Recursion and Variable Scope

[Doug Landauer]

In article <9n9vln072d at enews1.newsguy.com>, "Alex Martelli" 
<aleax at aleax.it> wrote:
  [... A very good exposition ...]
> 
> Personally, I find it clearest to frame such enumeration
> problems as "counting in a certain base"...

Here are the two silly versions that I came up with last night,
using that theme ... they probably won't work for sides > 9.

def ib ( i, b ):
        if i<b:  return `i`
        return ib(i/b,b) + `i%b`
def ibx ( i, b, d ):
        ibr = ib(i,b)
        while len(ibr) < d: ibr= '0'+ibr
        return ''.join( [ chr( ord(ch)+1 ) for ch in ibr ] )

def dicide1 ( sides, dice ):
        """ silly version, too bad it needs the "ib" aux function.  """
        lows= '0'*dice
        return [ [ int(ch) for ch in ibx(nr,sides,dice) ] \
                   for nr in range(int(lows,sides), int('1'+lows,sides) ) ]

def dicide2 ( sides, dice ):
        """ way silly version, slower.  """
        lows= '0'*dice
        return filter( lambda lst, d=dice: len(lst) == d, 
                [ [ int(ch) for ch in `nr` if ch in '123456789'[:sides] ] \
                      for nr in range(int(lows), int('1'+lows) ) ]
                )

def seeThem () :
        print '\nThis just counts in base "dice" ...'
        print 'dicide1:'
        print dicide1( 4, 2 )

        print '\nThis counts in base ten, and throws many away ...'
        print 'dicide2:'
        print dicide2( 4, 2 )
-- 
    Doug Landauer     landauer at got dot net