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Topic: Algorithm for deriving permutations
Replies: 26   Last Post: Oct 21, 2007 2:16 PM

 Messages: [ Previous | Next ]
 Patrick Hamlyn Posts: 154 Registered: 12/10/04
Re: Algorithm for deriving permutations
Posted: Oct 18, 2007 11:53 PM

Water Cooler v2 <wtr_clr@yahoo.com> wrote:

>If you have, say, 4 boxes to put the following 6 types of things in:
>
>Apples
>Oranges
>Pears
>Bananas
>Gooseberry
>Lemon
>
>
>Such that you could:
>
>a) only put one piece of each of the things in one box; and
>
>b) you could put the same thing in all the boxes, i.e you could put,
>say, an apple each in each of the boxes. In the mathematical jargon,
>if repetition was allowed
>
>
>Then, I know that we could have 6*6*6*6, i.e 1296 permutations.
>
>However, I want to know the algorithm to decide what those
>combinations are. Help appreciated.

I've seen a bunch of algorithms posted, whether loops or recursions, but you
don't need any of those.

Simply represent each box by a digit in a number in base 6.

Now each combination is numbered. If you want the 1000th combination, you can
generate it directly by converting 1000 to base 6. The nth digit gives the nth
bin's contents.

The same works for 1000000 types of object in 1000000 bins. The arithemetic is
more tedious and the numbers larger, but you can still produce the Xth
combination directly without loops.
--
Patrick Hamlyn posting from Perth, Western Australia
Windsurfing capital of the Southern Hemisphere
Moderator: polyforms group (polyforms-subscribe@egroups.com)

Date Subject Author
10/18/07 Water Cooler v2
10/18/07 Randy Poe
10/18/07 Water Cooler v2
10/18/07 hardwidg
10/18/07 Richard Heathfield
10/18/07 Proginoskes
10/18/07 Robert Israel
10/18/07 Proginoskes
10/19/07 David Bernier
10/19/07 Richard Heathfield
10/18/07 Randy Poe
10/19/07 David Breton
10/19/07 Proginoskes
10/19/07 Richard Harter
10/19/07 Marshall
10/19/07 Patricia Shanahan
10/18/07 briggs@encompasserve.org
10/18/07 Patrick Hamlyn
10/19/07 mensanator
10/19/07 hagman
10/19/07 Patrick Hamlyn
10/19/07 Richard Heathfield
10/19/07 mensanator
10/19/07 rossum
10/20/07 Grouchy