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Intro to

Binary Search

Trees

Updated 1/18/2017

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1. Parent/child relations
2. Each node can have n children
3. Sequential access

Trees, a review

1. Same as n-ary, plus:
2. Each node can have a max of 2 children

N-ary Tree

Binary Tree

1.  Same as binary tree above, plus:
2. Each node is comparable 
3. Each node's Left subtree < parent value and
4. Right subtree > parent value

 

Binary Search Tree

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BST

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Interface

Constructor

Methods

//Constructor

//Methods
  //insert

  //contains

Exercise Time!

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Fast

Value lookup by key

 

Slow

Inserting new values

Deleting values

Performance

Fast (usually)

Value lookup by key

Inserting new values

Deleting values

Sorted Array

BST

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1. Priority Queues
2. Twenty Questions

Binary Search Trees

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Implementing

BST

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Pseudocode

//Constructor

//Methods
  //insert

  //contains

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Exploring

BSTs

in-order, preorder,

post order

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Linked List

Array

Object

Stack/Queue

How do we explore the following data structures?

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In-Order Traversal

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In-Order Traversal

//Code here

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Pre-Order Traversal

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Post-Order Traversal

Exercise Time!

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Deleting Nodes

from BST

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1. Go left until the left is null

2. What do we do when the min or max has a child node?

Delete Min/Max

//Pseudocode!

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3 Cases:

1. When the node is a leaf node

 

2. When the node has 1 child

 

3. When the node as 2 children

Deleting a node from BST

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Delete Node

Case 1: a node with no children

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Delete Node

Case 2: a node with 1 child

Exercise Time!

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Pseudocode

//Code here

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Delete Node

Case 3: a node with 2 children

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Binary Search Tree

Analysis

of Time Complexity

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AVL Tree

Red-Black Tree

Splay Tree

Balanced BSTs