UVA1469 Ardenia（三维几何，分数类）

https://www.luogu.com.cn/problem/UVA1469

求空间两条线段距离，三维几何入门，存板子

#define IO std::ios::sync_with_stdio(0)
#include <bits/stdc++.h>
using namespace  std;
typedef long long ll;
const double eps=1e-6;
ll gcd(ll x,ll y){
    return x%y==0?y:gcd(y,x%y);
}
struct Point{
    int x,y,z;
    Point (int x=0,int y=0,int z=0):x(x),y(y),z(z){}

    bool operator <(const Point &u)const{
        return x-u.x<0
        ||(x-u.x==0&&y-u.y<0)
        ||(x-u.x==0&&y-u.y==0&&z-u.z<0);
    }

    bool operator >(const Point &u)const{
        return u<(*this);
    }
    bool operator ==(const Point &u)const{
        return !(u<(*this)||(*this)<u);
    }
    bool operator !=(const Point &u)const{
        return !((*this)==u);
    }
    bool operator <=(const Point &u)const{
        return *this<u||*this==u;
    }
    bool operator >=(const Point &u)const{
        return u<*this||*this==u;
    }
    Point operator +(const Point &u)const{
        return Point(x+u.x,y+u.y,z+u.z);
    }
    Point operator -(const Point &u)const{
        return Point(x-u.x,y-u.y,z-u.z);
    }
    Point operator *(const int u)const{
        return Point(x*u,y*u,z*u);
    }
    Point operator /(const int u)const{
        return Point(x/u,y/u,z/u);
    }
    void read(){
        scanf("%d%d%d",&x,&y,&z);
    }
};
typedef Point Vector;
struct rat{
    ll z,m;
    rat(ll z=0,ll m=1){
        ll d=gcd(z,m);
        z/=d;
        m/=d;
        if(m<0)z=-z,m=-m;
        this->z=z;
        this->m=m;
    }
    rat operator +(const rat &u)const{
        ll d=gcd(m,u.m);
        return rat(z*(u.m/d)+u.z*(m/d),m*(u.m/d));
    }
    rat operator -(const rat &u)const{
        ll d=gcd(m,u.m);
        return rat(z*(u.m/d)-u.z*(m/d),m*(u.m/d));
    }
    rat operator *(const rat &u)const{
        return rat(z*u.z,m*u.m);
    }
    bool operator <(const rat &u)const{
        return z*u.m<u.z*m;
    }
    bool operator >(const rat &u)const{
        return u<*this;
    }
    bool operator ==(const rat &u)const{
        return !(u<*this||*this<u);
    }
    bool operator !=(const rat &u)const{
        return !(*this==u);
    }
    bool operator <=(const rat &u)const{
        return *this<u||*this==u;
    }
    bool operator >=(const rat &u)const{
        return u<*this||*this==u;
    }
    
};

inline int dcmp(rat u){
    if(u.z==0)return 0;
    return u.z<0?-1:1;
}
ll Dot(Vector A,Vector B){
    return A.x*B.x+A.y*B.y+A.z*B.z;
}
ll Length(Vector A){
    return Dot(A,A);
}
Vector Cross(Vector A,Vector B){
    return Vector(A.y*B.z-A.z*B.y,A.z*B.x-A.x*B.z,A.x*B.y-A.y*B.x);
}
rat ptoseg(Point P,Point A,Point B){
    if(A==B)return Length(P-A);
    Vector v1=B-A,v2=P-A,v3=P-B;
    if(Dot(v1,v2)<0)return Length(v2);
    else if(Dot(v1,v3)>0)return Length(v3);
    else return rat(Length(Cross(v1,v2)),Length(v1));
}

bool linetoline(Point p1, Vector u,Point p2,Vector v,rat &s){
    ll b=Dot(u,u)*Dot(v,v)-Dot(u,v)*Dot(u,v);
    if(b==0)return false;
    ll a=Dot(u,v)*Dot(v,p1-p2)-Dot(v,v)*Dot(u,p1-p2);
    s=rat(a,b);
    return true;
}
int T;
Point p[10];

int main(){
    scanf("%d",&T);
    while(T--){
        for(int i=1;i<=4;i++){
            p[i].read();
        }
        rat r1,r2,ans;
        ans.z=1e9;
        int f1=linetoline(p[1],p[2]-p[1],p[3],p[4]-p[3],r1);
        int f2=linetoline(p[3],p[4]-p[3],p[1],p[2]-p[1],r2);

        if(f1&&f2&&r1.z>0&&r1.z<r1.m&&r2.z>0&&r2.z<r2.m){
            Vector u=p[2]-p[1],v=p[4]-p[3];
            rat x1=rat(p[1].x)+r1*u.x;
            rat y1=rat(p[1].y)+r1*u.y;
            rat z1=rat(p[1].z)+r1*u.z;

            rat x2=rat(p[3].x)+r2*v.x;
            rat y2=rat(p[3].y)+r2*v.y;
            rat z2=rat(p[3].z)+r2*v.z;

            ans=(x2-x1)*(x2-x1)+(y2-y1)*(y2-y1)+(z2-z1)*(z2-z1);
        }
        else{
            ans=min(ans,ptoseg(p[1],p[3],p[4]));
            ans=min(ans,ptoseg(p[2],p[3],p[4]));
            ans=min(ans,ptoseg(p[3],p[1],p[2]));
            ans=min(ans,ptoseg(p[4],p[1],p[2]));
        }
        printf("%lld %lld
",ans.z,ans.m);
    }

}