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; }