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

*To*: mathgroup at smc.vnet.net*Subject*: [mg115792] Re: Simple n-tuple problem - with no simple solution*From*: Sseziwa Mukasa <mukasa at jeol.com>*Date*: Fri, 21 Jan 2011 04:29:22 -0500 (EST)

A minor error, use: Flatten[Outer[If[Plus[##]==1,{##},Sequence@@{}]&,Sequence@@Table[Range[0,1.0,0.5],{n}]],n-1] On Jan 20, 2011, at 10:04 AM, Sseziwa Mukasa wrote: > > 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