HDU 3007 buried memory minimum circle coverage

The main idea of the topic: not seen. It's all about finding the smallest round overlay anyway.

Idea: A magical algorithm--random increment method. It can be proved that the algorithm can find the minimum circle coverage in the time complexity of O (n). Although it seems to be able to get out of the way, but add a random_shuffle on the card will not fall.

The specific process is this:

Records a circle globally, representing the current minimum circle overlay. Scan from the beginning. When you encounter the first point that is not within the current minimum circle overlay:

Make a circle of this point with the center of the current minimum circle covering the diameter as the current minimum circle cover. Scan from the beginning. When you encounter the first point that is not covered by the current minimum circle:

Make a triangle of the two points and the current point, and cover the circumscribed circle of the triangle as the smallest circle of the moment.

Specific or look at the code, about the proof see: http://blog.csdn.net/lthyxy/article/details/6661250

CODE:

#define _crt_secure_no_warnings#include <cmath> #include <cstdio> #include <cstring> #include < iostream> #include <algorithm> #define MAX 510using namespace std;struct point{double x, y; Point (Double _,double __): X (_), Y (__) {}point () {}point operator + (const-point &a) const {return-point (x + a.x,y + a.y); }point operator-(const point &a) const {return point (X-A.X,Y-A.Y);} Point operator * (double A) const {return point (x * a,y * a);} void Read () {scanf ("%lf%lf", &x,&y);}}  Point[max];inline Double Calc (const point &p1,const point &p2) {return sqrt ((p1.x-p2.x) * (p1.x-p2.x) + (P1.Y- P2.Y) * (P1.Y-P2.Y));} Inline point Mid (const-point &p1,const-&AMP;P2) {return point (p1.x + p2.x)/2, (P1.Y + p2.y)/2);} Inline Double Cross (const point &p1,const point &p2) {return p1.x * p2.y-p1.y * p2.x;} Inline point Change (const point &v) {return point (-v.y,v.x);} struct Circle{point o;double R; Circle (const point &_,double __): O (_),R (__) {}circle () {}bool incircle (const point &p) {return Calc (p,o) <= R;}} Now;struct Line{point p,v; Line (const point &_,const point &__):p (_), V (__) {}line () {}};inline point getintersection (const line &AMP;L1, Const line &AMP;L2) {point u = l1.p-l2.p;double t = Cross (L2.V,U)/Cross (L1.V,L2.V); return L1.P + l1.v * t;} int Points;int Main () {while (scanf ("%d", &points), points) {for (int i = 1; I <= points; ++i) Point[i]. Read (); Random_shuffle (point + 1,point + points + 1), now = Circle (point[1],.0), for (int i = 2; I <= points; ++i) if (!now.i NCircle (Point[i])) {now = Circle (point[i],.0), for (int j = 1; j < i; ++j) if (!now. InCircle (Point[j])) {now = Circle (Mid (Point[i],point[j]), Calc (Point[i],point[j])/2); for (int k = 1; k < J; ++k) if (!now . InCircle (Point[k]) {line L1 (Mid (Point[i],point[j]), change (Point[j]-point[i]); Line L2 (Mid (point[j],point[k]), change (Point[k]-point[j]); Point intersection = Getintersection (L1,L2), now = Circle (Intersection,calc (point[i],intersection));}}} printf ("%.2lf%.2lf%.2lf\n", NOW.O.X,NOW.O.Y,NOW.R);} return 0;}

HDU 3007 buried memory minimum circle coverage