CS 112b
Spring 2000
Ileana Streinu

• Trees. Examples: genealogical trees; the Unix file system; a few Unix features: root directory, navigation using .. and ~account, symbolic links (shortcuts).
• Mathematical versus Computer Science point of view on trees. Trees as connected graphs without cycles. Rooted trees.
• Binary trees.
• Implementation of binary trees. The binary tree node: data, left and right. Binary tree abstract data type.
• Applications: Binary arithmetic expression trees and Binary search trees.
• Binary arithmetic expresion trees. From a fully parenthesized expression to a binary expression tree to an arithmetic expression in postfix form.
• Definition of binary search trees.
• Application of binary tree traversal for search trees: Sorting using binary search trees.
• Tree traversal algorithms, sketch. Left node Right, Left Right node traversals.
• Start designing the BTree class. Discussion, in class: how to implement the node; what is in the private and in the public part of the class. See the next homework 9.
• Private: a pointer to the root ("root") and a pointer to the current element ("current").
• What member functions are needed; types of functions in the BTree class: constructor (destructor, next time); navigation (GoToRoot, MoveLeft, MoveRight); insertion (InsertRoot, InsertLeft, InsertRight); deletion (DeleteRoot, DeleteLeft, DeleteRight); Miscellenia: IsEmpty, IsEmptyLeft, IsEmptyRight; Printing: Print and PrintCrt.
• To implement Printing you need to traverse the tree, which we will do next time, using recursion. Right now, I will give you the code for the Print functions.
• In class, it was observed that to correctly implement the delete functions, we need to deallocate a whole subtree, and this needs traversal. Leave this as comments in your code, and we will discuss it in class next time.
• It was also observed that insert may overwrite a subtree, which will be then left unused: then it should also be deallocated. To be discussed next time.