LA 2572 Kanazawa

题意：

把n个圆盘依次放到桌面上，按照放置的先后顺序给出这n个圆盘的圆心和半径，输出有多少个圆盘可见(即未被全部覆盖)。

分析：

题中说对输入数据进行微小扰动后答案不变。

所露出的部分都是由若干小圆弧组成的。因此求出每个圆与其他圆相交的小圆弧，取圆弧的终点，分别向里和向外移动一个很小的距离的到P‘。标记包含P‘的最上面的那个圆为可见。

  1 //#define LOCAL
  2 #include <cstdio>
  3 #include <cstring>
  4 #include <algorithm>
  5 #include <cmath>
  6 #include <vector>
  7 using namespace std;
  8
  9 const int maxn = 110;
 10 const double PI = acos(-1.0);
 11 const double Two_PI = PI * 2;
 12 const double eps = 5 * 1e-13;
 13 int n;
 14 double radius[maxn];
 15 bool vis[maxn];
 16
 17 int dcmp(double x)
 18 {
 19     if(fabs(x) < eps)    return 0;
 20     else return x < 0 ? -1 : 1;
 21 }
 22
 23 struct Point
 24 {
 25     double x, y;
 26     Point(double x=0, double y=0):x(x), y(y) {}
 27 };
 28 typedef Point Vector;
 29 Point operator + (Point A, Point B)    { return Point(A.x+B.x, A.y+B.y); }
 30 Point operator - (Point A, Point B)    { return Point(A.x-B.x, A.y-B.y); }
 31 Vector operator * (Vector A, double p){ return Vector(A.x*p, A.y*p); }
 32 Vector operator / (Vector A, double p){ return Vector(A.x/p, A.y/p); }
 33 Point center[maxn];
 34
 35 double Dot(Vector A, Vector B){ return A.x*B.x + A.y*B.y; }
 36 double Length(Vector A){ return sqrt(Dot(A, A)); }
 37 double angle(Vector v)    { return atan2(v.y, v.x); }
 38 double NormalizeAngle(double rad)
 39 {//将所求角度化到0到2π之间
 40     return rad - Two_PI*(floor(rad/Two_PI));
 41 }
 42
 43 void getCCIntersection(Point c1, double r1, Point c2, double r2, vector<double>& rad)
 44 {
 45     double d = Length(c1 - c2);
 46     if(dcmp(d) == 0)    return;
 47     if(dcmp(d-r1-r2) > 0)    return;
 48     if(dcmp(d-fabs(r1-r2)) < 0)    return;
 49
 50     double a = angle(c2-c1);
 51     double ag = acos((r1*r1+d*d-r2*r2)/(2*r1*d));
 52     rad.push_back(NormalizeAngle(a + ag));
 53     rad.push_back(NormalizeAngle(a - ag));
 54 }
 55
 56 int topmost(Point P)
 57 {
 58     for(int i = n-1; i >= 0; --i)
 59         if(Length(P-center[i]) < radius[i])    return i;
 60     return -1;
 61 }
 62
 63 int main(void)
 64 {
 65     #ifdef LOCAL
 66         freopen("2572in.txt", "r", stdin);
 67     #endif
 68
 69     while(scanf("%d", &n) == 1 && n)
 70     {
 71         for(int i = 0; i < n; ++i)
 72             scanf("%lf%lf%lf", &center[i].x, &center[i].y, &radius[i]);
 73         memset(vis, 0, sizeof(vis));
 74
 75         for(int i = 0; i < n; ++i)
 76         {
 77             vector<double> rad;
 78             rad.push_back(0.0);
 79             rad.push_back(Two_PI);
 80             for(int j = 0; j < n && j != i; ++j)
 81                 getCCIntersection(center[i], radius[i], center[j], radius[j], rad);
 82             sort(rad.begin(), rad.end());
 83
 84             for(int j = 0; j < rad.size(); ++j)
 85             {
 86                 double mid = (rad[j] + rad[j+1]) / 2.0;
 87                 for(int side = -1; side <= 1; side += 2)
 88                 {
 89                     double r = radius[i] + side*eps;
 90                     int t = topmost(Point(center[i].x+r*cos(mid), center[i].y+r*sin(mid)));
 91                     if(t >= 0)    vis[t] = true;
 92                 }
 93             }
 94         }
 95         int ans = 0;
 96         for(int i = 0; i < n; ++i)    if(vis[i])    ++ans;
 97         printf("%d\n", ans);
 98     }
 99
100     return 0;
101 }

代码君