From: <HIDDEN>
Newsgroups: comp.soft-sys.matlab
Subject: integer solutions for x_1+x_2+...+x_n = k
Date: Sun, 2 Nov 2008 19:12:01 +0000 (UTC)
Organization: The MathWorks, Inc.
Lines: 25
Message-ID: <geku21$eku$>
Reply-To: <HIDDEN>
Content-Type: text/plain; charset="ISO-8859-1"
Content-Transfer-Encoding: 8bit
X-Trace: 1225653121 15006 (2 Nov 2008 19:12:01 GMT)
NNTP-Posting-Date: Sun, 2 Nov 2008 19:12:01 +0000 (UTC)
X-Newsreader: MATLAB Central Newsreader 1582760
Xref: comp.soft-sys.matlab:498534

Help.. please..

I need to write a function for solving

x_1+x_2+x_3+ ...+x_n = k

where n and k are inputs, k is some small positive integer, for example, k= 3, or k= 6, n is rather large positve integer, for example,, n = 20, or n= 60.

The unknowns x_1, x_2, ...x_n are non-negative integers.

I wrote a complicated loop to list out lexicographically all (x_1, x_2, ..., x_n) such that x_1+x_2+x_3+ ...+x_n <= k, then select out the ones that satisfy the desired equality. 

It works well when n is small, like n= 20, but when  n is bigger, it does not work out at all, Matlab is busy for many many hours without giving any result...

Are there any smarter ways to do it?

Thank you!!