POJ 2570 Fiber Network (传递闭包)

题意：给定n个城市之间的有向图，每条边是以字母标示的，输出在每条可行线路u->v中，其所经过的每一段线路的相同的字母。

思路：由于两点之间有多条线路，所以想到了对每个字母进行floyd，最后集中输出，然后华丽的TLE了.......后来知道可以用位运算优化，汗......没想出来.....然后就可以AC了。

  
    

   
     
   
     #include 
   
     <
   
     iostream
   
     >
   
     
#include 
   
     <
   
     cstdio
   
     >
   
     
#include 
   
     <
   
     algorithm
   
     >
   
     
#include 
   
     <
   
     memory.h
   
     >
   
     
#include 
   
     <
   
     cmath
   
     >
   
     
#include 
   
     <
   
     bitset
   
     >
   
     
#include 
   
     <
   
     queue
   
     >
   
     
#include 
   
     <
   
     vector
   
     >
   
     

   
     using
   
      
   
     namespace
   
      std;


   
     const
   
      
   
     int
   
      BORDER 
   
     =
   
      (
   
     1
   
     <<
   
     20
   
     )
   
     -
   
     1
   
     ;

   
     const
   
      
   
     int
   
      MAXSIZE 
   
     =
   
      
   
     37
   
     ;

   
     const
   
      
   
     int
   
      MAXN 
   
     =
   
      
   
     505
   
     ;

   
     const
   
      
   
     int
   
      INF 
   
     =
   
      
   
     1000000000
   
     ;

   
     #define
   
      CLR(x,y) memset(x,y,sizeof(x))
   
     

   
     #define
   
      ADD(x) x=((x+1)&BORDER)
   
     

   
     #define
   
      IN(x) scanf("%d",&x)
   
     

   
     #define
   
      OUT(x) printf("%d\n",x)
   
     

   
     #define
   
      MIN(m,v) (m)<(v)?(m):(v)
   
     

   
     #define
   
      MAX(m,v) (m)>(v)?(m):(v)
   
     

   
     #define
   
      ABS(x) ((x)>0?(x):-(x))
   
     



   
     int
   
      map[MAXN][MAXN];

   
     int
   
      n,m;

   
     bool
   
      mark[MAXN];


   
     int
   
      init()
{
 CLR(map,
   
     0
   
     );
 CLR(mark,
   
     0
   
     );
 
   
     return
   
      
   
     0
   
     ;
}

   
     int
   
      input()
{
 
   
     int
   
      i,u,v,k,len;
 
   
     char
   
      str[
   
     30
   
     ];
 
   
     for
   
     ( ; ; )
 {
 scanf(
   
     "
   
     %d%d
   
     "
   
     ,
   
     &
   
     u,
   
     &
   
     v);
 
   
     if
   
     (
   
     !
   
     u 
   
     ||
   
      
   
     !
   
     v)
 
   
     break
   
     ;
 scanf(
   
     "
   
     %s
   
     "
   
     ,str);
 len 
   
     =
   
      strlen(str);
 
   
     for
   
     (i 
   
     =
   
      
   
     0
   
     ; i 
   
     <
   
      len; 
   
     ++
   
     i)
 map[u][v] 
   
     |=
   
      (
   
     1
   
     <<
   
     (str[i]
   
     -
   
     '
   
     a
   
     '
   
     ));
 }
 
   
     return
   
      
   
     0
   
     ;
}

   
     int
   
      floyd()
{
 
   
     int
   
      i,j,k,tmp;
 
   
     for
   
     (k 
   
     =
   
      
   
     1
   
     ; k 
   
     <=
   
      n; 
   
     ++
   
     k)
 
   
     for
   
     (i 
   
     =
   
      
   
     1
   
     ; i 
   
     <=
   
      n; 
   
     ++
   
     i)
 
   
     for
   
     (j 
   
     =
   
      
   
