poj 2420 A Star not a Tree?

A Star not a Tree?

Time Limit: 1000MS Memory Limit: 65536KTotal Submissions: 3568 Accepted: 1778

Description

Luke wants to upgrade his home computer network from 10mbs to 100mbs. His existing network uses 10base2 (coaxial) cables that allow you to connect any number of computers together in a linear arrangement. Luke is particulary proud that he solved a nasty NP-complete problem in order to minimize the total cable length. 
Unfortunately, Luke cannot use his existing cabling. The 100mbs system uses 100baseT (twisted pair) cables. Each 100baseT cable connects only two devices: either two network cards or a network card and a hub. (A hub is an electronic device that interconnects several cables.) Luke has a choice: He can buy 2N-2 network cards and connect his N computers together by inserting one or more cards into each computer and connecting them all together. Or he can buy N network cards and a hub and connect each of his N computers to the hub. The first approach would require that Luke configure his operating system to forward network traffic. However, with the installation of Winux 2007.2, Luke discovered that network forwarding no longer worked. He couldn't figure out how to re-enable forwarding, and he had never heard of Prim or Kruskal, so he settled on the second approach: N network cards and a hub. 

Luke lives in a loft and so is prepared to run the cables and place the hub anywhere. But he won't move his computers. He wants to minimize the total length of cable he must buy.

Input

The first line of input contains a positive integer N <= 100, the number of computers. N lines follow; each gives the (x,y) coordinates (in mm.) of a computer within the room. All coordinates are integers between 0 and 10,000.

Output

Output consists of one number, the total length of the cable segments, rounded to the nearest mm.

Sample Input

40 00 1000010000 1000010000 0

Sample Output

28284

求一点距离给定点的距离和最小，输出最小值。

先随机出几十个答案，然后就开始在这些答案的周围找是否存在更优的答案，并且随着程序的进行，这个“周围”所表示的范围会越来越小。

g++ 会WA，要C++；

int n;struct Point{double x,y;void read(){scanf("%lf%lf",&x,&y);}void Rand(){x=rand()%10000;y=rand()%10000;}}a[110],p[55],t;double d[55];inline double dis(Point a,Point b){return sqrt(SQR(a.x-b.x)+SQR(a.y-b.y));}inline double dis(Point b){double ans=0;rep(i,0,n) ans+=dis(b,a[i]);return ans;}int main(){srand(49999);while(cin>>n){rep(i,0,n) a[i].read();rep(i,0,55){p[i].Rand();d[i]=dis(p[i]);}for(double step=1e6;step>=1e-6;step/=2){rep(i,0,55){rep(j,0,50){double tmp=rand();t.x=p[i].x+cos(tmp)*step;t.y=p[i].y+sin(tmp)*step;tmp=dis(t);if(tmp<d[i]){p[i].x=t.x,p[i].y=t.y;d[i]=tmp;}}}}double ans=d[0];rep(i,1,55) ans=min(ans,d[i]);printf("%.0lf\n",ans);}return 0;}