Li, Gang2024-08-142024-08-1419961996https://hdl.handle.net/1828/18651In this thesis we present two new recursive algorithms for generating unlabeled rooted trees and unlabeled free trees . We first simplify Beyer-Hedetniemi's [5] iter­ative algorithm for generating rooted trees by using the more natural parent array representation. We then develop a new recursive algorithm which is much simpler, more flexible and easier to analyze. With some simple modifications, our algorithm will generate rooted trees of size n with height lying in a given range and/or with the number of children of each node bounded by a given integer. Our recursive al­gorithm for generating rooted trees is then extended to generate free trees . We also show how to make some simple modifications to generate free trees with some height constraints and/or with a degree restriction. Both algorithms and their modifications run in constant amortized time which is the best possible.82 pagesAvailable to the World Wide WebThesis