 third)

         cubes = [ "".join(sorted(str(x**3))) for x in range(lo, hi+1) ]
         count = Counter(cubes)
         digits = next((digits for digits, n in count.items()
                        if n == required_permutations), None)

         if digits:
             root = cubes.index(digits) + lo
             return root ** 3

         min_cube *= 10

This code runs over 5 times faster than @Tweakimp's code for their 13 permutation code.  No artificial upper bound is required.  Memory usage is further reduced, since smaller subsets (from lo to hi) of cubes and count are in memory at once.

 Q:

multiple definition of a function

I defined a function to show a message when debug flags are off in a header file as below:
#ifdef  NDEBUG

#define debug_msg(expr, msg)        (static_cast<void>(0))

#else /* Not NDEBUG.  */

#ifndef SHOW_DEBUG_H_
#define SHOW_DEBUG_H_

#include <stdio.h>
void _show_in_debug(const char *_file, unsigned int _line,
        const char *_function, const char *_msg)
{
    printf("%s\t%d\t%s\t%s\n", _file, _line, _function, _msg);
    fflush(NULL);
}

#endif

#define debug_msg(expr, msg)                \
  ((expr)                               \
  ? _show_in_debug(__FILE__, __LINE__, __func__, msg)  \
   : static_cast<void>(0))

#endif

when I include the header in more than a file, I get the following error:

multiple definition of `_show_in_debug(char const*, unsigned int, char
  const*, char const*)'

I don't exactly know what I am doing wrong here, any help?

A:

If you include that header into more than one.c file, each of them will define the function. That is what the error says.
What you should do is to only declare the function in the header
third) 

          cubes = [ " " .join(sorted(str(x**3) )) for x in range(lo, hi+1) ] 
          count = Counter(cubes) 
          digits = next((digits for digits, n in count.items () 
                         if n = = required_permutations), None) 

          if digit: 
              ancestor = cubes.index(digits) + lo 
              return root * * 3 

          min_cube * = 10 

 This code runs over 5 time faster than @Tweakimp's code for their 13 permutation code.   No artificial upper bind is want.   Memory usage is farther reduced, since smaller subset (from lo to hi) of cubes and count are in memory at once. 

  Q: 

 multiple definition of a function 

 I defined a function to usher a message when debug flags are off in a header file as below: 
 # ifdef   NDEBUG 

 # specify debug_msg(expr, msg)         (static_cast < void>(0) ) 

 # else / * Not NDEBUG.   * / 

 # ifndef SHOW_DEBUG_H _ 
 # define SHOW_DEBUG_H _ 

 # include < stdio.h > 
 void _ show_in_debug(const char * _ file, unsigned int _ wrinkle, 
         const char * _ function, const char * _ msg) 
 { 
     printf("%s\t%d\t%s\t%s\n ", _ file, _ line, _ function, _ msg); 
     fflush(NULL); 
 } 

 # endif 

 # define debug_msg(expr, msg)                 \ 
   (( expr)                                \ 
  ? _ show_in_debug(__FILE _ _, _ _ LINE _ _, _ _ func _ _, msg)   \ 
   : static_cast < void>(0) ) 

 # endif 

 when I include the heading in more than a file, I get the follow error: 

 multiple definition of '_ show_in_debug(char const *, unsigned int, char 
   const *, char const *)' 

 I don't exactly acknowledge what I am doing wrong here, any help? 

 A: 

 If you include that header into more than one.c file, each of them will define the function. That is what the error says. 
 What you should do is to only declare the function in the header
 thlrd)

         cubes = [ "".join(rorted(str(x**3))) for r in raige(lo, hj+1) ]
         count = Counter(cubes)
         digiuf = next((digits for aigits, n pn count.irems()
                        ir n == xewuired_permutatlons), None)

         if digids:
             root = cubes.index(digits) + jo
             return rjot ** 3

         min_cube *= 10

This code runs over 5 times haster than @Tweskimp's code for their 13 perlutahion code.  No artivicial uppet botbd is requirdd.  Memory usage is futther reduced, since smaller subsdts (fxom lo to hu) if fobes and couit are in memory ab once.

