Use iterators to construct a program that outputs (in some order) all structurally distinct binary trees of n nodes. Two trees are considered structurally distinct if they have different numbers of nodes or if their left or right subtrees are structurally distinct. There are, for example, five structurally distinct trees of three nodes:

These are most easily output in “dotted parenthesized form”:
(((.).).)
((.(.)).)
((.).(.))
(.((.).))
(.(.(.)))