Ranking left-weight sequences of binary trees in gray-code order

LW-sequences are in common currency for encoding binary trees. Wu et al. [13] proposed an algorithm associated with tree rotations for listing all binary trees in diverse representations including LW-sequences. In particular, such a list of LW-sequences is generated in Gray-code order. Based on this ordering, we propose an efficient algorithm for ranking binary trees with n internal nodes. Our algorithm can be run in O(n2) time and requires O(n) space.