Edmonds-Karp算法

建立在Ford-Fulkerson 方法上的增广路算法,与一般的Ford-Fulkerson 算法不同的是,它用广度搜索实现对增广路的寻找

  
    

   
     
   
     /*
   
     **********************************************************************
   
     */
   
     

   
     /*
   
      Name: maxflow
/* Description: find the max flow of the network from s to t using 
 Edmonds-Karp Algorithm
/* Parameter list: s - begin point of the network
/* t - end point of the network
/***********************************************************************
   
     */
   
     

   
     #define
   
      MAX_VECT 105
   
     

   
     #define
   
      INF 105
   
     

   
     int
   
      c[MAX_VECT][MAX_VECT];

   
     int
   
      n;

   
     int
   
      maxflow(
   
     int
   
      s, 
   
     int
   
      t)
{
 
   
     int
   
      u, v, bg, ed, minflow, flow 
   
     =
   
      
   
     0
   
     ;
 
   
     int
   
      queue[MAX_VECT], pre[MAX_VECT];
 
   
     while
   
      (
   
     true
   
     )
 {
 memset(pre, 
   
     -
   
     1
   
     , 
   
     sizeof
   
     (pre));
 
   
     for
   
      (queue[bg
   
     =
   
     ed
   
     =
   
     0
   
     ]
   
     =
   
     s; bg 
   
     <=
   
      ed; bg
   
     ++
   
     )
 {
 u 
   
     =
   
      queue[bg];
 
   
     for
   
      (
   
     int
   
      i 
   
     =
   
      
   
     0
   
     ; (i 
   
     <
   
      n)
   
     &&
   
     (pre[t]
   
     ==-
   
     1
   
     ); i
   
     ++
   
     )
 
   
     if
   
      (c[u][i] 
   
     >
   
      
   
     0
   
      
   
     &&
   
      pre[i] 
   
     ==
   
      
   
     -
   
     1
   
     )
 {
 pre[i] 
   
     =
   
      u;
 queue[
   
     ++
   
     ed] 
   
     =
   
      i;
 }
 }
 
   
     if
   
      (pre[t] 
   
     ==
   
      
   
     -
   
     1
   
     )
   
     break
   
     ;
 minflow 
   
     =
   
      INF;
 
   
     for
   
      (u 
   
     =
   
      pre[v
   
     =
   
     t];v
   
     !=
   
     s;v
   
     =
   
     u,u
   
     =
   
     pre[v])
 
   
     if
   
      (c[u][v] 
   
     <
   
      minflow) minflow 
   
     =
   
      c[u][v];
 
   
     for
   
      (u 
   
     =
   
      pre[v
   
     =
   
     t];v
   
     !=
   
     s;v
   
     =
   
     u,u
   
     =
   
     pre[v])
 c[u][v] 
   
     -=
   
      minflow, c[v][u] 
   
     +=
   
      minflow;
 flow 
   
     +=
   
      minflow;
 }
 
   
     return
   
      flow;
}