UVa 10969 (圆与圆之间的覆盖问题) Sweet Dream

  1 #include <cstdio>
  2 #include <cmath>
  3 #include <vector>
  4 #include <algorithm>
  5 using namespace std;
  6 
  7 const int maxn = 100 + 10;
  8 const double eps = 1e-11;
  9 const double PI = acos(-1.0);
 10 const double TWO_PI = 2.0 * PI;
 11 double radius[maxn];
 12 
 13 double NormalizeAngle(double ang)
 14 { return ang - TWO_PI*floor(ang/TWO_PI); }
 15 
 16 int dcmp(double x)
 17 {
 18     if(fabs(x) < eps) return 0;
 19     return x < 0 ? -1 : 1;
 20 }
 21 
 22 struct Point
 23 {
 24     double x, y;
 25     Point(double x=0, double y=0):x(x), y(y) {}
 26 }p[maxn];
 27 typedef Point Vector;
 28 
 29 bool operator == (const Point& A, const Point& B)
 30 { return dcmp(A.x - B.x) == 0 && dcmp(A.y - B.y) == 0; }
 31 
 32 Point operator - (const Point& A, const Point& B)
 33 { return Point(A.x - B.x, A.y - B.y); }
 34 
 35 double Dot(const Point& A, const Point& B)
 36 { return A.x*B.x + A.y*B.y; }
 37 
 38 double Length(const Vector& A)
 39 { return sqrt(Dot(A, A)); }
 40 
 41 double Angle(const Vector& A)
 42 { return atan2(A.y, A.x); }
 43 
 44 void GetCCIntersection(const Point& c1, double r1, const Point& c2, double r2, vector<double>& rad)
 45 {
 46     double d = Length(c1 - c2);
 47     if(dcmp(d) == 0) return;
 48     if(dcmp(d-r1-r2) > 0) return;
 49     if(dcmp(d-fabs(r1-r2)) < 0) return;
 50 
 51     double base = Angle(c2 - c1);
 52     double ang = acos((r1*r1 + d*d - r2*r2) / (2.0*r1*d));
 53     rad.push_back(NormalizeAngle(base + ang));
 54     rad.push_back(NormalizeAngle(base - ang));
 55 }
 56 
 57 int n;
 58 
 59 bool isVisible(const Point& C, int id)
 60 {
 61     for(int i = id + 1; i < n; ++i)
 62     {
 63         double d = Length(C - p[i]);
 64         if(dcmp(d - radius[i]) <= 0) return false;    //这道题的关键所在 
 65     }
 66     return true;
 67 }
 68 
 69 int main(void)
 70 {
 71     //freopen("10969in.txt", "r", stdin);
 72     int T;
 73     scanf("%d", &T);
 74     while(T--)
 75     {
 76         scanf("%d", &n);
 77         for(int i = 0; i < n; ++i) scanf("%lf%lf%lf", &radius[i], &p[i].x, &p[i].y);
 78         
 79         double sum = 0.0;
 80         for(int i = 0; i < n; ++i)
 81         {
 82             vector<double> rad;
 83             rad.push_back(0.0);
 84             rad.push_back(TWO_PI);
 85             for(int j = 0; j < n; ++j)
 86             {
 87                 if(j == i) continue;
 88                 GetCCIntersection(p[i], radius[i], p[j], radius[j], rad);
 89             }
 90             sort(rad.begin(), rad.end());
 91             
 92             for(int j = 0; j < rad.size() - 1; ++j)
 93             {
 94                 double mid = (rad[j] + rad[j + 1]) / 2;
 95                 double ang = rad[j + 1] - rad[j];
 96                 Point C(p[i].x + radius[i]*cos(mid), p[i].y + radius[i]*sin(mid));
 97                 if(isVisible(C, i)) sum += radius[i] * ang;
 98             }
 99         }
100 
101         printf("%.3f\n", sum);
102     }
103 
104     return 0;
105 }