The Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Patrick Hamlyn

Posts: 154
Registered: 12/10/04
Re: Algorithm for deriving permutations
Posted: Oct 18, 2007 11:53 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

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
Read Algorithm for deriving permutations
Water Cooler v2
10/18/07
Read Re: Algorithm for deriving permutations
Randy Poe
10/18/07
Read Re: Algorithm for deriving permutations
Water Cooler v2
10/18/07
Read Re: Algorithm for deriving permutations
hardwidg
10/18/07
Read Re: Algorithm for deriving permutations
Richard Heathfield
10/18/07
Read Re: Algorithm for deriving permutations
Proginoskes
10/18/07
Read Re: Algorithm for deriving permutations
Robert Israel
10/18/07
Read Re: Algorithm for deriving permutations
Proginoskes
10/19/07
Read Re: Algorithm for deriving permutations
David Bernier
10/19/07
Read Re: Algorithm for deriving permutations
Richard Heathfield
10/21/07
Read Re: Algorithm for deriving permutations
Richard the Dreaded Libertarian
10/21/07
Read Re: Algorithm for deriving permutations
Richard the Dreaded Libertarian
10/18/07
Read Re: Algorithm for deriving permutations
Randy Poe
10/19/07
Read Re: Algorithm for deriving permutations
David Breton
10/19/07
Read Re: Algorithm for deriving permutations
Proginoskes
10/19/07
Read Re: Algorithm for deriving permutations
Richard Harter
10/19/07
Read Re: Algorithm for deriving permutations
Marshall
10/19/07
Read Re: Algorithm for deriving permutations
Patricia Shanahan
10/18/07
Read Re: Algorithm for deriving permutations
briggs@encompasserve.org
10/18/07
Read Re: Algorithm for deriving permutations
Patrick Hamlyn
10/19/07
Read Re: Algorithm for deriving permutations
mensanator
10/19/07
Read Re: Algorithm for deriving permutations
hagman
10/19/07
Read Re: Algorithm for deriving permutations
Patrick Hamlyn
10/19/07
Read Re: Algorithm for deriving permutations
Richard Heathfield
10/19/07
Read Re: Algorithm for deriving permutations
mensanator
10/19/07
Read Re: Algorithm for deriving permutations
rossum
10/20/07
Read Re: Algorithm for deriving permutations
Grouchy

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2017. All Rights Reserved.