Abstract
We use the set Tn of binary trees with n leaves to study decision trees of algorithms. The set Tn of binary trees with n leaves can be ordered by the so called “imbalance” order, where two trees are related in the order iff the second is less “balanced” than the first. This order forms a lattice. We show that this lattice is nonmodular and extend the imbalance lattice with an algebraic operation. The operation corresponds to the extension of a binary tree with new binary trees at the leafs, which reflects the effect of recursive calls in an algorithm on the decision tree and we will characterize as an illustration the decision tree of the insertion sort algorithm.We investigate the semivaluations on the binary trees which is related to the running time of the algorithm.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.