HDU6242Geometry Problem（随机化）

传送门

这个题就是随机选三个点，求外心，一开始外心求错了，一直T（因为找不到正确答案），TT

#include<bits/stdc++.h>
using namespace std;
const int N=1e5+10;
int n;
struct Point{
    double x, y;
}p[N], p0;
double r0;
inline Point operator - (const Point& a, const Point& b){
    return (Point){a.x-b.x, a.y-b.y};
}
inline double operator *(const Point& a, const Point& b){
    return a.x*b.x+a.y*b.y;
}
inline Point operator * (const Point& a, double b){
    return (Point){a.x*b, a.y*b};
}
inline Point operator +(const Point& a, const Point& b){
    return (Point){a.x+b.x, a.y+b.y};
}
inline double dis(Point a, Point b){
    return sqrt((a-b)*(a-b));
}
inline double Cross(Point a, Point b){
    return a.x*b.y-a.y*b.x;
}
inline int dcmp(double x){
    if(fabs(x)<1e-6) return 0;
    return x<0?-1:1;
}

Point waixin(Point& t1, Point& t2, Point& t3){
    Point v1=t2-t1, v2=t3-t1;
    Point m1=(Point){(t1.x+t2.x)/2, (t1.y+t2.y)/2}, m2={(t3.x+t1.x)/2, (t3.y+t1.y)/2};
    Point v3=m1-m2;
    swap(v1.x, v1.y); swap(v2.x, v2.y);
    v1.x=-v1.x, v2.x=-v2.x;
    double t=Cross(v2, v3)/Cross(v1, v2);
    return m1+v1*t;
}

bool check(){
    int cnt=0;
    int up=(n+1)/2;
    for(int i=0; i<n; i++){
        if(dcmp(dis(p[i], p0)-r0)==0) cnt++;
        if(cnt>=up) return true;
    }
    return false;
}

int main(){
    int T;
    scanf("%d", &T);
    while(T--){
        scanf("%d", &n);
        for(int i=0; i<n; i++)
            scanf("%lf%lf", &p[i].x, &p[i].y);

        if(n==1){
            printf("%f %f %f\n", p[0].x+1, p[0].y, 1.0);
            continue;
        }
        else if(n<=4){
            Point t={(p[0].x+p[1].x)/2, (p[0].y+p[1].y)/2};
            printf("%f %f %f\n", t.x, t.y, dis(t, p[0]));
            continue;
        }

        while(1){
            int t1, t2, t3;
            t1=rand()%n, t2=rand()%n, t3=rand()%n;
            if(t1==t2||t2==t3||t1==t3) continue;
            if(dcmp(Cross(p[t1]-p[t2], p[t3]-p[t2]))==0) continue;

            p0=waixin(p[t1], p[t2], p[t3]);
            //printf("%d %d %d\n", t1, t2, t3);
            r0=dis(p[t1], p0);
            if(check())
                break;
        }
        printf("%f %f %f\n", p0.x, p0.y, r0);
    }

    return 0;
}