(* Collect the nodes at a given level in a list
    A node of a binary tree is at level N if the path from the root to the node has length N-1. The root node is at level 1. Write a predicate atlevel/3 to collect all nodes at a given level in a list.

    % atlevel(T,L,S) :- S is the list of nodes of the binary tree T at level L

    Using atlevel/3 it is easy to construct a predicate levelorder/2 which creates the level-order sequence of the nodes. However, there are more efficient ways to do that. *)

type bin_tree = 
		Leaf of string
	|	Node of string * bin_tree * bin_tree
;;

let rec collect_nodes_at_level t l =
        if l<1 then [] else

        match t with
                Leaf(s) -> []
        |       Node(s,tl,tr) ->
                        List.flatten [
                                if l=1 then [s] else [];
                                collect_nodes_at_level tl (l-1);
                                collect_nodes_at_level tr (l-1) ]
;;