uva 1469 - Ardenia（几何+分数）

题目链接：uva 1469 - Ardenia

#include <cstdio>#include <cstring>#include <cmath>#include <algorithm>using namespace std;typedef long long ll;struct Point3 {int x, y, z;Point3 (int x = 0, int y = 0, int z = 0): x(x), y(y), z(z) {}bool operator < (const Point3& 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 Point3& u) const { return u < (*this); }bool operator == (const Point3& u) const { return !(u < (*this) || (*this) < u); }bool operator != (const Point3& u) const { return !((*this) == u); }bool operator <= (const Point3& u) const { return *this < u || *this == u; }bool operator >= (const Point3& u) const { return *this > u || *this == u; }Point3 operator + (const Point3& u) const { return Point3(x+u.x, y+u.y, z+u.z); }Point3 operator - (const Point3& u) const { return Point3(x-u.x, y-u.y, z-u.z); }Point3 operator * (const int u) const { return Point3(x*u, y*u, z*u); }Point3 operator / (const int u) const { return Point3(x/u, y/u, z/u); }void read () { scanf("%d%d%d", &x, &y, &z); }};typedef Point3 Vector3;ll getDot(Vector3 a, Vector3 b) { return a.x*b.x+a.y*b.y+a.z*b.z; }Vector3 getCross (Vector3 a, 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); }ll getPowerLength(Vector3 u) { return getDot(u, u); }ll gcd(ll a, ll b) { return b == 0 ? a : gcd(b, a%b); }struct Rat {ll s, m;Rat (ll s = 0, ll m = 1) {ll d = gcd(s, m);s /= d, m /= d;if (m < 0) m=-m,s=-s;this->s = s;this->m = m;}Rat operator + (const Rat& u) const { ll d = gcd(m, u.m); return Rat(s*(u.m/d)+u.s*(m/d), m * (u.m / d)); }Rat operator - (const Rat& u) const { ll d = gcd(m, u.m); return Rat(s*(u.m/d)-u.s*(m/d), m * (u.m / d)); }Rat operator * (const Rat& u) const { return Rat(s*u.s, m*u.m); }//Rat operator * (const int& u) const { return Rat(s*u, m); }//Rat operator / (const Rat& u) const { return Rat(s*u.m, m*u.s); }//Rat operator / (const int& u) const { return Rat(s, m*u); }bool operator < (const Rat& u) const { return s*u.m < u.s*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 *this > u || *this == u; }};inline int dcmp(Rat u) { if (u.s == 0) return 0; else return u.s < 0 ? -1 : 1; }Rat getDistancePointToSegment (Point3 p, Point3 a, Point3 b) {if (a == b) return getPowerLength(p-a);Vector3 v1 = b-a, v2 = p-a, v3 = p-b;if (getDot(v1, v2) < 0) return getPowerLength(v2);else if (getDot(v1, v3) > 0) return getPowerLength(v3);else return Rat(getPowerLength(getCross(v1, v2)), getPowerLength(v1));}bool getDistanceLineToLine(Point3 p1, Vector3 u, Point3 p2, Vector3 v, Rat& s) {ll b = getDot(u, u) * getDot(v, v) - getDot(u, v) * getDot(u, v);if (b == 0) return false;ll a = getDot(u, v) * getDot(v, p1-p2) - getDot(v, v) * getDot(u, p1-p2);s = Rat(a, b);return true;}const ll inf = 0x3f3f3f3f;int main () {int cas;scanf("%d", &cas);while (cas--) {Point3 a, b, c, d;a.read(), b.read(), c.read(), d.read();Rat s, t, ans(inf);bool flag1 = getDistanceLineToLine(a, b-a, c, d-c, s);bool flag2 = getDistanceLineToLine(c, d-c, a, b-a, t);if (flag1 && flag2 && s.s > 0 && s.s < s.m && t.s > 0 && t.s < t.m) {Vector3 u = b-a, v = d-c;Rat x1 = Rat(a.x) + s * u.x, y1 = Rat(a.y) + s * u.y, z1 = Rat(a.z) + s * u.z;Rat x2 = Rat(c.x) + t * v.x, y2 = Rat(c.y) + t * v.y, z2 = Rat(c.z) + t * v.z;ans = (x2-x1)*(x2-x1) + (y2-y1)*(y2-y1) + (z2-z1)*(z2-z1);} else {ans = min(ans, getDistancePointToSegment(a, c, d));ans = min(ans, getDistancePointToSegment(b, c, d));ans = min(ans, getDistancePointToSegment(c, a, b));ans = min(ans, getDistancePointToSegment(d, a, b));}printf("%lld %lld\n", ans.s, ans.m);}return 0;}