How to generate all n-choose-k combinations?

[Andrew Gill]

I want an array[1..n_choose_k,1..k] of int: combos but don't know how to (a) calculate n_choose_k=n!/((k!(n-k)!) and (b) enumerate all of the combos of k integers from the first n positive integers :-(. 

I looked through the MiniZinc Handbook but couldn't find either of these, but surely this has been done before?!

Any pointers gratefully accepted.

Andrew

[Boris Okner]

If this is for static data, I would generate .dzn file using your favorite host language, even if it was possible to generate inline data with MiniZinc.

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[Andrew Gill]

Thanks Boris. I am getting the sense that 'hard-coding' data in MiniZinc is preferred (presumably for compile/compute times?), although its not as pretty!

[d...@irvine.com]

Hi Andrew,
For factorial, see
https://gist.github.com/jarble/f8a9d0f99c106837401bbb9b22b1ecb2
which has:

function int:factorial(int:t) =
if t = 0 then 1 else t * factorial(t-1) endif;

For enumeration, I think you want alldifferent and strictly_increasing,
both of which are global predicates.

-- Dan

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