UVaLive2572 poj1418 UVa1308 Viva Confetti

一次放下n个圆

问最终可见的圆的数量

应该是比较经典的问题吧

考虑一个圆与其他每个圆的交点O(n)个

将其割成了O(n)条弧

那么看每条弧的中点 分别向内向外调动eps这个点 则最上面的覆盖这个点的圆可见O(n)

总时间复杂度O(n ** 3)

怕炸精度，代码基本抄的rjl的

 #include<cstdio>
 #include<cstring>
 #include<cstdlib>
 #include<algorithm>
 #include<iostream>
 #include<cmath>
 #include<vector>

 using namespace std;

 typedef double data_type;

 const data_type eps =  * 1e-;
 int dcmp(const data_type& x) {
     if(fabs(x) < ) return ; return x <  ? - : ;
 }

 const data_type pi = acos(-1.0), dpi =  * acos(-1.0);

 double NormalizeAngle(double rad) {
     return rad - dpi * floor(rad / dpi);
 }

 typedef const struct Point& Point_cr;
 typedef struct Point {
     data_type x, y;
     Point() {}
     Point(data_type x, data_type y) : x(x), y(y) {}
     Point operator + (Point_cr rhs) const {
         return Point(x + rhs.x, y + rhs.y);
     }
     Point operator - (Point_cr rhs) const {
         return Point(x - rhs.x, y - rhs.y);
     }
     Point operator * (data_type k) const {
         return Point(x * k, y * k);
     }
     Point operator / (double k) const {
         return Point(x / k, y / k);
     }
     double length() const {
         return hypot(x, y);
     }
     double angle() const {
         return atan2(y, x);
     }
 }Vector;

 double Dot(const Vector& v1, const Vector& v2) {
     return v1.x * v2.x + v1.y * v2.y;
 }

 double length(const Vector& v) {
     return sqrt(Dot(v, v));
 }

 typedef const Vector& Vector_cr;
 void CircleCircleIntersection(Point_cr c1, double r1, Point c2, double r2, vector<double> &rad) {
     double d = (c1 - c2).length();
     if(dcmp(d) == ) return;
     if(dcmp(r1 + r2 - d) < ) return;
     if(dcmp(fabs(r1 - r2) - d) > ) return;
     double a = (c2 - c1).angle();
     double da = acos((r1 * r1 + d * d - r2 * r2) / ( * r1 * d));
     rad.push_back(NormalizeAngle(a + da));
     rad.push_back(NormalizeAngle(a - da));
 }

 const int N =  + ;
 int n;
 Point centre[N];
 double radius[N];
 bool vis[N];

 int topmost(Point p) {
     for(int i = n - ; i >= ; i--) {
         if((centre[i] - p).length() < radius[i]) return i;
     }
     return -;
 }

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

     while(scanf("%d", &n) ==  && n) {
         for(int i = ; i < n; i++) {
             double x, y, r;
             scanf("%lf%lf%lf", &x, &y, &r);
             centre[i] = Point(x, y);
             radius[i] = r;
         }
         memset(vis, , sizeof vis);
         for(int i = ; i < n; i++) {
             vector<double> rad;
             rad.push_back();
             rad.push_back(dpi);

             for(int j = ; j < n; j++) {
                 CircleCircleIntersection(centre[i], radius[i], centre[j], radius[j], rad);
             }

             sort(rad.begin(), rad.end());

             for(unsigned j = ; j < rad.size(); j++) {
                 double mid = (rad[j] + rad[j+]) / 2.0;
                 for(int side = -; side <= ; side += ) {
                     double r2 = radius[i] - side * eps;
                     int t = topmost(Point(centre[i].x + cos(mid) * r2, centre[i].y + sin(mid) * r2));
                     if(t >= ) vis[t] = ;
                 }
             }
         }
         int ans = ;
         for(int i = ; i < n; i++) if(vis[i]) {
             ans++;
         }
         printf("%d\n", ans);
     }

     return ;
 }