HDU 6242 Geometry Problem（计算几何 + 随机化）

题目链接：http://acm.hdu.edu.cn/showproblem.php?pid=6242

思路：当 n == 1 时 任取一点 p 作为圆心即可。

　　　　n >= 2 && n < 5 时 此时有可能出现所有点共线，所以取任意俩点间中点作为圆的圆心。

　　　　n >= 5 保证了有解。所以不可能有所有点共线的情况，随机取三个点在正解圆上的概率是 1/8，还是蛮大的...。

　　　　外学了下随机算法的写法....时间种子 time（0）要强制转成int，不然会WA，不造为啥....

AC代码：

 #include<bits/stdc++.h>
 using namespace std;
 const double eps = 1e-;
 const double INF = 1e18;
 const int maxn = 1e5 + ;
 int sgn(double x)
 {
     if(fabs(x) < eps) return ;
     else return x <  ? - : ;
 }
 struct Point{
     double x, y;
     Point(){}
     Point(double _x, double _y){
         x = _x; y = _y;
     }
     void input()
     {
         scanf("%lf %lf", &x, &y);
     }
     bool operator ==(const Point &b) const{
         return sgn(x - b.x) ==  && sgn(y - b.y) == ;
     }
     bool operator <(const Point &b) const{
         return sgn(x - b.x) ==  ? sgn(y - b.y) <  : x < b.x;
     }
     Point operator -(const Point &b) const{
         return Point(x - b.x, y - b.y);
     }
     Point operator +(const Point &b) const{
         return Point(x + b.x, y + b.y);
     }
     double operator ^(const Point &b) const{
         return x*b.y - b.x*y;
     }
     double operator *(const Point &b) const{
         return x*b.x + y*b.y;
     }
     Point operator*(const double &k)const{
         return Point(x*k,y*k);
     }
     Point operator/(const double &k)const{
         return Point(x/k,y/k);
     }
     Point rotleft(){
         return Point(-y, x);
     }
     double distance(Point p)
     {
         return hypot(x - p.x,y - p.y);
     }
 } p[maxn];
 struct Line{
     Point s, e;
     Line(){}
     Line(Point _s, Point _e){
         s = _s, e = _e;
     }
     Point crosspoint(Line v){
         double a1 = (v.e - v.s) ^ (s - v.s);
         double a2 = (v.e - v.s) ^ (e - v.s);
         return Point((s.x*a2-e.x*a1)/(a2-a1),(s.y*a2-e.y*a1)/(a2-a1));
     }
 };
 struct circle{
     Point p;
     double r;
     circle(){}
     circle(Point a, Point b, Point c){
         Line u = Line( (a + b) / , ( (a + b) / ) + ( (b - a).rotleft() ));
         Line v = Line( (b + c) / , ( (b + c) / ) + ( (c - b).rotleft() ));
         p = u.crosspoint(v);
         r = p.distance(a);
     }
     int relation(Point b){
         double dst = b.distance(p);
         if(sgn(dst - r)<) return ;
         else if(sgn(dst - r) == ) return ;
         return ;
     }
 };
 int main()
 {
     int t;
     scanf("%d",&t);
     srand((int)time());
     while(t--)
     {
         int n;
         scanf("%d",&n);
         for(int i = ;i < n;i++) p[i].input();
         if(n == ) printf("0.000 0.000 %.6f\n",p[].distance(Point(,)));
         else if(n >=  && n < ){
             Point v = (p[] + p[])/;
             printf("%.6f %.6f %.6f\n", v.x, v.y, 0.5*p[].distance(p[]));
         }
         else{
             while(){
                 int a = rand() % n, b = a, c = a;
                 while(b = rand() % n){
                     if(b != a) break;
                 }
                 while(c = rand() % n){
                     if(c != a && c != b) break;
                 }
                 circle C = circle(p[a], p[b], p[c]);
                 int num = ;
                 for(int i = ;i < n;i++)
                 {
                     if(C.relation(p[i]) == ) num++;
                 }
                 if(num >= (n + ) / ){
                     printf("%.6f %.6f %.6f\n",C.p.x ,C.p.y, C.r);
                     break;
                 }
             }
         }
     }
     return ;
 }