uvalive 4973 Ardenia

题意：给出空间两条线段，求距离。

注意输出格式！

 #include<cstdio>
 #include<cmath>
 #include<algorithm>
 using namespace std;

 struct Point3
 {
     int x, y, z;
     Point3(int x=, int y=, int z=):x(x),y(y),z(z) { }
 };

 typedef Point3 Vector3;

 Vector3 operator + (const Vector3& A, const Vector3& B)
 {
     return Vector3(A.x+B.x, A.y+B.y, A.z+B.z);
 }
 Vector3 operator - (const Point3& A, const Point3& B)
 {
     return Vector3(A.x-B.x, A.y-B.y, A.z-B.z);
 }
 Vector3 operator * (const Vector3& A, int p)
 {
     return Vector3(A.x*p, A.y*p, A.z*p);
 }

 bool operator == (const Point3& a, const Point3& b)
 {
     return a.x==b.x && a.y==b.y && a.z==b.z;
 }

 Point3 read_point3()
 {
     Point3 p;
     scanf("%d%d%d", &p.x, &p.y, &p.z);
     return p;
 }

 int Dot(const Vector3& A, const Vector3& B)
 {
     return A.x*B.x + A.y*B.y + A.z*B.z;
 }
 int Length2(const Vector3& A)
 {
     return Dot(A, A);
 }
 Vector3 Cross(const Vector3& A, const Vector3& B)
 {
     return Vector3(A.y*B.z - A.z*B.y, A.z*B.x - A.x*B.z, A.x*B.y - A.y*B.x);
 }

 typedef long long LL;

 LL gcd(LL a, LL b)
 {
     return b ? gcd(b, a%b) : a;
 }
 LL lcm(LL a, LL b)
 {
     return a / gcd(a,b) * b;
 }

 struct Rat
 {
     LL a, b;
     Rat(LL a=):a(a),b() { }
     Rat(LL x, LL y):a(x),b(y)
     {
         if(b < ) a = -a, b = -b;
         LL d = gcd(a, b);
         if(d < ) d = -d;
         a /= d;
         b /= d;
     }
 };

 Rat operator + (const Rat& A, const Rat& B)
 {
     LL x = lcm(A.b, B.b);
     return Rat(A.a*(x/A.b)+B.a*(x/B.b), x);
 }

 Rat operator - (const Rat& A, const Rat& B)
 {
     return A + Rat(-B.a, B.b);
 }
 Rat operator * (const Rat& A, const Rat& B)
 {
     return Rat(A.a*B.a, A.b*B.b);
 }

 void updatemin(Rat& A, const Rat& B)
 {
     if(A.a*B.b > B.a*A.b) A.a = B.a, A.b = B.b;
 }

 // 点P到线段AB的距离的平方
 Rat Rat_Distance2ToSegment(const Point3& P, const Point3& A, const Point3& B)
 {
     if(A == B) return Length2(P-A);
     Vector3 v1 = B - A, v2 = P - A, v3 = P - B;
     if(Dot(v1, v2) < ) return Length2(v2);
     else if(Dot(v1, v3) > ) return Length2(v3);
     else return Rat(Length2(Cross(v1, v2)), Length2(v1));
 }

 // 求异面直线p1+su和p2+tv的公垂线对应的s。如果平行/重合，返回false
 bool Rat_LineDistance3D(const Point3& p1, const Vector3& u, const Point3& p2, const Vector3& v, Rat& s)
 {
     LL b = (LL)Dot(u,u)*Dot(v,v) - (LL)Dot(u,v)*Dot(u,v);
     if(b == ) return false;
     LL a = (LL)Dot(u,v)*Dot(v,p1-p2) - (LL)Dot(v,v)*Dot(u,p1-p2);
     s = Rat(a, b);
     return true;
 }

 void Rat_GetPointOnLine(const Point3& A, const Point3& B, const Rat& t, Rat& x, Rat& y, Rat& z)
 {
     x = Rat(A.x) + Rat(B.x-A.x) * t;
     y = Rat(A.y) + Rat(B.y-A.y) * t;
     z = Rat(A.z) + Rat(B.z-A.z) * t;
 }

 Rat Rat_Distance2(const Rat& x1, const Rat& y1, const Rat& z1, const Rat& x2, const Rat& y2, const Rat& z2)
 {
     return (x1-x2)*(x1-x2)+(y1-y2)*(y1-y2)+(z1-z2)*(z1-z2);
 }

 int main()
 {
     int T;
     scanf("%d", &T);
     LL maxx = ;
     while(T--)
     {
         Point3 A = read_point3();
         Point3 B = read_point3();
         Point3 C = read_point3();
         Point3 D = read_point3();
         Rat s, t;
         bool ok = false;
         Rat ans = Rat();
         if(Rat_LineDistance3D(A, B-A, C, D-C, s))
             if(s.a >  && s.a < s.b && Rat_LineDistance3D(C, D-C, A, B-A, t))
                 if(t.a >  && t.a < t.b)
                 {
                     ok = true; // 异面直线/相交直线
                     Rat x1, y1, z1, x2, y2, z2;
                     Rat_GetPointOnLine(A, B, s, x1, y1, z1);
                     Rat_GetPointOnLine(C, D, t, x2, y2, z2);
                     ans = Rat_Distance2(x1, y1, z1, x2, y2, z2);
                 }
         if(!ok)   // 平行直线/重合直线
         {
             updatemin(ans, Rat_Distance2ToSegment(A, C, D));
             updatemin(ans, Rat_Distance2ToSegment(B, C, D));
             updatemin(ans, Rat_Distance2ToSegment(C, A, B));
             updatemin(ans, Rat_Distance2ToSegment(D, A, B));
         }
         printf("%lld %lld\n", ans.a, ans.b);
     }
     return ;
 }