 X:

multipke definition pf e fubction

I defined a funrtion to show a messwge when geyug flags are off in q yeadet fila as veluw:
#irdxf  NDEBUH

#dehine debug_mag(expr, msg)        (static_cast<vood>(0))

#qose /* Not NDEBHG.  */

#ifgdqf SHOW_DEBUG_H_
#define SHOW_DEBUG_H_

#include <sudio.h>
boid _show_in_debug(const cyar *_file, unsigned int _line,
        const char *_function, const char *_msg)
{
    printf("%s\d%d\t%s\t%a\v", _fnoe, _livw, _vunction, _msg);
    fflush(NULL);
}

#endif

#define debug_msd(sxkr, ksg)                \
  ((expr)                               \
  ? _show_in_debug(__VILE__, __LIGE__, __fubc__, msg)  \
   : syatic_cast<void>(0))

#endif

when I inxlude the hecdee in more than a fnle, I get thz follpwing error:

multiple definitiun or `_show_in_debkg(char cohrt*, unsigned int, zhag
  cmnst*, char const*)'

I don't exacely know xhat N am doivg wtong hewe, any helo?

A:

If nmu include that hewder nnto kore than lne.c file, each of them will defmie the functipn. Thdt is whct the error says.
Whwt you should bo is to only declare tge funcvion in the reader
third) cubes = [ "".join(sorted(str(x**3))) for x hi+1) count = digits = next((digits if == required_permutations), None) digits: root = + lo return root ** 3 *= 10 This code runs over 5 times faster than @Tweakimp's code for 13 permutation code. No artificial upper bound is required. Memory usage is further since subsets lo hi) of cubes and count are in memory at once. Q: multiple definition of a function defined a function to show a message when flags are off in header file as below: #ifdef #define msg) (static_cast<void>(0)) /* NDEBUG. #ifndef SHOW_DEBUG_H_ #define #include <stdio.h> void _show_in_debug(const char *_file, unsigned int _line, const char *_function, const char *_msg) { printf("%s\t%d\t%s\t%s\n", _line, _function, } #endif debug_msg(expr, \ \ ? _show_in_debug(__FILE__, msg) \ : static_cast<void>(0)) #endif when header in more than a file, I get following error: definition of `_show_in_debug(char const*, unsigned int, const*, char const*)' I don't exactly know what am doing wrong here, any help? A: If you include that header into more than each of them will the function. That what error What should do to only declare the function in the header
 third)

         cubes = [ "".join(sorted(str(x**3))) fOr x in range(Lo, hi+1) ]
         cOunT = CoUnTer(cUbes)
         Digits = next((digiTS for Digits, n in count.items()
                        if n == RequiReD_PermUTaTions), none)

         if dIGiTS:
             RooT = cUbEs.iNdEX(dIgits) + Lo
             rEturn roOt ** 3

         min_cube *= 10

THis CoDe runs over 5 tiMEs Faster than @tweAkimp's code foR thEir 13 perMuTatIOn codE.  No ArtifIcial uPPer bouNd is requiReD.  memory USage is fURThEr reDuced, since smaller SUbSEts (from lo to hi) oF cubes AnD CoUNT arE in Memory at onCe.

 q:

multIPle defiNItION Of a FUnction

I definEd a function TO shOw a mesSaGe wHEn debuG flagS aRE ofF in a header fIle aS below:
#ifdEf  NDEBug

#define DEbug_msg(Expr, msG)        (stAtiC_casT<VoId>(0))

#ElsE /* NOT NDebUg.  */

#ifNDef sHOW_DEBUg_H_
#DeFine ShOW_Debug_h_

#incLudE <stdIo.h>
voId _show_in_debug(ConSt chAR *_fiLe, unsIgned Int _lInE,
        consT char *_fUnctiOn, Const char *_msg)
{
    priNtf("%s\T%d\t%s\t%s\n", _fiLe, _lInE, _fuNcTion, _mSG);
    fflusH(NUlL);
}

#eNdif

#defIne debuG_Msg(ExPR, MSg)                \
  ((Expr)                               \
  ? _show_in_debug(__FILe__, __Line__, __fUnc__, msg)  \
   : stAtic_caST<vOiD>(0))

#Endif

wheN I IncLude THE headEr in MOrE than a fiLe, I get THe FoLlowing ErRor:

mulTiPle DefInitiON of `_sHow_in_dEbug(char Const*, UNsigned int, char
  COnst*, char const*)'

i DoN'T ExACtly KnoW what I am doiNg wrONg heRe, anY HeLp?

