P358: Enumeration of all binary trees with $n$ vertices in the lexicographic ordering

P358: Enumeration of all binary trees with $n$ vertices in the lexicographic ordering
Input:
An integer $n$.
Output:
All binary trees with $n$ vertices in the lexicographic ordering
Complexity:
$O(1)$ time per solution on average.
Comment:
Reference:
[Zerling1985] (Bibtex)