Re: Combinatorics question

On Apr 6, 8:21�am, Ketakop...@xxxxxxxxx wrote:
I understood the general method, but I don't quite get the Python
algorithm. Let's see, you first create some kind of vector with all
combinations of S elements, that is, size 2^S, filled with binaries.

Just a for..loop, no need to track all of them,
just the solutons.

You then enter the method for those with popcount=4.

This is called inside the for..loop, while the binary numbers
are created, not afterwards.

But I don't get what gmpy is,

It's an extension module for Python. Third party, not
part of the standard distribution. I don't recall the
site, but it's easily found by Google.

It's a math library, specifically, the GNU Multi-Precision
(GMP) library with a Python wrapper. Highly recommended
as it's very fast, supports things Python doesn't have
like Rationals & unlimited precision Floats and includes
a lot of specialized math functions including the
bit manipulations popcount and Hamming Distance.
Also does base two conversion which makes the mapping
easier.

nor the_combos; is it a string, integer...?

That's the list of numbers that gets created that matches
your requested criteria, every one has 4 bits and no
pair in the list have a Hamming Distance of 2 or less
(meaning no pair has more than 2 matching bits).

The rest of the program maps these binary numbers to
the letters 'abcdef', complicated by bit order being
reversed.

If you use MSA's corrected algorithm to generate 4-bit
numbers, I think you still have to do the Hamming
Distance and you may want to note that for mapping
purposes I make sure each base 2 string has the appropriate
leading 0's so that 15 becomes 001111. That's waht the
.zfill(6) does.


.

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