     1
   
     ; j 
   
     <=
   
      n; 
   
     ++
   
     j)
 map[i][j] 
   
     |=
   
      (map[i][k] 
   
     &
   
      map[k][j]);
 
   
     return
   
      
   
     0
   
     ;
}

   
     int
   
      work()
{
 
   
     int
   
      i,j,tmp,u,v;
 
   
     bool
   
      tag;
 floyd();
 
   
     for
   
     ( ; ; )
 {
 scanf(
   
     "
   
     %d%d
   
     "
   
     ,
   
     &
   
     u,
   
     &
   
     v);
 
   
     if
   
     (
   
     !
   
     u 
   
     ||
   
      
   
     !
   
     v)
 
   
     break
   
     ;
 tag 
   
     =
   
     false
   
     ;
 
   
     for
   
     (i 
   
     =
   
      
   
     0
   
     ; i 
   
     <
   
      
   
     26
   
     ; 
   
     ++
   
     i)
 
   
     if
   
     (map[u][v] 
   
     &
   
      (
   
     1
   
     <<
   
     i))
 {
 tag 
   
     =
   
      
   
     true
   
     ;
 printf(
   
     "
   
     %c
   
     "
   
     ,
   
     '
   
     a
   
     '
   
     +
   
     i);
 }
 
   
     if
   
     (tag)
 printf(
   
     "
   
     \n
   
     "
   
     );
 
   
     else
   
     
 printf(
   
     "
   
     -\n
   
     "
   
     );
 }
 printf(
   
     "
   
     \n
   
     "
   
     );
 
   
     return
   
      
   
     0
   
     ;
}

   
     int
   
      main()
{
 
   
     while
   
     (IN(n))
 {
 
   
     if
   
     (
   
     !
   
     n)
 
   
     break
   
     ;
 init();
 input();
 work();
 }
 
   
     return
   
      
   
     0
   
     ;

  
    

TLE code：

  
    

   
     
   
     #include 
   
     <
   
     iostream
   
     >
   
     
#include 
   
     <
   
     cstdio
   
     >
   
     
#include 
   
     <
   
     algorithm
   
     >
   
     
#include 
   
     <
   
     memory.h
   
     >
   
     
#include 
   
     <
   
     cmath
   
     >
   
     
#include 
   
     <
   
     bitset
   
     >
   
     
#include 
   
     <
   
     queue
   
     >
   
     
#include 
   
     <
   
     vector
   
     >
   
     

   
     using
   
      
   
     namespace
   
      std;


   
     const
   
      
   
     int
   
      BORDER 
   
     =
   
      (
   
     1
   
     <<
   
     20
   
     )
   
     -
   
     1
   
     ;

   
     const
   
      
   
     int
   
      MAXSIZE 
   
     =
   
      
   
     37
   
     ;

   
     const
   
      
   
     int
   
      MAXN 
   
     =
   
      
   
     505
   
     ;

   
     const
   
      
   
     int
   
      INF 
   
     =
   
      
   
     1000000000
   
     ;

   
     #define
   
      CLR(x,y) memset(x,y,sizeof(x))
   
     

   
     #define
   
      ADD(x) x=((x+1)&BORDER)
   
     

   
     #define
   
      IN(x) scanf("%d",&x)
   
     

   
     #define
   
      OUT(x) printf("%d\n",x)
   
     

   
     #define
   
      MIN(m,v) (m)<(v)?(m):(v)
   
     

   
     #define
   
      MAX(m,v) (m)>(v)?(m):(v)
   
     

   
     #define
   
      ABS(x) ((x)>0?(x):-(x))
   
     

typedef 
   
     struct
   
     {
 
   
     bool
   
      alp[
   
     26
   
     ];
}Node;

Node map[MAXN][MAXN];

   
     int
   
      n,m;

   
     bool
   
      mark[MAXN];


   
     int
   
      init()
{
 CLR(map,
   
     0
   
     );
 CLR(mark,
   
     0
   
     );
 
   
     return
   
      
   
