Generation of rooted trees and free trees
Date
1996
Authors
Li, Gang
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Abstract
In 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.