LA 4973

// LA4973 Ardenia// Rujia Liu#include<cstdio>#include<cmath>#include<algorithm>using namespace std;struct Point3 {  int x, y, z;  Point3(int x=0, int y=0, int z=0):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=0):a(a),b(1) { }  Rat(LL x, LL y):a(x),b(y) {    if(b < 0) a = -a, b = -b;    LL d = gcd(a, b); if(d < 0) 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) < 0) return Length2(v2);  else if(Dot(v1, v3) > 0) 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falsebool 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 == 0) 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 = 0;  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(1000000000);    if(Rat_LineDistance3D(A, B-A, C, D-C, s))      if(s.a > 0 && s.a < s.b && Rat_LineDistance3D(C, D-C, A, B-A, t))        if(t.a > 0 && 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 0;}

厄，直接看了刘汝佳的代码；

分两种情况讨论，两直线平行或重合的情况，求端点到另一条直线的距离，取最小值即可，异面直线的情况，直接套用模板就可以了。