Re: permutations

• To: mathgroup at smc.vnet.net
• Subject: [mg62438] Re: [mg62418] permutations
• From: Igor Antonio <igora at wolf-ram.com>
• Date: Thu, 24 Nov 2005 06:33:37 -0500 (EST)
• Organization: Wolfram Research, Inc.
• References: <200511231127.GAA23646@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Francisco Gutierrez wrote:
> Dear Group:
>   If I do for example:
>   Permutations[{x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12}],
>   my computer runs out of memory.
>   This is not such a poor computer.  Actually, I would need to do permutations of lists of Length 20, perhaps 25.  I am aware these calculations are big (Length[x]!), but I wonder if there is some way around the problem. Compilating Permutations? But then how? Can somebody help me?
>   Francisco Gutiérrez
>
>

Francisco,

Your best bet is to work with smaller lists and manually create subsets of the
final list containing all permutations.  Have you calculated how much memory you
would actually need?  You're looking at 33GBs and that's considering list
overhead + each element being just an unassigned variable.  If the list
contained, say, integers (16 bytes), you're looking @ 120GBs.

In[56]:= lst = {x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12}; ByteCount@lst

Out[57]= 72

In[58]:= lst2 = {1,2,3,4,5,6,7,8,9,10,11,12}; ByteCount@lst2

Out[59]= 264

In[60]:= ByteCount@lst * Length@lst!/1024.0^2

Out[60]= 32890.4

In[61]:= ByteCount@lst2 * Length@lst2!/1024.0^2

Out[61]= 120598.

I'm sure there are multiple ways to create subsets of the full list of
permutations, but here's one that's easy to write (I'm working with a smaller
set so I don't run out of memory):

In[98]:= result = Flatten[
Table[Insert[#, x6, i]&/@Permutations[{x1,x2,x3,x4,x5}], {i,1,6}], 1];

In[99]:= Length@result

Out[99]= 720

which is the same as:

In[100]:= Length@Permutations[{x1,x2,x3,x4,x5,x6}]

Out[100]= 720

--

Igor C. Antonio
Wolfram Research, Inc.
http://www.wolfram.com

To email me personally, remove the dash.

```

• References:
• permutations
• From: Francisco Gutierrez <fgutiers2002@yahoo.com>
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