UVa 10674 (求两圆公切线) Tangents

题意:

给出两个圆的圆心坐标和半径，求这两个圆的公切线切点的坐标及对应线段长度。若两圆重合，有无数条公切线则输出-1.

输出是按照一定顺序输出的。

分析：

首先情况比较多，要一一判断，不要漏掉。

如果高中的那点老底还在的话，代码还是很好理解的。

 //#define LOCAL
 #include <cstdio>
 #include <cstring>
 #include <algorithm>
 #include <cmath>
 #include <vector>
 using namespace std;

 const double PI = acos(-1.0);
 const double EPS = 1e-;
 struct Point
 {
     double x, y;
     Point(double x=, double y=):x(x), y(y) {}

 };
 typedef Point Vector;
 Vector operator + (Vector A, Vector B)
 {
     return Vector(A.x+B.x, A.y+B.y);
 }
 Vector operator - (Vector A, Vector B)
 {
     return Vector(A.x-B.x, A.y-B.y);
 }
 Vector operator * (Vector A, double p)
 {
     return Vector(A.x*p, A.y*p);
 }
 Vector operator / (Vector A, double p)
 {
     return Vector(A.x/p, A.y/p);
 }
 double dcmp(double x)
 {
     if(fabs(x) < EPS)    return ;
     else return x <  ? - : ;
 }
 bool operator < (const Vector& a, const Vector& b)
 {
     return dcmp(a.x-b.x) <  || dcmp(a.x-b.x) ==  && dcmp(a.y-b.y) < ;
 }
 bool operator == (const Vector& a, const Vector& b)
 {
     return dcmp(a.x-b.x) ==  && dcmp(a.y-b.y) == ;
 }
 double Dot(Vector a, Vector b)
 {
     return a.x*b.x + a.y*b.y;
 }
 double Cross(Vector a, Vector b)
 {
     return a.x*b.y - a.y*b.x;
 }
 double Length(Vector a)
 {
     return sqrt(Dot(a, a));
 }
 struct Circle
 {
     double x, y, r;
     Circle(double x, double y, double r):x(x), y(y), r(r) {}
     Point point(double a)
     {
         return Point(x + r*cos(a), y + r*sin(a));
     }
 };
 int getTangents(Circle A, Circle B, Point* a, Point* b)
 {
     int cnt = ;
     if(A.r < B.r)    { swap(A, B); swap(a, b); }
     double d2 = (A.x-B.x)*(A.x-B.x) + (A.y-B.y)*(A.y-B.y);
     double rdiff = A.r - B.r;
     double rsum = A.r + B.r;
     if(d2 < rdiff*rdiff)    return ;    //内含

     double base = atan2(B.y-A.y, B.x-A.x);
     if(dcmp(d2) ==  && dcmp(A.r - B.r) == )    return -; //重合
     if(dcmp(d2 - rdiff*rdiff) == )    //内切
     {
         a[cnt] = A.point(base); b[cnt] = B.point(base); cnt++;
         return ;
     }

     //有外公切线
     double ang = acos((A.r - B.r) / sqrt(d2));
     a[cnt] = A.point(base + ang); b[cnt] = B.point(base + ang); cnt++;
     a[cnt] = A.point(base - ang); b[cnt] = B.point(base - ang); cnt++;
     if(dcmp(rsum*rsum - d2) == )
     {//外切
         a[cnt] = b[cnt] = A.point(base); cnt++;
     }
     else if(dcmp(d2 - rsum*rsum) > )
     {
         ang = acos((A.r + B.r) / sqrt(d2));
         a[cnt] = A.point(base + ang); b[cnt] = B.point(PI + base + ang); cnt++;
         a[cnt] = A.point(base - ang); b[cnt] = B.point(PI + base - ang); cnt++;
     }
     return cnt;
 }

 int main(void)
 {
     #ifdef    LOCAL
         freopen("10674in.txt", "r", stdin);
     #endif

     int x1, y1, r1, x2, y2, r2;
     while(scanf("%d%d%d%d%d%d", &x1, &y1, &r1, &x2, &y2, &r2) ==  && r1 && r2)
     {
         Point a[], b[];
         Circle C1(x1, y1, r1), C2(x2, y2, r2);
         int n = getTangents(C1, C2, a, b);
         printf("%d\n", n);
         int p[] = {, , , };
         for(int i = ; i < n; ++i)
             for(int j = i+; j < n; ++j)
                 if(a[p[j]] < a[p[i]] || (a[p[j]] == a[p[i]] && b[p[j]] < b[p[i]]))    swap(p[i], p[j]);
         for(int i = ; i < n; ++i)
             printf("%.5lf %.5lf %.5lf %.5lf %.5lf\n", a[p[i]].x, a[p[i]].y, b[p[i]].x, b[p[i]].y, Length(a[p[i]] - b[p[i]]));
     }

     return ;
 }

代码君

写的第一份，样例过，自己随机生成的1000组数据和lrj的代码对比，输出也是一模一样的，可就是无线WA。

这里还是贴一下这份“神奇”的代码吧，也许日后能发现这个隐藏的错误。

 //#define LOCAL
 #include <cstdio>
 #include <cstring>
 #include <algorithm>
 #include <vector>
 #include <cmath>
 using namespace std;