     0
   
     ;
}

   
     int
   
      input()
{
 
   
     int
   
      i,u,v,k,len;
 
   
     char
   
      str[
   
     30
   
     ];
 
   
     for
   
     ( ; ; )
 {
 scanf(
   
     "
   
     %d%d
   
     "
   
     ,
   
     &
   
     u,
   
     &
   
     v);
 
   
     if
   
     (
   
     !
   
     u 
   
     ||
   
      
   
     !
   
     v)
 
   
     break
   
     ;
 scanf(
   
     "
   
     %s
   
     "
   
     ,str);
 len 
   
     =
   
      strlen(str);
 
   
     for
   
     (i 
   
     =
   
      
   
     0
   
     ; i 
   
     <
   
      len; 
   
     ++
   
     i)
 {
 map[u][v].alp[str[i]
   
     -
   
     '
   
     a
   
     '
   
     ] 
   
     =
   
      
   
     true
   
     ;
 mark[str[i]
   
     -
   
     '
   
     a
   
     '
   
     ] 
   
     =
   
      
   
     true
   
     ;
 }
 }
 
   
     return
   
      
   
     0
   
     ;
}

   
     int
   
      floyd(
   
     const
   
      
   
     int
   
     &
   
      ind)
{
 
   
     int
   
      i,j,k,tmp;
 
   
     for
   
     (k 
   
     =
   
      
   
     1
   
     ; k 
   
     <=
   
      n; 
   
     ++
   
     k)
 
   
     for
   
     (i 
   
     =
   
      
   
     1
   
     ; i 
   
     <=
   
      n; 
   
     ++
   
     i)
 
   
     for
   
     (j 
   
     =
   
      
   
     1
   
     ; j 
   
     <=
   
      n; 
   
     ++
   
     j)
 map[i][j].alp[ind] 
   
     |=
   
      (map[i][k].alp[ind]
   
     &
   
     map[k][j].alp[ind]);
 
   
     return
   
      
   
     0
   
     ;
}

   
     int
   
      work()
{
 
   
     int
   
      i,j,tmp,u,v;
 
   
     bool
   
      tag;
 
   
     for
   
     (i 
   
     =
   
      
   
     0
   
     ; i 
   
     <
   
      
   
     26
   
     ; 
   
     ++
   
     i)
 {
 
   
     if
   
     (
   
     !
   
     mark[i])
 
   
     continue
   
     ;
 floyd(i);
 }
 
   
     for
   
     ( ; ; )
 {
 scanf(
   
     "
   
     %d%d
   
     "
   
     ,
   
     &
   
     u,
   
     &
   
     v);
 
   
     if
   
     (
   
     !
   
     u 
   
     ||
   
      
   
     !
   
     v)
 
   
     break
   
     ;
 tag 
   
     =
   
     false
   
     ;
 
   
     for
   
     (i 
   
     =
   
      
   
     0
   
     ; i 
   
     <
   
      
   
     26
   
     ; 
   
     ++
   
     i)
 
   
     if
   
     (map[u][v].alp[i])
 {
 tag 
   
     =
   
      
   
     true
   
     ;
 printf(
   
     "
   
     %c
   
     "
   
     ,
   
     '
   
     a
   
     '
   
     +
   
     i);
 }
 
   
     if
   
     (tag)
 printf(
   
     "
   
     \n
   
     "
   
     );
 
   
     else
   
     
 printf(
   
     "
   
     -\n
   
     "
   
     );
 }
 
   
     return
   
      
   
     0
   
     ;
}

   
     int
   
      main()
{
 
   
     while
   
     (IN(n))
 {
 
   
     if
   
     (
   
     !
   
     n)
 
   
     break
   
     ;
 init();
 input();
 work();
 }
 
   
     return
   
      
   
     0
   
     ;
}