[Tutor] Algorithm Question

[Kirby Urner]

>  find all possible arrangements :
>(0001,0010,0100,1000,1001,1011,1111,0000,0110,1010,0101,1100, etc)


Don't forget 0000 (maybe not legal in bank world).

In this case, doing binary, the simplest approach is to
just increment in base 2.

A lot of these permutation generators can be thought of
as counting problems, where you have a sequence with a
defined order, i.e. lowest to highest.  If you can think
of a rule which defines the increment, and repeat it...

For example, if you wanted all permutations of 0,1,2,3,4,
with 3 slots to fill, then you could just increment
in base 5:

    def base(n,b):
        """
        Convert n in base 10 to list of digits
        in some positive integral base b < 10
        """
         digits = []
         while n>0:
            r = n%b
            n = n//b
            digits = [r] + digits
         return digits

   >>> ["".join(map(str,([0,0,0]+base(i,5)))[-3:]) for i in range(125)]

will give:

['000', '001', '002', '003', '004', '010', '011', '012',
'013', '014'

<<SNIP>>

'412', '413', '414', '420', '421', '422', '423', '424', '430',
'431', '432', '433', '434', '440', '441', '442', '443', '444']

Kirby