UVa 10794 The Deadly Olympic Returns!!!

Link To The Problem

Solution : 数学，计算

Code:

//UVa 10794// | a-b |^2 = |a|^2 + |b|^2 + 2*(a*b) #include<cstdio>#include<cstring>#include<iostream>#include<algorithm>#include<vector>#include<cmath>using namespace std;#define dbg(x)  cout << __LINE__ << ": " << #x << " = " << (x) << endl#define nMax 10010#define sf scanf#define pf printf#define rep(i,n) for(int (i)=0;(i)<(n);(i)++)#define pb push_back#define mp make_pairdouble const eps = 1e-9;double const pi = acos(-1.0);inline int dcmp(double x) {if(x>=-eps && x<=eps) return 0;return x > 0 ? 1 : -1;}/***********¿?¿?*************/struct Point3 {  double x, y, z;  Point3() {};  Point3(double x, double y, double z):x(x),y(y),z(z) { }  void read() { sf("%lf%lf%lf",&x,&y,&z); }  double len() { return x*x+y*y+z*z; }  void out() { pf("(%.3lf , %.3lf , %.3lf)\n",x,y,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, double p) { return Vector3(A.x*p, A.y*p, A.z*p); }Vector3 operator * (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); }Vector3 operator / (const Vector3& A, double p) { return Vector3(A.x/p, A.y/p, A.z/p); }double  operator ^ (const Vector3& A, const Vector3& B) { return A.x*B.x + A.y*B.y + A.z*B.z; }bool operator == (const Point3& A,const Point3& B)  { return dcmp(A.x-B.x)==0 && dcmp(A.y-B.y)==0 && dcmp(A.z-B.z)==0 ; }double Dot(const Vector3& A, const Vector3& B) { return A.x*B.x + A.y*B.y + A.z*B.z; }double Length(const Vector3& A) { return sqrt(Dot(A, A)); }double Angle(const Vector3& A, const Vector3& B) { return acos(Dot(A, B) / Length(A) / Length(B)); }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); }double Area2(const Point3& A, const Point3& B, const Point3& C) { return Length(Cross(B-A, C-A)); }double Volume6(const Point3& A, const Point3& B, const Point3& C, const Point3& D) { return fabs(Dot(D-A, Cross(B-A, C-A))); }// ¿?¿?¿?¿?¿?¿?Point3 Centroid(const Point3& A, const Point3& B, const Point3& C, const Point3& D) { return (A + B + C + D)/4.0; }struct line3{Point3 a,b;line3() {};line3(Point3 a,Point3 b):a(a),b(b){};void read() { a.read(),b.read(); }void out() { pf("-line-: \n");a.out(),b.out(),pf("---end---\n"); }};struct plane3{Point3 a,b,c;Vector3 n;plane3() {};plane3(Point3 a,Point3 b,Point3 c):a(a),b(b),c(c){n=(a-b)*(b-c);};Vector3 prev() {return n = (a-b)*(b-c);}};/************¿?¿?¿?*************/// ¿?p¿?¿?¿?p0-n¿?¿?¿?¿?n¿?¿?¿?¿?¿?¿?¿?double DistanceToPlane(const Point3& p, const Point3& p0, const Vector3& n) {  return fabs(Dot(p-p0, n)); // ¿?¿?¿?¿?¿?¿?¿?¿?¿?¿?¿?¿?¿?¿?¿?¿?}// ¿?p¿?¿?¿?p0-n¿?¿?¿?¿?¿?n¿?¿?¿?¿?¿?¿?¿?Point3 GetPlaneProjection(const Point3& p, const Point3& p0, const Vector3& n) {  return p-n*Dot(p-p0, n);}//¿?¿?p1-p2 ¿?¿?¿?p0-n¿?¿?¿?Point3 LinePlaneIntersection(Point3 p1, Point3 p2, Point3 p0, Vector3 n){    Vector3 v = p2-p1;    double t = (Dot(n, p0-p1) / Dot(n, p2-p1));//¿?