 struct Point
 {
     double x, y;
     Point(double x=, double y=) :x(x),y(y) {}
 };
 typedef Point Vector;
 const double EPS = 1e-;
 Vector operator + (Vector A, Vector B)    { return Vector(A.x + B.x, A.y + B.y); }
 Vector operator - (Vector A, Vector B)    { return Vector(A.x - B.x, A.y - B.y); }
 Vector operator * (Vector A, double p)    { return Vector(A.x*p, A.y*p); }
 Vector operator / (Vector A, double p)    { return Vector(A.x/p, A.y/p); }
 bool operator < (const Point& a, const Point& b)
 { return a.x < b.x || (a.x == b.x && a.y < b.y); }
 int dcmp(double x)
 { if(fabs(x) < EPS) return ; else return x <  ? - : ; }
 bool operator == (const Point& a, const Point& b)
 { return dcmp(a.x-b.x) ==  && dcmp(a.y-b.y) == ; }
 double Dot(Vector A, Vector B)
 { return A.x*B.x + A.y*B.y; }
 double Length(Vector A)    { return sqrt(Dot(A, A)); }

 struct Circle
 {
     Point c;    //Ô²ÐÄ
     double r;    //°ë¾¶
     //Circle(Point c, double r):c(c), r(r)    {}
     Point point(double a)
     {//Çó¶ÔÓ¦Ô²ÐĽǵĵã
         return Point(c.x + r*cos(a), c.y + r*sin(a));
     }
 };
 double angle(Vector v)    { return atan2(v.y, v.x); }
 const double PI = acos(-1.0); 

 int getTangents(Circle A, Circle B, Point* a, Point* b)
 {
     int cnt = ;
     if(A.r < B.r)    { swap(A, B); swap(a, b); }
     double d2 = (A.c.x-B.c.x)*(A.c.x-B.c.x) + (A.c.y-B.c.y)*(A.c.y-B.c.y);
     double rdiff = A.r - B.r;
     double rsum  = A.r + B.r;
     if(d2 < rdiff*rdiff)    return ;    //ÄÚº¬

     double base = atan2(B.c.y-A.c.y, B.c.x-A.c.x);
     if(dcmp(d2) ==  && dcmp(A.r-B.r) == )    return -;    //Á½Ô²Öغϣ¬ÎÞÇî¶àÌõÇÐÏß
     if(dcmp(d2 - rdiff*rdiff) == )                //ÄÚÇÐ
     {
         a[cnt] = A.point(base);
         b[cnt] = B.point(base);
         cnt++;
         return ;
     }
     //ÓÐÍ⹫ÇÐÏß
     double ang = acos((A.r-B.r) / sqrt(d2));
     a[cnt] = A.point(base+ang); b[cnt] = B.point(base+ang); cnt++;
     a[cnt] = A.point(base-ang); b[cnt] = B.point(base-ang); cnt++;

     if(dcmp(d2 - rsum*rsum) == )    //Ò»ÌõÄÚ¹«ÇÐÏß
     {
         a[cnt] = b[cnt] = A.point(base); cnt++;
     }
     else if(dcmp(d2 - rsum*rsum) > )
     {
         double ang = acos((A.r+B.r) / sqrt(d2));
         a[cnt] = A.point(base+ang); b[cnt] = B.point(base+ang+PI); cnt++;
         a[cnt] = A.point(base-ang); b[cnt] = B.point(base-ang+PI); cnt++;
     }
     //for(int i = 0; i < cnt; ++i)
       //    printf("%.5lf %.5lf %.5lf %.5lf\n", a[i].x, a[i].y, b[i].x, b[i].y);
     return cnt;
 }

 int main(void)
 {
     #ifdef    LOCAL
         freopen("10674in.txt", "r", stdin);
         //freopen("10674out.txt", "w", stdout);
     #endif

     int x1, y1, r1, x2, y2, r2;
     while(scanf("%d%d%d%d%d%d", &x1, &y1, &r1, &x2, &y2, &r2) ==  && dcmp(r1) > )
     {
         Point a[], b[];
         /*Point p1(x1, y1), p2(x2, y2);
         Circle C1(p1, r1), C2(p2, r2);*/
         Circle C1, C2;
         C1.c.x=x1, C1.c.y=y1, C1.r=r1;
         C2.c.x=x2, C2.c.y=y2, C2.r=r2;
         int n = getTangents(C1, C2, a, b);
         printf("%d\n", n);
         if(n > )
         {
             int p[] = {, , , };
             for(int i = ; i < n; ++i)
                 for(int j = i+; j < n; ++j)
                     if(a[p[j]] < a[p[i]] || (a[p[j]] == a[p[i]] && b[p[j]] < b[p[i]]))    swap(p[i], p[j]);
             for(int i = ; i < n; ++i)
                 printf("%.5lf %.5lf %.5lf %.5lf %.5lf\n", a[p[i]].x, a[p[i]].y, b[p[i]].x, b[p[i]].y, Length(a[p[i]] - b[p[i]]));
         }
     }

     return ;
 }

WA掉的代码君