On the generation of binary trees in A-order

Abstract

In this paper A-sequences, which are integer sequences characterizing binary trees are introduced. These sequences generate directly and lexicographically all the binary trees in the reverse order of A-order. The generation algorithm with ranking and unranking are provided. Furthermore, the similarities and the differences of A-sequences with the similar previous works are discussed.

Keywords:

• Binary tree
• code
• recursion
• traversal

^*Corresponding author.

^†This author was supported in parts by a grant from IPM.

^*Corresponding author.

^†This author was supported in parts by a grant from IPM.

Notes

^*Corresponding author.

^†This author was supported in parts by a grant from IPM.