Re: Simple n-tuple problem - with no simple solution

*To*: mathgroup at smc.vnet.net*Subject*: [mg115790] Re: Simple n-tuple problem - with no simple solution*From*: Sseziwa Mukasa <mukasa at jeol.com>*Date*: Fri, 21 Jan 2011 04:28:59 -0500 (EST)

On Jan 20, 2011, at 6:33 AM, Don wrote: > Problem: Given an n-tuple (n >= 1). with each element able to take > on the values in > Range[0, 1.0, .05] , produce all the n-tuples that sum to 1.0. > > The most direct way to solve this problem is to generaate all possible > n-tuples and Select out all those that sum to 1.0. > > For example, when n = 2 : > > n = 2; > Select[Tuples[Table[Range[0, 1.0, .05], {n}]], Total[#] == 1 &] > > The problem with this solution is that the number of n-tuples that are > generated before the Select is used grows exponentially fast as a > function > of n - causing the system to run out of memory (RAM) very quickly. > > Is there a more memory efficient way to solve this problem that > doesn't > use so much memory but still is not too slow in terms of processor > time? Use Outer Flatten[Outer[If[Plus[##]==1,{##},Sequence@@{}]&,Sequence@@Table[Range[0,1.0,0.5],{n}]],1] Regards, Ssezi