Binary Search Trees Data Structures and Algorithms CSE 373 SP 18 - - - PowerPoint PPT Presentation

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Dec 28, 2022 230 likes •344 views

Binary Search Trees Data Structures and Algorithms CSE 373 SP 18 - KASEY CHAMPION 1 Warm Up From CS CSE 143 43: - what is a binary tree - how do you write code to build a tree from scratch? - how do you write code to traverse an

SLIDE 1

Binary Search Trees

Data Structures and Algorithms

CSE 373 SP 18 - KASEY CHAMPION 1

SLIDE 2

Warm Up

From CS CSE 143 43:

what is a “binary tree”
how do you write code to build a tree from scratch?
how do you write code to traverse an existing tree?
how do you write code to change an existing tree?
What is the runtime to traverse a tree and print out every node?

Socrative:

www.socrative.com Room Name: CSE373 Please enter your name as: Last, First

CSE 373 SP 18 - KASEY CHAMPION 2

SLIDE 3

Storing Sorted Items in an Array

get() – O(logn) put() – O(n) remove() – O(n) Can we do better with insertions and removals?

CSE 373 SP 18 - KASEY CHAMPION 3

SLIDE 4

Trees!

A tree is a collection of nodes

Each node has at most 1 parent and 0 or more children

Root node: e: the single node with no parent, “top” of the tree Branc nch h node: e: a node with one or more children Leaf f node: e: a node with no children Edge: : a pointer from one node to another Subtree: ee: a node and all it descendants Heig ight: ht: the number of edges contained in the longest path from root node to some leaf node

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1 2 5 3 6 7 4 8

SLIDE 5

Tree Height

What is the height of the following trees?

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1 2 5 7 7

verallRoot
verallRoot
verallRoot

null Height = 2 Height = 0 Height = -1 or NA

SLIDE 6

Traversals

trave aversal al: An examination of the elements of a tree.

– A pattern used in many tree algorithms and methods

Common orderings for traversals:

– pre-order er: process root node, then its left/right subtrees

– 17 41 29 6 9 81 40

– in in-or

rder

er: process left subtree, then root node, then right

– 29 41 6 17 81 9 40

– post-or

rder

er: process left/right subtrees, then root node

– 29 6 41 81 40 9 17

Traversal Trick: Sailboat method

– Trace a path around the tree. – As you pass a node on the proper side, process it.

pre-order: left side
in-order: bottom
post-order: right side

CSE 373 SP 17 – ZORA FUNG 6

40 81 9 41 17 6 29

verallRoot

SLIDE 7

Binary Search Trees

A bina nary y search ch tree e is a binary tree that contains comparable items such that for every node, all children to the left contain smaller data and all children to the right contain larger data.

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10 9 15 7 12 18 8 17

SLIDE 8

Implement Dictionary

Binary Search Trees allow us to:

quickly find what we’re looking for
add and remove values easily

Dictionary Operations: Runtime in terms of height, “h” get() – O(h) put() – O(h) remove() – O(h)

What do you replace the node with? Largest in left sub tree or smallest in right sub tree

CSE 373 SP 18 - KASEY CHAMPION 8

10 “foo” 7 “bar” 12 “baz” 9 “sho” 5 “fo” 15 “sup” 13 “boo” 8 “poo” 1 “burp”

SLIDE 9

CSE 373 SP 18 - KASEY CHAMPION 9