Question

Any ideas how to retrieve the maximally repeated element in a list.

i.e. something like below,

?- maxRepeated([1,2,7,3,6,1,2,2,3],M).
M = 2.

Answer 1

This solution sorts the list, granting elements to appear sequentially — there’s no need to maintain all elements, once they’re not repeating later.

Your prolog interpreter must have the function msort(), which sorts a list maintaining duplicated entries.

maxRepeated([], []).
maxRepeated(L, E) :-
    msort(L, [H|T]),
    maxRepeated(T, H, H, 1, 0, E).

maxRepeated([], H, _, C1, C2, H) :- C1 >= C2.
maxRepeated([], _, X, C1, C2, X) :- C1 < C2.

maxRepeated([H|T], H, LastF, C1, C2, E) :-
    maxRepeated(T, H, LastF, C1 + 1, C2, E).

maxRepeated([X|T], H, LastF, C1, C2, E) :-
    (
        C1 > C2
        ->  maxRepeated(T, X, H, 1, C1, E)
        ;   maxRepeated(T, X, LastF, 1, C2, E)
    ).

The complexity is given by the sort used, usually O(n log n), once, after the sort, the list is traversed only once, aggregating the elements and keeping track of the most frequent one.

Regards!