CPSC 221: Data Structures Dictionary ADT Binary Search Trees
CPSC 221: Data Structures Dictionary ADT
Binary Search Trees
Alan J. Hu (Using Steve Wolfman's Slides)
Learning Goals
After this unit, you should be able to...
? Determine if a given tree is an instance of a particular type
(e.g. binary search tree, heap, etc.)
? Describe and use pre-, in- and post-order traversal
algorithms
? Describe the properties of binary trees, binary search trees,
and more general trees; Implement iterative and recursive algorithms for navigating them in C++
? Compare and contrast ordered versus unordered trees in
terms of complexity and scope of application
? Insert and delete elements from a binary tree
Today's Outline
? Binary Trees ? Dictionary ADT ? Binary Search Trees ? Deletion ? Some troubling questions
Binary Trees
? Binary tree is recursive definition!
? an empty tree (NULL, in our case)
A
? or, a root node with two subtrees
? Properties
B
C
? max # of leaves: ? max # of nodes:
D
EF
? Representation:
G
H
Data
left right pointer pointer
I
J
Binary Trees
? Binary tree is recursive definition!
? an empty tree (NULL, in our case)
A
? or, a root node with two subtrees
? Properties
? max # of leaves: 2h
B
C
? max # of nodes: 2h+1-1
D
EF
? Representation:
G
H
Data
left right pointer pointer
I
J
................
................
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