UVA10012

 1 #include <cstdio>
 2 #include <cstring>
 3 #include <cstdlib>
 4 #include <cctype>
 5 #include <cmath>
 6 #include <ctime>
 7 #include <string>
 8 #include <map>
 9 #include <stack>
10 #include <set>
11 #include <vector>
12 #include <algorithm>
13 #include <iostream>
14 using namespace std;
15 typedef long long ll;
16 #define PI acos( -1.0 )
17 const double E = 1e-8;
18 double a[15], b[15], d[15];
19 int mark[15];
20 double ans;
21 int n;
22 
23 void cheak( int x )
24 {
25     d[x] = b[x];
26     for( int i = x-1; i >= 0; --i )
27     {
28         double x1 = b[i] - b[x];
29         double x2 = b[i] + b[x];
30         x1 = d[i] + sqrt( x2*x2 - x1*x1 );
31         if( x1 > d[x] )
32             d[x] = x1;
33     }
34 }
35 
36 void dfs( int x, double num )
37 {
38     if( num > ans )
39         return;
40     if( x == n )
41     {
42         double k = b[0];
43         num += b[x-1];
44         for( int i = 0; i < n; ++i )
45             if( num < b[i] + d[i] )
46                 num = b[i] + d[i];
47         for( int i = 1; i < n; ++i )//检查是否存在一点边长比前面所用的长度要大
48             if( k < b[i] - d[i] )
49                 k = b[i] - d[i];
50         num += k;
51         if( num < ans )
52             ans = num;
53         return;
54     }
55     for( int i = 0; i < n; ++i )
56         if( !mark[i] )
57         {
58             mark[i] = 1;
59             b[x] = a[i];
60             cheak( x );
61             dfs( x+1, d[x] );
62             mark[i] = 0;
63         }
64 }
65 
66 int main()
67 {
68     int T;
69     scanf( "%d", &T );
70     while( T-- )
71     {
72         scanf( "%d", &n );
73         for( int i = 0; i < n; ++i )
74             scanf( "%lf", &a[i] );
75         ans = 0x7fffffffffff;
76         for( int i = 0; i < n; ++i )
77         {
78             memset( mark, 0, sizeof( mark ) );
79             mark[i] = 1;
80             b[0] = a[i];
81             d[0] = 0;
82             dfs( 1, 0 );
83         }
84         printf( "%.3lf\n", ans );
85     }
86     return 0;
87 }