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

*To*: mathgroup at smc.vnet.net*Subject*: [mg115844] Re: Simple n-tuple problem - with no simple solution*From*: DrMajorBob <btreat1 at austin.rr.com>*Date*: Sat, 22 Jan 2011 03:23:45 -0500 (EST)

The range was Range[0,1,.05], not Range[0,1,.5]. For the latter range, the problem has only two solutions aside from rearrangements. Bobby On Fri, 21 Jan 2011 03:29:22 -0600, Sseziwa Mukasa <mukasa at jeol.com> wrote: > 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 > -- DrMajorBob at yahoo.com