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

• To: mathgroup at smc.vnet.net
• Subject: [mg115825] Re: Simple n-tuple problem - with no simple solution
• From: Bob Hanlon <hanlonr at cox.net>
• Date: Fri, 21 Jan 2011 04:35:46 -0500 (EST)

```Load Combinatorica then use  0.05 * Compositions[20, n]

Needs["Combinatorica`"] // Quiet

n = 5;

Timing[c1 = Select[Tuples[Table[Range[0, 1.0, .05], {n}]], Total[#] == 1 &];]

{14.4972, Null}

Timing[c2 = 0.05 Compositions[20, n];]

{0.044528, Null}

c1 == c2

True

Bob Hanlon

---- 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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