【bzoj2823】 AHOI2012—信号塔

http://www.lydsy.com/JudgeOnline/problem.php?id=2823 (题目链接)

题意

　　求最小圆覆盖

Solution

　　关于最小圆覆盖的做法，论文里面都有。其实真正麻烦的是求三角形的外心。

代码

// bzoj2823
#include<algorithm>
#include<iostream>
#include<cstring>
#include<cstdlib>
#include<cstdio>
#include<cmath>
#include<vector>
#define eps 1e-10
#define inf 2147483640
#define LL long long
#define free(a) freopen(a".in","r",stdin);freopen(a".out","w",stdout);
using namespace std;
inline LL getint() {
    LL x=0,f=1;char ch=getchar();
    while (ch>'9' || ch<'0') {if (ch=='-') f=-1;ch=getchar();}
    while (ch>='0' && ch<='9') {x=x*10+ch-'0';ch=getchar();}
    return x*f;
}

const int maxn=1000010;
struct point {double x,y;}p[maxn];
int n;

double dis(point a,point b) {
    return sqrt((a.x-b.x)*(a.x-b.x)+(a.y-b.y)*(a.y-b.y));
}
point center(point a,point b,point c) {
    double a1=b.x-a.x,b1=b.y-a.y,c1=(a1*a1+b1*b1)/2;
    double a2=c.x-a.x,b2=c.y-a.y,c2=(a2*a2+b2*b2)/2;
    double d=a1*b2-a2*b1;
    return (point){a.x+(c1*b2-c2*b1)/d,a.y+(a1*c2-a2*c1)/d};
}
int main() {
    scanf("%d",&n);
    for (int i=1;i<=n;i++) {scanf("%lf%lf",&p[i].x,&p[i].y);swap(p[i],p[rand()%i+1]);}
    point c=p[1];double r=0;
    for (int i=2;i<=n;i++) {
        if (dis(c,p[i])<=r+eps) continue;
        c=p[i];r=0;
        for (int j=1;j<i;j++) {
            if (dis(c,p[j])<=r+eps) continue;
            c.x=(p[i].x+p[j].x)/2;
            c.y=(p[i].y+p[j].y)/2;
            r=dis(c,p[j]);
            for (int k=1;k<j;k++) {
                if (dis(c,p[k])<=r+eps) continue;
                c=center(p[i],p[j],p[k]);
                r=dis(p[k],c);
            }
        }
    }
    printf("%.2f %.2f %.2f",c.x,c.y,r);
    return 0;
}