Generation of Valid Labeled Binary Trees

摘要

Generating binary trees is a well-known problem. In this paper, we add some constraints to leaves of these trees. such trees are used in the morphing of polygons, where a polygon P is represented by a binary tree T and each angle of P is a weight on a leaf of T. In the following, we give two algorithms to generate all binary trees, without repetitions, having the same weight distribution to their leaves and representing all parallel polygons to P.