hdu 2215(凸包+最小圆覆盖)
/* 凸包+最小圆覆盖 枚举任意3点找其最小覆盖圆 (当为钝角三角形时不是外接圆,而是以其最长边为直径的圆)。 当为外接圆时,半径公式为r=abc/4s;(推导为如下: 由正弦定理,a/sinA=b/sinB=c/sinC=2R,得sinA=a/(2R), 又三角形面积公式S=(bcsinA)/2,所以S=(abc)/(4R),故R=(abc)/(4S). */ #include <cmath> #include <cstdio> #include <cstdlib> #include <iostream> using namespace std; const int N = 105; const double eps = 1e-8; struct point { int x; int y; }p[N], stack[N]; bool isZero(double x) { return (x > 0 ? x : -x) < eps; } double dis(point A, point B) { return sqrt((A.x-B.x)*(A.x-B.x)+(A.y-B.y)*(A.y-B.y)); } double crossProd(point A, point B, point C) { return (B.x-A.x)*(C.y-A.y) - (B.y-A.y)*(C.x-A.x); } int cmp(const void *a, const void *b) { point *c = (point *)a; point *d = (point *)b; double k = crossProd(p[0], *c, *d); if (k<eps || (isZero(k)&&dis(p[0], *c)>dis(p[0], *d))) return 1; return -1; } int Graham(int n) { int x = p[0].x; int y = p[0].y; int mi = 0; for (int i=1; i<n; ++i) { if (p[i].x<x || (p[i].x==x&&p[i].y<y)) { x = p[i].x; y = p[i].y; mi = i; } } point tmp = p[mi]; p[mi] = p[0]; p[0] = tmp; qsort(p+1, n-1, sizeof(point), cmp); p[n] = p[0]; for (int i=0; i<3; ++i) stack[i] = p[i]; int top = 2; for (int i=3; i<n; ++i) { if (crossProd(stack[top-1], stack[top], p[i])<=eps && top>=2) --top; stack[++top] = p[i]; } return top; } double max(double a, double b) { return a > b ? a : b; } int main() { int n; while (scanf("%d", &n), n) { for (int i=0; i<n; ++i) scanf ("%d%d", &p[i].x, &p[i].y); if (n == 1) printf ("0.50\n"); else if (n == 2) printf ("%.2lf\n", dis(p[0], p[1])*0.50+0.50); else { int top = Graham(n); double maxr = -1; double a, b, c, r, s; for (int i=0; i<top; ++i) {//枚举凸包上的点 for (int j=i+1; j<top; ++j) { for (int k=j+1; k<=top; ++k) { a = dis(stack[i], stack[j]); b = dis(stack[i], stack[k]); c = dis(stack[j], stack[k]); if (a*a+b*b<c*c || a*a+c*c<b*b || b*b+c*c<a*a) r = max(max(a, b), c) / 2.0;//钝角 else { s = fabs(crossProd(stack[i], stack[j], stack[k])) / 2.0; r = a * b * c / (s * 4.0);//三角形外接圆公式 } if (maxr < r) maxr = r; } } } printf ("%.2lf\n", maxr+0.5); } } return 0; }