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All Permutations of integers with sum criteria

version (2.69 KB) by Bruno Luong
All Pernutations of integers with sum criteria


Updated 01 Aug 2020

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This function provides all combinations of integer vector that must verify a criteria on the sum.

Supported criteria is
sum(v) == L1
sum(v) <= L1
sum(v) < L1

Cite As

Bruno Luong (2020). All Permutations of integers with sum criteria (, MATLAB Central File Exchange. Retrieved .

Comments and Ratings (10)

Bruno Luong

@ Jang: the number of combination grows fast, like a factorial (i.e., more than a exponential). So it is not surprising that your computer (or any computer in fact) won't handle well large value.

Thanks for your great work!!
It is very useful function program.
I have a question.
I checked allVL1(64,1), allVL1(64,2), allVL1(64,3) and allVL1(64,4) worked.
However, for large number n and L1, for example, allVL1(64,5), it gives errors and sometimes computer stops.
MATLAB cannot support large numbers n and L1, for allVL1(n,L1)?

Daesang Kim


Ben Petschel

Nice program. Users might also be interested in a looped solution using the function "nextwhile" in the NextVector toolbox <pre class="link"></pre>. If the entire matrix of combinations is needed then Bruno's version is faster (because row concatenation is slow) otherwise the looped solution is faster.

Greg von Winckel

Great stuff. I used your work in my code that I just submitted here, but forgot to give credit. I will fix that as soon as I can modify the entry. Thanks for your help!

John D'Errico

A slick solution to this problem, that uses an elegant recursive code for its work.

Good help, error checks, defaults for arguments where they apply. One minor flaw that I'll hope the author fixes. There is no H1 line. An H1 line is the first line of help. It should be a descriptive line that the function lookfor keys on, including all reasonable keywords that you might search on.

Lookfor is useful when you need to find this function in a year. Will you remember the name "allVL1" next year? No, probably not. But lookfor will find this function for you, if you supply an H1 line.


Fix BUG for AllVL1(1,1) that returns incorrect result

+ non-recursive engine

Correct a bug when the number of solutions is inquired

Possibility to get the number of permutations to check feasibility

Add H1 line as suggested by John D'Errico

MATLAB Release Compatibility
Created with R14SP3
Compatible with any release
Platform Compatibility
Windows macOS Linux