On 14/09/2015 13:50, Oscar Benjamin wrote:
On 10 September 2015 at 08:45, Francesco Loffredo via Tutor
<tutor@python.org> wrote:
I wrote a small routine (below) to check when and if my code and the formula
do match. It easily shows that
they only match for len(pool) == (2 ** N) - 1, with N greater or equal to 2.
That's interesting. I'm not sure exactly why that would happen.
My problem remains: WHY don't they match for every length?
Your algorithm is not generally guaranteed to find a full solution.
How did you build your 12-triples set?
I took it from this diagram:
https://upload.wikimedia.org/wikipedia/commons/e/eb/Hesse_configuration.svg
What's wrong with my algorithm? And, most of all (and on topic, too): how can
you build a Python program that builds your triples list?
Perhaps if we compare this problem to a different problem then we can
see how your algorithm may not be optimal. Imagine solving a sudoku
puzzle.
Your algorithm loops through all triples and accepts any triple if it
doesn't immediately conflict with any of the triples already accepted.
If you were solving a sudoku puzzle then an analogous algorithm would
take each empty square and fill it with any number that doesn't
contradict any of the currently filled squares. If you try this on a
real puzzle then you will reach a dead end and you won't fill the
grid. The problem is that some of the squares you filled in could have
had a number of possible values and you've just chosen them
arbitrarily (and incorrectly).
...
Also there will be many possible solutions and you only really need to
find one. Up to isomorphism there is 1 solution for N=9 but that means
there will be 9! isomorphic solutions (the number of ways of
relabelling the numbers 1 through 9). This means that you may not have
to go far in the search before coming across a solution.
--
Oscar
Thank you for your explanation, Oscar! I'll study a better algorithm and
I'll post it here. While I hope Marcus Luetolf ( the OP) will find it
useful, I will certainly get some learning from this exercise.
Francesco
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