¿?¿?0¿?¿?¿?¿?¿?¿?¿?¿?¿?¿?¿?¿?¿?    return p1 + v*t; //¿?¿?¿?¿?¿? ¿?¿?t¿?¿?¿?0~1¿?¿?}// p1¿?p2¿?¿?¿?¿?¿?a-b¿?¿?¿?bool SameSide(const Point3& p1, const Point3& p2, const Point3& a, const Point3& b) {  return dcmp(Dot(Cross(b-a, p1-a), Cross(b-a, p2-a))) >= 0;}// ¿?P¿?¿?¿?¿?P0, P1, P2¿?bool PointInTri(const Point3& P, const Point3& P0, const Point3& P1, const Point3& P2) {  return SameSide(P, P0, P1, P2) && SameSide(P, P1, P0, P2) && SameSide(P, P2, P0, P1);}//¿?¿?¿?¿?¿?¿?¿?int same_side(Point3 a,Point3 b,plane3 s){Vector3 n = s.prev();return dcmp( Dot(n,a-s.a) * Dot(n,b-s.a) ) > 0;}//¿?¿?¿?¿?¿?¿?Point3 PointProjectPlane(Point3 p,plane3 s){Vector3 n = s.prev();n = n/n.len();return GetPlaneProjection(p,s.a,n);}// ¿?P¿?¿?¿?AB¿?¿?¿?double PointToLine(const Point3& P, const Point3& A, const Point3& B) {  Vector3 v1 = B - A, v2 = P - A;  return Length(Cross(v1, v2)) / Length(v1);}//¿?¿?¿?¿?¿?¿?¿?double PointToSeg(Point3 p, Point3 a, Point3 b){    if(a == b) return Length(p-a);    Vector3 v1 = b-a, v2 = p-a, v3 = p-b;    if(dcmp(Dot(v1, v2)) < 0) return Length(v2);    else if(dcmp(Dot(v1, v3)) > 0) return Length(v3);    else return Length(Cross(v1, v2)) / Length(v1);  }//¿?¿?¿?¿?¿?int parallel(Point3 a,Point3 b,Point3 u,Point3 v){return dcmp(((a-b)*(u-v)).len())==0;}//¿?¿?¿?¿?¿?¿?¿?¿?double LineToLine(Point3 a,Point3 b,Point3 u,Point3 v){if(parallel(a,b,u,v)) return PointToLine(a,u,v);    //¿?¿?¿?¿?¿?¿?¿?¿?¿?¿?¿?¿?Point3 n = (a-b)*(u-v);return fabs((a-u)^n)/n.len();}//¿?¿?¿?¿?¿?¿?¿?¿?¿?¿?¿?int InterSection(Point3 a,Point3 b,Point3 u,Point3 v){Vector3 n = (a-b)*(u-v);if(same_side(u,v,plane3(a,b,a+n))) return 0;if(same_side(a,b,plane3(u,v,u+n))) return 0;return 1;}//¿?¿?¿?¿?¿?¿?¿?¿?double SegToSeg(Point3 a,Point3 b,Point3 u,Point3 v) {if(!parallel(a,b,u,v))if(InterSection(a,b,u,v)) return LineToLine(a,b,u,v);double ret = 1e9;ret = min(ret,PointToSeg(a,u,v));ret = min(ret,PointToSeg(b,u,v));ret = min(ret,PointToSeg(v,a,b));ret = min(ret,PointToSeg(u,a,b));return ret;}//¿?¿?¿?¿?¿?¿?¿?¿?¿?¿?¿?double PointToPlane(Point3 p,Point3 a,Point3 b,Point3 c){Point3 P0 = PointProjectPlane(p,plane3(a,b,c));if(PointInTri(P0,a,b,c)) return (p-P0).len();double ret = 1e9;ret = min(ret,PointToSeg(p,a,b));ret = min(ret,PointToSeg(p,a,c));ret = min(ret,PointToSeg(p,b,c));return ret;}Point3 p,q,u,v,tmp;double t;int cas = 1;void work() {double a = (u-v).len();double c = (p-q).len();double b = 2.0 * ((u-v)^(p-q));double x = 0 ;if(dcmp(a)) x = -b/(2.0*a);else if(dcmp(b)) {x = -c/b;}if(dcmp(x) < 0) x=0;double ans = a*x*x + b*x + c;ans = sqrt(ans);pf("Case %d: %.4lf\n",cas++,ans);}int main() {#ifndef ONLINE_JUDGEfreopen("in.txt","r",stdin);#endifint T;cin >> T;while(T--) {sf("%lf",&t);p.read() , tmp.read() , u=tmp-p; u = u/t; q.read() , tmp.read() , v=tmp-q; v = v/t;work() ;}return 0;}