poj1379——Run Away

模拟退火算法。

其中 delta 取 (max(矩行边长))/sqrt(m).算法的正确性与L  N的取值有关系。

来源于《浅谈随机化思想在几何问题中的应用》  By顾研

参考：http://boatswain.info/lovers/wordpress/?p=117

#include<iostream>#include<cstdio>#include<cstring>#include<cmath>using namespace std;#define N 30#define L 30#define esp 1e-2//即1/100 与所求精度有关class node{public:double x,y,d;node(){x=y=d=0.0;}}rp[10086],date[10086];int m,X,Y;double delta;double mindate(double a,double b){if(a>b) return b;return a;}double dist(double sx,double sy,double x,double y){return sqrt((sx-x)*(sx-x)+(sy-y)*(sy-y));}void randrp()//随机撒点 即候选解{int i,j;for(i=0;i<N;i++){rp[i].x =rand()%X+1;rp[i].y =rand()%Y+1;rp[i].d =1e10;for(j=0;j<m;j++){rp[i].d =mindate(rp[i].d ,dist(rp[i].x,rp[i].y,date[j].x,date[j].y ));}}}int main(){int i,j,t;cin>>t;while(t--){cin>>X>>Y>>m;for(i=0;i<m;i++)cin>>date[i].x>>date[i].y;randrp();delta=(X>Y?X:Y)/sqrt((double)m)+1;while(delta>esp){for(i=0;i<N;i++){for(j=0;j<=L;j++){node now;double dis;double phi=rand();now.x=rp[i].x +cos(phi)*delta;//试图产生新的优解now.y=rp[i].y +sin(phi)*delta;if(now.x>=0&&now.x<=X&&now.y>=0&&now.y<=Y){now.d =1e10;for(int k=0;k<m;k++){now.d =mindate(now.d ,dist(now.x,now.y,date[k].x,date[k].y));}if(now.d >rp[i].d ) rp[i]=now;}}}delta*=0.65;}double ans=-1;int right;for(i=0;i<N;i++)if(rp[i].d >ans){ans=rp[i].d;right=i;}printf("The safest point is (%.1f, %.1f)./n",rp[right].x ,rp[right].y);}return 0;}