)/div;
    frac t = cross(ba,ac)/div;
    if(s < 0 || s > 1 || t < 0 || t > 1) return NG;
if(s <= 0 || s >= 1 || t <= 0 || t >= 1) return NG; //端点NG.
    return Point{a.x+s*ba.x,a.y+s*ba.y};
}


int main(){
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);

    int N = 4;
    vector<Point> P(4);
    for(auto &p : P){
        int x,y; cin >> x >> y;
        p = {x,y};
    }

    bool yes = false;
    Point c = findInt(P.at(0),P.at(1),P.at(2),P.at(3));
    frac one = dist(c,P.at(0)),two = dist(c,P.at(1)),three = dist(c,P.at(2)),four = dist(c,P.at(3));
    if(c.x != INF && one*two == three*four) yes = true;
    c = findInt(P.at(0),P.at(3),P.at(1),P.at(2));
    one = dist(c,P.at(0)),two = dist(c,P.at(1)),three = dist(c,P.at(2)),four = dist(c,P.at(3));
    if(c.x != INF && one*four == two*three) yes = true;
    c = findInt(P.at(0),P.at(2),P.at(1),P.at(3));
    one = dist(c,P.at(0)),two = dist(c,P.at(1)),three = dist(c,P.at(2)),four = dist(c,P.at(3));
    if(c.x != INF && one*three == two*four) yes = true;
    
    if(yes) cout << "YES\n";
    else cout << "NO\n";
}
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