Complete graph traversal algorithm in Prolog

Question

Given a table, I want to explore all possible transition between the elements in the table. ex: for a table with size 3 [0,1,2], the output of the algorithm should be 0->1, 1->0, 0->2, 2->1, 1->2, 2->0. I guess this can be regarded as traversing a complete graph.

I have an implementation of an algorithm doing this in Python:

def test1(n):
   theList=[]
   theList.append(0)

   for x in range(0,n+1):
      for y in range(n,x+1,-1):
         theList.append(y)
         theList.append(x)

      if x!=n:
         theList.append(x+1)

   for x in range(n,0,-1):
      theList.append(x-1)
   return theList

This code always start at element 0, and return a list of all the transitions.

But I need my algorithm i Prolog. So I have done an attempt to port the Python-code to Prolog. My main focus has been on writing readable and maintainable code. But I guess there is great room for improvement wrt. performance of the Prolog code:

:- use_module(library(clpfd)).
:- use_module(library(between)).
:- use_module(library(lists)).

dynappend( List, X ) :-
   (
   foreach( Item, List ),
   param(X,T)
   do
      var( Item ), var(T) ->
      Item = X ,
      T = 1
      ;
      true
   ).   

s3(List,N):-
   LSize is N*(N+1)+1,
   length(List,LSize),

   dynappend( List, 0 ),
   (
      for(X1, 0, N ),
      param( N, List )
      do
         X1T is X1+2,
         ( between:numlist( X1T, N, YList ) -> true ; YList=[] ) , 
         lists:reverse(YList,RYList),

         (
            foreach(Y, RYList ),
            param( X1, List )
            do
               dynappend( List, Y ),
               dynappend( List, X1 )
         ),

         (   X1 #\= N -> X1T2 is X1+1, dynappend( List, X1T2 ) ;  true )
   ),
   N1 is N-1,
   numlist( 0, N1, XList ), 
   lists:reverse(XList,RXList),
   (
   foreach(X2, RXList ),
   param(List)
   do
      dynappend( List, X2 )
   ).

Running the code:

| ?- s3(L, 2).
L = [0,2,0,1,2,1,0] ? 
yes

Any suggestions for improvements of the Prolog code?

Answer 1

Consider describing what a transition is:

list_transition(List, (E1->E2)) :-
        select(E1, List, Rest),
        member(E2, Rest).

Example query:

?- list_transition([0,1,2], T).
T = (0->1) ;
T = (0->2) ;
T = (1->0) ;
T = (1->2) ;
T = (2->0) ;
T = (2->1) ;
false.

And to get all transitions:

?- findall(T, list_transition([0,1,2], T), Transitions).
Transitions = [ (0->1), (0->2), (1->0), (1->2), (2->0), (2->1)].