[GAP Forum] Iteration Over Lists of Lists

[Wolstenholme, Robert]

Thanks for the reply. I don't think I was clear enough with my initial question though so have given the example below:

###################################################################################
Consider

    lists := []
    lists[1] := [1,2,3]
    lists[2] := [4,5]

I would now like to iterate over the cartesian product of `lists[1]` and `lists[2]` i.e. `[[1,4],[1,5],[2,4],[2,5],[3,4],[3,5]]`.

For an example this small, you could simply store the cartesian product itself in a list and iterate over that. This obviously becomes very inefficient if we have more lists with a larger number of values.


A better way is, if we have `n` lists and `size_rc[i] := Size(list[i])`, we can avoid storing/calculating the Cartesian product with

    base := List([1..n], x -> 1); #We store the iteration step state in base
    while base <> size_rc do

        #Perform whatever list[i][base[i]] calculations here

        #Execute the incrementor
        base[1] := base[1] + 1;
            for j in [2..n] do
                if base[j-1] = size_rc[j-1] + 1 then
                        base[j] := base[j] + 1;
                            base[j-1] := 1;
                fi;
            od;
    od;

then at each loop of the while `base` contains the values we need.

However this is still far slower than the Python implementation I mentioned before. I was wondering if there was a way in GAP to speed up this iteration (maybe by pointing to the memory locations of the lists)?

Thanks,
Rob

________________________________________
From: Alexander Konovalov [alexander.konovalov at gmail.com]
Sent: 16 January 2014 22:01
To: Wolstenholme, Robert
Cc: forum at mail.gap-system.org
Subject: Re: [GAP Forum] Iteration Over Lists of Lists

On 16 Jan 2014, at 20:03, "Wolstenholme, Robert" <robert.wolstenholme08 at imperial.ac.uk> wrote:

> Is there a way in GAP to 'quickly' iterate of lists of lists i.e. like the Python itertools.product() function?
>

Yes, see `21.20 Operations for Lists' from the GAP Reference Manual. You may enter `?Operations for Lists' in GAP or see it online at

        http://www.gap-system.org/Manuals/doc/ref/chap21.html#X7DF510F7848CBBFD

A random example just to expose the syntax and some functions:

gap> l:=List([1..10],i -> [1..i]);
[ [ 1 ], [ 1, 2 ], [ 1 .. 3 ], [ 1 .. 4 ], [ 1 .. 5 ], [ 1 .. 6 ],
  [ 1 .. 7 ], [ 1 .. 8 ], [ 1 .. 9 ], [ 1 .. 10 ] ]
gap> Sum( List( l, x -> Product( List( x, Fibonacci ) ) ) );
124819000


HTH,
Alexander