UVa 10794 The Deadly Olympic Returns!!!

Link To The Problem

Solution : 數學，計算

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_pair

double 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_JUDGE
	freopen("in.txt","r",stdin);
#endif

	int 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;
}