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Groups > comp.lang.forth > #41829

Re: Strings and numbers

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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]]

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Thread

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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