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

• To: mathgroup at smc.vnet.net
• Subject: [mg115799] Re: Simple n-tuple problem - with no simple solution
• From: Leonid Shifrin <lshifr at gmail.com>
• Date: Fri, 21 Jan 2011 04:30:43 -0500 (EST)

```If I understood the problem correctly, here is what I would do:

In:=
n = 2;
N[IntegerPartitions[20, {n}]/20]

Out= {{0.95, 0.05}, {0.9, 0.1}, {0.85, 0.15}, {0.8, 0.2}, {0.75,
0.25}, {0.7, 0.3}, {0.65, 0.35}, {0.6, 0.4}, {0.55, 0.45}, {0.5,
0.5}}

Regards,
Leonid

On Thu, Jan 20, 2011 at 2:33 PM, Don <donabc at comcast.net> 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?
>
> Thank you.
>
>

```

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