Gym 2009-2010 ACM ICPC Southwestern European Regional Programming Contest (SWERC 2009) A. Trick or Treat (三分)

• 题意:在二维坐标轴上给你一堆点,在x轴上找一个点,使得该点到其他点的最大距离最小.

• 题解:随便找几个点画个图,不难发现,答案具有凹凸性,有极小值,所以我们直接三分来找即可.

  

• 代码：

  int n;
  long double x[N],y[N];
   
  long double check(long double s){
      long double res=0;
      long double tmp;
      for(int i=1;i<=n;++i){
          tmp=sqrt((s-x[i])*(s-x[i])+(y[i]*y[i]));
          if(res<tmp) res=tmp;
      }
      return res;
  }
   
  int main() {
      while(scanf("%d",&n)!=EOF){
          if(n==0) break;
          for(int i=1;i<=n;++i){
              scanf("%Lf %Lf",&x[i],&y[i]);
          }
          long double l=-200000,r=200000;
          long double lmid,rmid;
          while(l+eps<r){
              lmid=l+(r-l)/3;
              rmid=r-(r-l)/3;
              if(check(lmid)<check(rmid)) r=rmid;
              else l=lmid;
          }
          printf("%Lf %Lf\n",rmid,check(lmid));
      }
   
      return 0;
  }