The 3n+1 problem

一道很经典的题，各大OJ上面都有，经典的递归设计。

 

 

  
    

   
     
   
      1 
   
     #include 
   
     <
   
     stdio.h
   
     >
   
     

   
      2 
   
     #include 
   
     <
   
     string
   
     .h
   
     >
   
     

   
      3 
   
      
   
     #define
   
      SWP(x,y,t) ((t)=(x),(x)=(y),(y)=(t))
   
     

   
      4 
   
      
   
     #define
   
      NL 10010
   
     

   
      5 
   
     

   
      6 
   
      
   
     int
   
      cyl[NL];

   
      7 
   
     

   
      8 
   
      
   
     int
   
      f(
   
     int
   
      k)

   
      9 
   
     {

   
     10 
   
      
   
     if
   
      (k 
   
     ==
   
      
   
     1
   
     ) 
   
     return
   
      
   
     1
   
     ;

   
     11 
   
      
   
     if
   
      (k
   
     <
   
     NL 
   
     &&
   
      cyl[k]) 
   
     return
   
      cyl[k];

   
     12 
   
      
   
     if
   
      (k
   
     &
   
     1
   
     ) {

   
     13 
   
      
   
     if
   
      (k
   
     <
   
     NL) 
   
     return
   
      cyl[k] 
   
     =
   
      f(
   
     3
   
     *
   
     k
   
     +
   
     1
   
     ) 
   
     +
   
      
   
     1
   
     ; //注意不要越界

   
     14 
   
      
   
     else
   
      
   
     return
   
      f(
   
     3
   
     *
   
     k
   
     +
   
     1
   
     ) 
   
     +
   
      
   
     1
   
     ;

   
     15 
   
      }
   
     else
   
      {

   
     16 
   
      
   
     if
   
      (k
   
     <
   
     NL) 
   
     return
   
      cyl[k] 
   
     =
   
      f(k
   
     /
   
     2
   
     ) 
   
     +
   
      
   
     1
   
     ;

   
     17 
   
      
   
     else
   
      
   
     return
   
      f(k
   
     /
   
     2
   
     ) 
   
     +
   
      
   
     1
   
     ;

   
     18 
   
      }

   
     19 
   
     }

   
     20 
   
     //打表计算

   
     21 
   
      
   
     void
   
      getCyl()

   
     22 
   
     {

   
     23 
   
      memset(cyl, 
   
     0
   
     , 
   
     sizeof
   
     (cyl));

   
     24 
   
      
   
     for
   
      (
   
     int
   
      i
   
     =
   
     1
   
     ; i
   
     <
   
     NL; i
   
     ++
   
     ) {

   
     25 
   
      
   
     if
   
      (cyl[i]) 
   
     continue
   
     ;

   
     26 
   
      cyl[i] 
   
     =
   
      f(i);

   
     27 
   
      }

   
     28 
   
     }

   
     29 
   
     

   
     30 
   
      
   
     int
   
      main()

   
     31 
   
     {

   
     32 
   
      getCyl();

   
     33 
   
      
   
     int
   
      a, b, t;

   
     34 
   
      
   
     while
   
      (scanf(
   
     "
   
     %d%d
   
     "
   
     , 
   
     &
   
     a, 
   
     &
   
     b) 
   
     !=
   
      EOF) {

   
     35 
   
      printf(
   
     "
   
     %d %d 
   
     "
   
     , a, b);

   
     36 
   
      
   
     if
   
      (a 
   
     >
   
      b) SWP(a,b,t);

   
     37 
   
      
   
     int
   
      max 
   
     =
   
      
   
     0
   
     ;

   
     38 
   
      
   
     for
   
      (
   
     int
   
      i
   
     =
   
     a; i
   
     <=
   
     b; i
   
     ++
   
     ) {

   
     39 
   
      
   
     if
   
      (cyl[i] 
   
     >
   
      max) max 
   
     =
   
      cyl[i];

   
     40 
   
      }

   
     41 
   
      printf(
   
     "
   
     %d\n
   
     "
   
     , max);

   
     42 
   
      }

   
     43 
   
      
   
     return
   
      
   
     0
   
     ;

   
     44 
   
     }

   
     45 
   
     

   
     46