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Re: Strings and numbers

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WJ wrote:

> WJ wrote:
> 
> > WJ wrote:
> > 
> > > Steve Graham wrote:
> > > 
> > > > 
> > > > http://programmingpraxis.com/2015/07/21/a-number-puzzle/#comments
> > > 
> > > 
> > > 
> > > >  Find a 10-digit number, with all digits unique, such that the first n
> > > >  digits of the number are divisible by n. For instance, in the 3-digit
> > > >  number 345, the 1-digit prefix, 3, is divisible by 1, the 2-digit
> > > >  prefix, 34, is divisible by 2, and the 3-digit prefix, 345, is
> > > >  divisible by 3.
> > > 
> > > Gauche Scheme:
> > > 
> > > (define (next divisor integer digits)
> > >   (filter-map
> > >     (lambda (d)
> > >       (let1 new-int (+ (* 10 integer) d)
> > >         (and (zero? (mod new-int divisor))
> > >              (list new-int (delete d digits)))))
> > >     digits))
> > > 
> > > 
> > > ;; Recursion.
> > > (let go ((divisor 1) (candidates (list (list 0 (iota 10)))))
> > >   (if (> divisor 10)
> > >     (caar candidates)
> > >     (go (+ divisor 1)
> > >         (append-map
> > >           (lambda (x) (apply next divisor x))
> > >           candidates))))
> > > 
> > > 3816547290
> > 
> > Ruby:
> > 
> > def next_digit( divisor, digits_so_far )
> >   number_so_far = digits_so_far.join.to_i * 10
> >   ((0..9).to_a - digits_so_far).select{|d|
> >     ((number_so_far + d).modulo divisor).zero? }.
> >     map{|d| digits_so_far + [d]}
> > end
> > 
> > candidates = [[]]
> > 1.upto(10){|divisor|
> >   candidates = candidates.map{|digit_list|
> >     next_digit( divisor, digit_list) }.flatten(1) }
> > candidates
> > 
> >  ===>
> > [[3, 8, 1, 6, 5, 4, 7, 2, 9, 0]]
> 
> No one has yet posted a Forth solution.  Perhaps this Ruby version
> will be more understandable than the previous one.
> 
> def divisible( n, divisor )
>   n.modulo(divisor).zero?
> end
> 
> def one_more_digit( divisor, digits_so_far )
>   digits_avail = (0 .. 9).to_a - digits_so_far
>   base_for_new_number = digits_so_far.join.to_i * 10
>   digits_avail.select{ |d| divisible( base_for_new_number + d, divisor )}.
>     map{|d| digits_so_far + [d] }
> end
> 
> 
> Here's an example of how this function works:
> 
> one_more_digit( 4, [3, 8, 1] )
>     ==>[[3, 8, 1, 2], [3, 8, 1, 6]]
> 
> 
> 
> candidates = [[]]
> 1.upto(10){|divisor|
>   candidates = candidates.map{|digit_list|
>     one_more_digit( divisor, digit_list) }.flatten(1) }
> candidates
> 
> [[3, 8, 1, 6, 5, 4, 7, 2, 9, 0]]
> 
> Here's an example of how the "flatten" command works in Ruby:
> 
> [[[3, 8, 1, 2], [3, 8, 1, 6]]].flatten
>     ==>[3, 8, 1, 2, 3, 8, 1, 6]
> [[[3, 8, 1, 2], [3, 8, 1, 6]]].flatten(1)
>     ==>[[3, 8, 1, 2], [3, 8, 1, 6]]


Oforth:

: flatten-1 { [] swap apply( #+ ) }

: digits-avail( digits-used )
  { seqFrom(0,9) filter( #[ digits-used include not ] ) }

: divisible( divisor, list-of-digits )
  { list-of-digits asString asInteger isMultiple( divisor ) }

: one-more-digit( divisor, digits-so-far )
{ digits-so-far digits-avail map( #[ digits-so-far swap + ] )
  filter( #[ divisible( divisor ) ] ) }

: go( divisor, candidates )
{ divisor 10 >
  ifTrue: [ candidates println ]
  else: [ candidates map( #[ one-more-digit(divisor) ] )
    flatten-1  divisor 1 +  go ] }

go(1, [[]])

[[3, 8, 1, 6, 5, 4, 7, 2, 9, 0]]

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Strings and numbers Steve Graham <solitary.wanderer52@gmail.com> - 2015-08-03 13:24 -0700
  Re: Strings and numbers Julian Fondren <julian.fondren@gmail.com> - 2015-08-03 13:51 -0700
    Re: Strings and numbers "Rod Pemberton" <boo@fasdfrewar.cdm> - 2015-08-03 17:38 -0400
    Re: Strings and numbers Steve Graham <solitary.wanderer52@gmail.com> - 2015-08-03 14:44 -0700
  Re: Strings and numbers Paul Rubin <no.email@nospam.invalid> - 2015-08-03 20:59 -0700
    Re: Strings and numbers Steve Graham <solitary.wanderer52@gmail.com> - 2015-08-04 12:19 -0700
      Re: Strings and numbers "WJ" <w_a_x_man@yahoo.com> - 2015-08-07 09:29 +0000
        Re: Strings and numbers "WJ" <w_a_x_man@yahoo.com> - 2015-09-04 15:14 +0000
          Re: Strings and numbers "WJ" <w_a_x_man@yahoo.com> - 2015-09-07 19:34 +0000
            Re: Strings and numbers Julian Fondren <julian.fondren@gmail.com> - 2015-09-08 11:48 -0700
            Re: Strings and numbers Paul Rubin <no.email@nospam.invalid> - 2015-09-09 00:41 -0700
              Re: Strings and numbers Richard Todd <richard.wesley.todd@gmail.com> - 2015-09-10 00:32 -0700
                Re: Strings and numbers Richard Todd <richard.wesley.todd@gmail.com> - 2015-09-10 10:29 -0700
                Re: Strings and numbers Paul Rubin <no.email@nospam.invalid> - 2015-09-10 17:22 -0700
                Re: Strings and numbers Richard Todd <richard.wesley.todd@gmail.com> - 2015-09-10 21:34 -0700
                Re: Strings and numbers humptydumpty <ouatubi@gmail.com> - 2015-09-11 02:16 -0700
                Re: Strings and numbers humptydumpty <ouatubi@gmail.com> - 2015-09-11 07:33 -0700
                Re: Strings and numbers Paul Rubin <no.email@nospam.invalid> - 2015-09-13 00:12 -0700
                Re: Strings and numbers humptydumpty <ouatubi@gmail.com> - 2015-09-13 02:09 -0700
                Re: Strings and numbers Paul Rubin <no.email@nospam.invalid> - 2015-09-11 15:53 -0700
                Re: Strings and numbers Andrew Haley <andrew29@littlepinkcloud.invalid> - 2015-12-18 16:02 -0600
            Re: Strings and numbers "WJ" <w_a_x_man@yahoo.com> - 2015-09-12 23:38 +0000
              Re: Strings and numbers "WJ" <w_a_x_man@yahoo.com> - 2015-09-13 19:41 +0000
            Re: Strings and numbers "WJ" <w_a_x_man@yahoo.com> - 2015-11-29 18:09 +0000

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