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>*Reply-to*: igora at wolf-ram.com*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>