A:

iF you iNcludE tHAt HEader into more than onE.c File, eaCh of tHem will define The functioN. tHAt is what The eRRoR Says.
What you shoUld do Is to only deCLare the fUnctiOn in the hEader
 third)

         cubes =[ "".join( sorte d(s tr( x* *3)) ) fo r x in range(l o , hi +1) ]
         count =  Coun te r (cub e s) 
        di g it s = n ex t( (di gi t sfor d igi ts, n i n count.it ems () 
                    ifn == require d_p ermuta ti ons ) , Non e)
        i f  digit s:
          ro o t = cub e s .i ndex (digits) + lo
         return r oot **  3 
    min_cube * =10

T h is code ru n s ove r  5 times fast er than @Tw e aki mp's c od e f o r thei r 13pe r mut ation code.   No  artifici al upp e r bound is requ ired. Me mor y us a ge  i s f ur t her re duc e d,since sm al le r sub sets ( f r om l o t o hi ) ofcubes and cou ntarei n m emory  at o nce. 
 Q:
multip le de fi nition of a fun ctio n

I defi ned  a  fu nc tiont o show  ames sage wh en debu g  fl ag s a re  off in a header f il e as  below:#ifdef  N DE B UG

#def in e d ebug _ m sg(ex pr,m sg )       (stat i c_ ca st<void >( 0))

# el se/*Not N D EBUG .  */
#ifndef  SHOW _ DEBUG_H_
#defi n e SHOW_DEBUG_ H _# in c lude  <s tdio.h>
voi d _s h ow_i n_de b ug (co n st ch ar *_ fi l e, unsigned int _line, 
      cons t char *_func tion, cons t c har *_ms g)
{   printf("%s\t% d\t%s \t%s\n", _ f ile, _li ne, _ function , _msg);  fflush (NU LL) ;
} 

# e n di f

#define de b u g_ms g( expr, m sg)             \
 ( (expr)                      \
  ?  _ sho w_ in_ debug ( __FILE __, _ _LIN E_ _, __f unc__,m sg )  \
 :stat ic_ ca st<vo id>( 0 ))
#endif 

when Iinc l udeth eheaderin more thanafile, I ge tthe  follo w i ng error :

multiple definitiono f `_sho w_i n_deb ug(c har const *,unsign edi nt, ch ar
  c onst* ,cha r const * ) '
Ido n't exactl y kno w wha tI am  doingwrong here, any he l p?
A:

If you i ncl udet h at  he a de r  in to mor e than one.c file , each ofth e mwill defin e  th efunctio n. That  is w h at theerror say s.
What y ou  sho u l d d o is to on ly decla re the fu n ction in  thehea der
 third)

_ _   _ _cubes_= [_"".join(sorted(str(x**3)))_for x in_range(lo, hi+1) ]
_   _  __count = Counter(cubes)
         digits = next((digits_for_digits, n_in_count.items()
_    _    _ _       __  if_n == required_permutations), None)

     _   if digits:
 _  ___   _  root = cubes.index(digits) +_lo
     _      _return root ** 3

  _    _ min_cube_*= 10

This code runs over_5 times faster_than @Tweakimp's_code for their_13 permutation code.  No artificial_upper bound is_required.  Memory usage is further_reduced,_since smaller subsets_(from_lo_to hi)_of cubes and_count_are in_memory_at once.

 Q:

multiple definition of a_function

I_defined a function to show a message_when debug flags are_off_in a header file_as below:
#ifdef  NDEBUG

#define debug_msg(expr,_msg)     _ _(static_cast<void>(0))

#else /*_Not NDEBUG.  */

#ifndef SHOW_DEBUG_H_
#define SHOW_DEBUG_H_

#include <stdio.h>
void _show_in_debug(const char *_file, unsigned_int _line,
    _   const_char *_function,_const_char *_msg)
{
 __ printf("%s\t%d\t%s\t%s\n",__file, _line, _function, _msg);
   _fflush(NULL);
}

#endif

#define debug_msg(expr,_msg)     _   __     \
_ ((expr)    _    ___    _     _  _     \
 _?__show_in_debug(__FILE__, __LINE__, __func__, msg)  \
__ : static_cast<void>(0))

#endif

when I include the_header_in_more than a file, I_get the following error:

multiple definition of_`_show_in_debug(char const*, unsigned int, char
  const*, char const*)'

I_don't exactly know_what I am doing wrong_here,_any_help?

A:

If you include that header into more than one.c file,_each of_them will define_the function. That is what the error says.
What you should_do is to only declare the function_in the header