[seqfan] Re: A general programming question involving recursion

[Felix Fröhlich]

A small clarification to the above:

If I have a vector like [2, 3, 5, 7], then I need all permutations like [2,
3, 7, 5], [2, 5, 3, 7], etc. I have working code for that part. Then I need
all vectors like [6, 5, 7], [2, 15, 7], [2, 3, 35] and [10, 3, 7], [2, 15,
7], [2, 5, 21] and again all permutations of each of those vectors, i.e.,
[6, 5, 7], [5, 6, 7], [6, 7, 5], [5, 7, 6], [7, 5, 6], [7, 6, 5] and again
all vectors from multiplying any two elements of those vectors: [30, 7],
[6, 35], [42, 5], [35, 6], etc and all permutations of those vectors until
only single element vectors remain.

Felix

2018-04-25 23:43 GMT+02:00 Felix Fröhlich <felix.froe at gmail.com>:

> Dear SeqFans,
>
> I am trying to write a somewhat complex PARI program for a sequence I am
> preparing. While preparing that program, I have run into a general
> algorithmic problem. Without going into detail about why I need to perform
> those operations, let me describe what I am trying to do:
>
> I take a number n and compute the list of prime factors with repetition.
> Now, from that list of prime factors I want to compute recursively all
> possible permutations of all sets of numbers that can be obtained by
> multiplying two prime factors in the list. In this way I want to obtain ALL
> possible products from multplying any two prime factors from the original
> set and from all permutations of that set and, recursively, all products
> from all permutations resulting from multiplying two factors until the
> products result in single numbers.
>
> Normally, I would do this using two nested loops, one for going through
> the permutations and one for going through the multiply over each vector.
> But then, I also need to go through the permutations of the resulting
> vector with multiplied elements and through the vectors resulting from
> multiplying two neighboring elements of those vectors permutations, ...,
> and so on.
>
> How is this best done in order to obtain all different permutations from
> all vectors from multiplying two neighboring vector elements, starting with
> a vector of any length down to a single element?
>
> Ideas anyone?
>
> Best regards
>
> Felix
>