Pairwise disjoint intervals

solution.erl

-module(solution).
-export([start/2]).

-spec start([any()],[any()]) -> 'ok'.
start(A, B) ->
  interval(A, B, []).

-spec interval([any()],[any()],[[any(),...]]) -> 'ok'.
interval([], [], Intv) ->
  [[_|_]|Tail] = Intv,
  pairwise(Intv, Tail, [], []);
interval([HeadA|TailA], [HeadB|TailB], Intv) ->
  interval(TailA, TailB, Intv ++ [[HeadA,HeadB]]).

-spec pairwise([[any(),...],...],[[any(),...]],[[any(),...]],[[any(),...]]) -> 'ok'.
pairwise([[Inf|Sup]|Tail], [], Union, Overlap) ->
  case Tail of
    [] ->
      io:write(length(Union));
    _ ->
      [[_|_]|SubTail] = Tail,
      [Elem|_] = Sup,
      case lists:member([Inf,Elem], Overlap) of
        true ->
          pairwise(Tail, SubTail, Union , Overlap);
        false ->
          pairwise(Tail, SubTail, Union ++ [[Inf, Elem]], Overlap)
      end
  end;
pairwise([[Inf|Sup]|Tail], [[H|T]|NextTail], Union, Overlap) when Inf >= H , Sup >= T ->
  [Elem|_] = T,
  case Inf =< Elem of
    true ->
      [NewSup|_] = Sup,
      pairwise([[Inf|Sup]|Tail], NextTail, Union ++ [[H, NewSup]], Overlap ++ [[Inf,NewSup],[H,Elem]]);
    false ->
      pairwise([[Inf|Sup]|Tail], NextTail, Union, Overlap)
  end;
pairwise([[Inf|Sup]|Tail], [[H|T]|NextTail], Union, Overlap) when Sup =< T , Inf =< H ->
  [Elem|_] = Sup,
  case Elem >= H of
    true ->
      [NewT|_] = T,
      pairwise([[Inf|Sup]|Tail], NextTail, Union ++ [[Inf, NewT]], Overlap ++ [[Inf,Elem],[H,NewT]]);
    false ->
      pairwise([[Inf|Sup]|Tail], NextTail, Union, Overlap)
  end.

% A = [1, 12, 42, 70, 36, -4, 43, 15]
% B = [5, 15, 44, 72, 36, 2, 69, 24 ]