A Gray Code of Ordered Trees

TL;DR

This paper presents a Gray code for ordered trees where each step involves removing and reattaching a leaf, enabling efficient enumeration of all such trees with minimal change.

Contribution

It introduces a novel Gray code for ordered trees that uses a simple remove-and-append leaf operation, ensuring minimal change between consecutive trees.

Findings

Efficient enumeration of ordered trees with minimal leaf modifications

A systematic sequence covering all ordered trees of size n

Potential applications in combinatorial algorithms and data structure enumeration

Abstract

A combinatorial Gray code for a set of combinatorial objects is a sequence of all combinatorial objects in the set so that each object is derived from the preceding object by changing a small part. In this paper we design a Gray code for ordered trees with n vertices such that each ordered tree is derived from the preceding ordered tree by removing a leaf then appending a leaf elsewhere. Thus the change is just remove-and-append a leaf, which is the minimum.