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Literature.
[1] J. Komara and P. J. Voda. Metamathematics of Computer Programming. 2001.
[CL] CL-TeX.
[CL] Remark. The module Msyntax in the file msyntax.cl contains the syntax of the system CL.
Chapter. Programs Operating on Trees.
Section. Braun Trees. See also the section Perfectly Balanced Binary Trees in [1].
Braun trees.
We have
Indexing in Braun trees.
Modification of Braun trees. Define the function t [i≔x] such that
New Braun tree. Define the function New (n) such that
Filling a Braun tree. Define the function Fill (n,x) such that
Insertion of a new first label. Define the function Insfirst (t,x) such that
Deletion of the first label. Define the function Delfirst (t) such that
Hint. Note that the application t [0] yields root element for non-empty trees.
Insertion of a new last label. Define the function Inslast (n,t,x) such that
Deletion of the last label. Define the function Dellast (n,t) such that
Quick computation of the size for Braun trees. Find 𝒪 d (t) 2 -algorithm for computing the size of Braun trees. That is, define the function ∣t∣ 1 such that