Sightseeing tour--POJ 1637

1、题目类型：图论、混合图欧拉回路、Edmonds_Karp算法。

2、解题思路：（1）将图的无向边随便定向，计算每个点的入度和出度。如果有某个点出入度之差为奇数，那么肯定不存在欧拉回路；（2）构建流网络模型，Edmonds_Karp算法，察看是否有满流的分配。存在即有欧拉回路，没有就是没有欧拉回路。

3、注意事项：Edmonds_Karp算法中残留网络的更新。

4、参考博客：http://blog.csdn.net/bobten2008/archive/2009/11/11/4800084.aspx

5、实现方法:

  
    

   
     
   
     #include
   
     <
   
     iostream
   
     >
   
     
#include
   
     <
   
     cmath
   
     >
   
     
#include
   
     <
   
     queue
   
     >
   
     

   
     using
   
      
   
     namespace
   
      std;

   
     #define
   
      Max 210
   
     

   
     #define
   
      INF 99999999
   
     


   
     int
   
      m,s,cnt;

   
     int
   
      pre[Max],degree[Max];

   
     int
   
      map[Max][Max],flag[Max][Max];

   
     bool
   
      vis[Max];
queue 
   
     <
   
     int
   
     >
   
      Q;


   
     int
   
      BFS()
{
 
   
     int
   
      i,tmp,min,tmppre;
 
   
     for
   
     (i
   
     =
   
     0
   
     ;i
   
     <=
   
     m
   
     +
   
     1
   
     ;i
   
     ++
   
     )
 {
 vis[i]
   
     =
   
     false
   
     ;
 pre[i]
   
     =-
   
     1
   
     ;
 }
 vis[
   
     0
   
     ]
   
     =
   
     true
   
     ;
 
   
     while
   
     (
   
     !
   
     Q.empty())
 Q.pop();
 Q.push(
   
     0
   
     );
 
   
     while
   
     (
   
     !
   
     Q.empty())
 {
 tmp
   
     =
   
     Q.front();
 Q.pop();
 
   
     for
   
     (i
   
     =
   
     1
   
     ;i
   
     <=
   
     m
   
     +
   
     1
   
     ;i
   
     ++
   
     )
 {
 
   
     if
   
     (i
   
     ==
   
     tmp 
   
     ||
   
      vis[i] 
   
     ||
   
      
   
     !
   
     map[tmp][i])
 
   
     continue
   
     ;
 vis[i]
   
     =
   
     true
   
     ;
 pre[i]
   
     =
   
     tmp;
 Q.push(i);
 }
 }
 
   
     if
   
     (pre[m
   
     +
   
     1
   
     ]
   
     ==-
   
     1
   
     )
 
   
     return
   
      
   
     -
   
     1
   
     ;
 min
   
     =
   
     INF,tmp
   
     =
   
     m
   
     +
   
     1
   
     ;
 
   
     while
   
     ((tmppre
   
     =
   
     pre[tmp]) 
   
     !=
   
      
   
     -
   
     1
   
     )
 {
 
   
     if
   
     (map[tmppre][tmp]
   
     <
   
     min)
 min
   
     =
   
     map[tmppre][tmp];
 tmp
   
     =
   
     tmppre;
 }
 
   
     return
   
      min;
}


   
     bool
   
      Edmonds_Karp(
   
     int
   
      cnt)
{
 
   
     int
   
      i,tmp,val,tmppre,total;
 
   
     while
   
     ((val
   
     =
   
     BFS()) 
   
     !=-
   
     1
   
     )
 {
 tmp
   
     =
   
     m
   
     +
   
     1
   
     ;
 
   
     while
   
     ((tmppre
   
     =
   
     pre[tmp]) 
   
     !=
   
      
   
     -
   
     1
   
     )
 {
 map[tmppre][tmp]
   
     -=
   
     val;
 map[tmp][tmppre]
   
     +=
   
     val;
 flag[tmppre][tmp]
   
     +=
   
     val;
 flag[tmp][tmppre]
   
     =-
   
     flag[tmppre][tmp];
 tmp
   
     =
   
     tmppre;
 }
 }
 total
   
     =
   
     0
   
     ;
 
   
     for
   
     (i
   
     =
   
     1
   
     ;i
   
     <=
   
     m;i
   
     ++
   
     )
 total
   
     +=
   
     flag[
   
     0
   
     ][i];
 
   
     return
   
      total
   
     ==
   
     cnt;
}

   
     int
   
      main()
{
 
   
     int
   
      i,n,start,end,type;
 
   
     bool
   
      mark;
 cin
   
     >>
   
     n;
 
   
     while
   
     (n
   
     --
   
     )
 {
 cin
   
     >>
   
     m
   
     >>
   
     s;
 mark
   
     =
   
     true
   
     ;
 memset(degree,
   
     0
   
     ,
   
     sizeof
   
     (degree));
 memset(map,
   
     0
   
     ,
   
     sizeof
   
     (map));
 memset(flag,
   
     0
   
     ,
   
     sizeof
   
     (flag));
 
   
     for
   
     (i
   
     =
   
     0
   
     ;i
   
     <
   
     s;i
   
     ++
   
     )
 {
 cin
   
     >>
   
     start
   
     >>
   
     end
   
     >>
   
     type;
 degree[start]
   
     ++
   
     ;
 degree[end]
   
     --
   
     ;
 
   
     if
   
     (type
   
     !=
   
     1
   
     )
 map[start][end]
   
     ++
   
     ;
 }
 
   
     for
   
     (i
   
     =
   
     1
   
     ;i
   
     <=
   
     m;i
   
     ++
   
     )
 {
 
   
     if
   
     (abs(degree[i])
   
     %
   
     2
   
     ==
   
     1
   
     )
 {
 mark
   
     =
   
     false
   
     ;
 
   
     break
   
     ;
 }
 
   
     else
   
      
 degree[i]
   
     =
   
     degree[i]
   
     /
   
     2
   
     ;
 }
 
   
     if
   
     (mark)
 {
 cnt
   
     =
   
     0
   
     ;
 
   
     for
   
     (i
   
     =
   
     1
   
     ;i
   
     <=
   
     m;i
   
     ++
   
     )
 {
 
   
     if
   
     (degree[i]
   
     <
   
     0
   
     )
 map[i][m
   
     +
   
     1
   
     ]
   
     =
   
     abs(degree[i]);
 
   
     else
   
      
   
     if
   
     (degree[i]
   
     >
   
     0
   
     )
 {
 map[
   
     0
   
     ][i]
   
     =
   
     degree[i];
 cnt
   
     +=
   
     degree[i];
 }
 }
 
   
     if
   
     (
   
     !
   
     Edmonds_Karp(cnt))
 mark
   
     =
   
     false
   
     ;
 }
 
   
     if
   
     (mark)
 cout
   
     <<
   
     "
   
     possible
   
     "
   
     <<
   
     endl;
 
   
     else
   
     
 cout
   
     <<
   
     "
   
     impossible
   
     "
   
     <<
   
     endl;
 }
 
   
     return
   
      
   
     1
   
     ;
}