pku 2195 KM算法求最小权二分匹配

  
    

   
     
   
     /*
   
     pku 2195 KM算法求最小权二分匹配
   
     */
   
     
#include
   
     <
   
     stdio.h
   
     >
   
     
#include
   
     <
   
     string
   
     .h
   
     >
   
     
#include
   
     <
   
     math.h
   
     >
   
     

   
     #define
   
      MAX 101
   
     

   
     int
   
      hx[MAX],mx[MAX],hy[MAX],my[MAX];

   
     char
   
      map[MAX][MAX];

   
     int
   
      usedx[MAX],usedy[MAX],match[MAX],w[MAX][MAX],n,m;
   
     ///
   
     / match[]存放的右顶点的匹配信息,w[][]存放的是权值,N是右顶点数
   
     

   
     int
   
      lx[MAX],ly[MAX],slack[MAX];
   
     //
   
      lx[],ly[]分别存放的是左右顶标的信息,slack[]是松弛量
   
     

   
     int
   
      k1,k2;

   
     int
   
      dfs(
   
     int
   
      x)
{
 usedx[x]
   
     =
   
     1
   
     ;
 
   
     for
   
     (
   
     int
   
      y
   
     =
   
     0
   
     ;y
   
     <
   
     k2;y
   
     ++
   
     )
 {
 
   
     if
   
     (
   
     !
   
     usedy[y])
 {
 
   
     int
   
      temp
   
     =
   
     lx[x]
   
     +
   
     ly[y]
   
     -
   
     w[x][y];
 
   
     if
   
     (temp
   
     ==
   
     0
   
     )
 {
 usedy[y]
   
     =
   
     1
   
     ;
 
   
     if
   
     (match[y]
   
     ==-
   
     1
   
      
   
     ||
   
      dfs(match[y]))
 {
 match[y]
   
     =
   
     x;
 
   
     return
   
      
   
     1
   
     ;
 }
 }
 
   
     else
   
     
 {
 
   
     if
   
     (slack[y]
   
     >
   
     temp)
 {
 slack[y]
   
     =
   
     temp;
 }
 }
 }
 }
 
   
     return
   
      
   
     0
   
     ;
}

   
     void
   
      KM()
{
 
   
     int
   
      i,j; 
 memset(match,
   
     -
   
     1
   
     ,
   
     sizeof
   
     (match)); 
   
     //
   
     match[]中存储的是y的匹配信息
   
     

   
      
   
     for
   
     (i
   
     =
   
     0
   
     ;i
   
     <
   
     k1;i
   
     ++
   
     )
 {
 lx[i]
   
     =-
   
     999999999
   
     ; 
   
     //
   
     每个X节点的可行顶标设为它出发的所有弧的最大权
   
     

   
      
   
     for
   
     (j
   
     =
   
     0
   
     ;j
   
     <
   
     k2;j
   
     ++
   
     )
 {
 
   
     if
   
     (lx[i]
   
     <
   
     w[i][j])
 {
 lx[i]
   
     =
   
     w[i][j];
 }
 }
 }
 memset(ly,
   
     0
   
     ,
   
     sizeof
   
     (ly));
 
   
     for
   
     (
   
     int
   
      x
   
     =
   
     0
   
     ;x
   
     <
   
     k1;x
   
     ++
   
     )
 {
 
   
     for
   
     (j
   
     =
   
     0
   
     ;j
   
     <
   
     k2;j
   
     ++
   
     )
 {
 slack[j]
   
     =
   
     999999999
   
     ;
 }
 
   
     while
   
     (
   
     1
   
     )
 {
 memset(usedx,
   
     0
   
     ,
   
     sizeof
   
     (usedx));
 memset(usedy,
   
     0
   
     ,
   
     sizeof
   
     (usedy));
 
   
     if
   
     (dfs(x)) 
   
     //
   
      用匈牙利算法寻找完备匹配
   
     

   
      {
 
   
     break
   
     ;
 }
 
   
     int
   
      min
   
     =
   
     99999999
   
     ;
 
   
     for
   
     (i
   
     =
   
     0
   
     ;i
   
     <
   
     k2;i
   
     ++
   
     )
 {
 
   
     if
   
     (
   
     !
   
     usedy[i] 
   
     &&
   
      min
   
     >
   
     slack[i])
 {
 min
   
     =
   
     slack[i];
 }
 }
 
   
     for
   
     (i
   
     =
   
     0
   
     ;i
   
     <
   
     k1;i
   
     ++
   
     )
 {
 
   
     if
   
     (usedx[i])
 {
 lx[i]
   
     -=
   
     min;
 }
 }
 
   
     for
   
     (i
   
     =
   
     0
   
     ;i
   
     <
   
     k2;i
   
     ++
   
     )
 {
 
   
     if
   
     (usedy[i])
 {
 ly[i]
   
     +=
   
     min;
 }
 
   
     else
   
     
 {
 slack[i]
   
     -=
   
     min;
 }
 }
 }
 }
}

   
     int
   
      main()
{
 
   
     int
   
      i,j;
 
   
     while
   
     (scanf(
   
     "
   
     %d%d
   
     "
   
     ,
   
     &
   
     n,
   
     &
   
     m)
   
     !=
   
     EOF 
   
     &&
   
      n 
   
     ||
   
      m)
 {
 
   
     for
   
     (i
   
     =
   
     0
   
     ;i
   
     <
   
     n;i
   
     ++
   
     )
 scanf(
   
     "
   
     %s
   
     "
   
     ,map[i]);
 k1
   
     =
   
     k2
   
     =
   
     0
   
     ;
 
   
     for
   
     (i
   
     =
   
     0
   
     ;i
   
     <
   
     n;i
   
     ++
   
     )
 {
 
   
     for
   
     (j
   
     =
   
     0
   
     ;j
   
     <
   
     m;j
   
     ++
   
     )
 {
 
   
     if
   
     (map[i][j]
   
     ==
   
     '
   
     m
   
     '
   
     )
 {
 hx[k1]
   
     =
   
     i;
 hy[k1
   
     ++
   
     ]
   
     =
   
     j;
 }
 
   
     else
   
      
   
     if
   
     (map[i][j]
   
     ==
   
     '
   
     H
   
     '
   
     )
 {
 mx[k2]
   
     =
   
     i;
 my[k2
   
     ++
   
     ]
   
     =
   
     j;
 }
 }
 }
 
   
     for
   
     (i
   
     =
   
     0
   
     ;i
   
     <
   
     k1;i
   
     ++
   
     )
 {
 
   
     for
   
     (j
   
     =
   
     0
   
     ;j
   
     <
   
     k2;j
   
     ++
   
     )
 {
 w[i][j]
   
     =-
   
     (fabs(hx[i]
   
     -
   
     mx[j])
   
     +
   
     fabs(hy[i]
   
     -
   
     my[j]));
 }
 }
 KM();
 
   
     int
   
      ans
   
     =
   
     0
   
     ;
 
   
     for
   
     (i
   
     =
   
     0
   
     ;i
   
     <
   
     k2;i
   
     ++
   
     )
 {
 ans
   
     +=-
   
     w[match[i]][i];
 }
 printf(
   
     "
   
     %d\n
   
     "
   
     ,ans);
 }
 
   
     return
   
      
   
     0
   
     ;
}