       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

```

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