题目：http://www.lydsy.com/JudgeOnline/problem.php?id=1337

随机增量法O（n）了事

代码：

#include <cstdio>

#include <algorithm>

#include <cstring>

#include <cmath>

#include <cstdlib>

  

using namespace std ;

  

#define rep( i , l , r ) for ( int i = l ; i <= r ; ++ i )

  

const int maxn = 100100 ;

  

typedef long double ld ;

  

const ld esp = 0.000000001 ;

  

ld sqr( ld x ) {

    return x * x ;

}

  

struct point {

    ld x , y ;

    void oper( ld _x , ld _y ) {

        x = _x , y = _y ;

    }

    ld dist( point p ) {

        return sqrt( sqr( x - p.x ) + sqr( y - p.y ) ) ;

    }

} P[ maxn ] , p0 ;

  

int n ;

ld r ;

  

void cal( point a , point b , point c ) {

    ld a1 = 2 * ( b.x - a.x ) , b1 = 2 * ( b.y - a.y ) , c1 = sqr( b.x ) + sqr( b.y ) - sqr( a.x ) - sqr( a.y ) ;

    ld a2 = 2 * ( c.x - a.x ) , b2 = 2 * ( c.y - a.y ) , c2 = sqr( c.x ) + sqr( c.y ) - sqr( a.x ) - sqr( a.y ) ;

    p0.y = ( c1 * a2 - c2 * a1 ) / ( b1 * a2 - a1 * b2 ) ;

    p0.x = ( c1 - b1 * p0.y ) / a1 ;

    r = p0.dist( a ) ;

}

  

int main(  ) {

    scanf( "%d" , &n ) ;

    rep( i , 1 , n ) {

        double x , y ; scanf( "%lf%lf" , &x , &y ) ;

        P[ i ].oper( ld( x ) , ld( y ) ) ;

    }

    random_shuffle( P + 1 , P + n + 1 ) ;

    p0 = P[ 1 ] , r = 0 ;

    rep( i , 2 , n ) if ( p0.dist( P[ i ] ) > r - esp ) {

        p0.x = ( P[ i ].x + P[ 1 ].x ) / 2.0 , p0.y = ( P[ i ].y + P[ 1 ].y ) / 2.0 ;

        r = p0.dist( P[ i ] ) ;

        rep( j , 2 , i - 1 ) if ( p0.dist( P[ j ] ) > r - esp ) {

            p0.x = ( P[ i ].x + P[ j ].x ) / 2.0 , p0.y = ( P[ i ].y + P[ j ].y ) / 2.0 ;

            r = p0.dist( P[ j ] ) ;

            rep( k , 1 , j - 1 ) if ( p0.dist( P[ k ] ) > r - esp ) cal( P[ i ] , P[ j ] , P[ k ] ) ;

        }

    }

    printf( "%.3f\n" , double( r ) ) ;

    return 0 ;

}