Building a Space Station--POJ 2031

1、题目类型：计算几何，最小生成树。

2、解题思路：（1）获得所有点路径长度的矩阵map[][]；（2）利用Prim算法求解最小生成树。

3、注意事项：数学操作，中间值全部用double保存。

4、实现方法:

  
    

   
     
   
     #include
   
     <
   
     iostream
   
     >
   
     
#include
   
     <
   
     cmath
   
     >
   
     
#include
   
     <
   
     algorithm
   
     >
   
     

   
     #define
   
      _Max 10000000
   
     

   
     #define
   
      _Min 0.00000000001
   
     

   
     using
   
      
   
     namespace
   
      std;


   
     struct
   
      Node
{
 
   
     double
   
      x,y,z;
 
   
     double
   
      r;
};

Node Arr[
   
     101
   
     ];

   
     int
   
      n;

   
     double
   
      map[
   
     101
   
     ][
   
     101
   
     ],dis[
   
     101
   
     ],ans;

   
     bool
   
      visted[
   
     101
   
     ];


   
     double
   
      Lengh(Node A,Node B)
{
 
   
     double
   
      x
   
     =
   
     (A.x
   
     -
   
     B.x)
   
     *
   
     (A.x
   
     -
   
     B.x);
 
   
     double
   
      y
   
     =
   
     (A.y
   
     -
   
     B.y)
   
     *
   
     (A.y
   
     -
   
     B.y);
 
   
     double
   
      z
   
     =
   
     (A.z
   
     -
   
     B.z)
   
     *
   
     (A.z
   
     -
   
     B.z); 
 
   
     if
   
     ((sqrt(x
   
     +
   
     y
   
     +
   
     z)
   
     -
   
     A.r
   
     -
   
     B.r)
   
     >
   
     _Min)
 
   
     return
   
      sqrt(x
   
     +
   
     y
   
     +
   
     z)
   
     -
   
     A.r
   
     -
   
     B.r;
 
   
     else
   
     
 
   
     return
   
      
   
     0
   
     ;
}


   
     void
   
      Init()
{
 
   
     for
   
     (
   
     int
   
      i
   
     =
   
     1
   
     ;i
   
     <=
   
     n;i
   
     ++
   
     )
 cin
   
     >>
   
     Arr[i].x
   
     >>
   
     Arr[i].y
   
     >>
   
     Arr[i].z
   
     >>
   
     Arr[i].r; 
 
   
     for
   
     (
   
     int
   
      j
   
     =
   
     1
   
     ;j
   
     <=
   
     n;j
   
     ++
   
     )
 
   
     for
   
     (
   
     int
   
      k
   
     =
   
     j;k
   
     <=
   
     n;k
   
     ++
   
     )
 map[j][k]
   
     =
   
     map[k][j]
   
     =
   
     Lengh(Arr[j],Arr[k]);
 ans
   
     =
   
     0.0
   
     ;
}


   
     void
   
      Prim()
{
 
   
     int
   
      i,j; 
 memset(visted,
   
     0
   
     ,
   
     sizeof
   
     (visted)); 
 
   
     for
   
     (i
   
     =
   
     1
   
     ;i
   
     <=
   
     n;i
   
     ++
   
     )
 dis[i]
   
     =
   
     map[
   
     1
   
     ][i]; 
 visted[
   
     1
   
     ]
   
     =
   
     1
   
     ;
 dis[
   
     1
   
     ]
   
     =
   
     _Max; 
 
   
     for
   
     (i
   
     =
   
     1
   
     ;i
   
     <
   
     n;i
   
     ++
   
     )
 {
 
   
     int
   
      pos
   
     =
   
     min_element(dis
   
     +
   
     1
   
     ,dis
   
     +
   
     n
   
     +
   
     1
   
     )
   
     -
   
     dis; 
 ans
   
     +=
   
     dis[pos];
 visted[pos]
   
     =
   
     1
   
     ;
 dis[pos]
   
     =
   
     _Max; 
 
   
     for
   
     (j
   
     =
   
     1
   
     ;j
   
     <=
   
     n;j
   
     ++
   
     )
 {
 
   
     if
   
     (dis[j]
   
     >
   
     map[pos][j]
   
     &&!
   
     visted[j])
 dis[j]
   
     =
   
     map[pos][j];
 }
 } 
}


   
     int
   
      main()
{ 
 
   
     while
   
     (cin
   
     >>
   
     n
   
     &&
   
     n)
 {
 Init();
 Prim();
 printf(
   
     "
   
     %.3f\n
   
     "
   
     ,ans); 
 } 
 
   
     return
   
      
   
     0
   
     ;
}