dynamic data structures stacks, queues and binary trees hold dynamic data

Dynamic Data Structures

• Stacks, Queues and Binary Trees hold dynamic data

The Stack

Empty Stack with 7 Spaces

Jack

Stephen

Alex

Janine

Andrew

Ben

Stelhan

James

Stack Pointer

Jack

Stephen

Alex

Janine

Andrew

Ben

Stelhan

JamesStack Pointer

Stack is Pushed

Jack

Stephen

Alex

Janine

Andrew

Ben

Stelhan

James

Stack Pointer

Stack is Pushed

Jack

Stephen

Alex

Janine

Andrew

Ben

Stelhan

James

Stack Pointer

Stack is Pushed

Jack

Stephen

Alex

JanineAndrew

Ben

Stelhan

James

Stack Pointer

Stack is Pushed

Jack

Stephen

Alex

Janine

Andrew

Ben

Stelhan

James

Stack Pointer

Stack is Pushed

Jack

Stephen

Alex

Janine

Andrew

Ben

Stelhan

James

Stack Pointer

Stack is Pushed

Jack

Stephen

Alex

Janine

Andrew

Ben

Stelhan

James

Stack Pointer

Stack is Pushed

Jack

Stephen

Alex

Janine

Andrew

Ben

Stelhan

James

Stack Pointer

Stack is Pushed

ERROR!

Stack Overflow

Jack cannot be added

Jack

Stephen

Alex

Janine

Andrew

Ben

Stelhan

James

Stack Pointer

We would now like to remove Stephen from the stack

Stacks work on a last in first out principal (LIFO)

Jack

Stephen

Alex

Janine

Andrew

Ben

Stelhan

James

Stack Pointer

Stack is Popped

Stephen remains in the stack but the pointer moves down

Jack

Stephen

Alex

Janine

Andrew

Ben

Stelhan

James

Stack Pointer

We now wish to add Jack

Jack

Alex

Janine

Andrew

Ben

Stelhan

James

Stack Pointer

Stack is Pushed

Jack overwrites Stephen and the stack pointer moves back up

Jack

Alex

Janine

Andrew

Ben

Stelhan

James

Stack Pointer

Stack is Popped

Jack

Alex

Janine

Andrew

Ben

Stelhan

James

Stack Pointer

Stack is Popped

Jack

Alex

Janine

Andrew

Ben

Stelhan

James

Stack Pointer

Stack is Popped

Jack

Alex

Janine

Andrew

Ben

Stelhan

James

Stack Pointer

Stack is Popped

Jack

Alex

Janine

Andrew

Ben

Stelhan

James

Stack Pointer

We now wish to add Jim

Jim

Jack

Alex

Janine

Jim

Ben

Stelhan

James

Stack Pointer

Stack is Pushed

What if the stack is empty and you pop it?

ERROR!

Stack Underflow

Uses of a stack

• When a program is being run, and another program interrupts it e.g. to access the hard disk, the details of the first program are put on the stack until the interruption is dealt with. The details are then taken off the stack (popped) in order to continue.

• Or if you are using a loop, the details of each successive loop may be stored on the stack

The Queue

• A good example is a print queue or when you type on a keyboard the letters typed are queued

• There are two pointers in a queue, the first points at the next item to be leave the queue and the other points at the location for the next item to go into the queue

• Unlike a stack, a queue uses FIFO – first in first out

The Queue

Stephen

Next item to take

Next available location

AndrewStelhan

James

Ben

Janine

Alex

Jack

The Queue

Stephen

Next item to take

Next available location

AndrewStelhan

James

Ben

Janine

Alex

Jack

The Queue

Stephen

Next item to take

Next available location

AndrewStelhan

James

Ben

JanineAlex

Jack

The Queue

Next item to take

Next available location

AndrewStelhan

James

Ben

JanineAlex Jack

The Queue

Next item to take

Next available location

Stelhan

James

BenJanineAlex Jack

The Queue

Next item to take

Next available location

James BenJanineAlex Jack

Circular Queue

Next Location to take

Next available location

Steve

Ben

JackJames

Using a stack to reverse the elements of a queue

The Queue

Back of queue

Front of queue

James BenJanineAlex Jack

Stack

The Queue

Back of queue

Front of queue

James

Ben

Janine

Alex

Jack Stack

The Queue

Back of queue

Front of queue

JamesBen Janine AlexJack

Stack

The Binary Tree

ABCDEFGHIJKLMNOPQRSTUVWXYZ

This alphabet is a visual aid to help us assemble our binary tree

Jack

Stephen

Alex

Janine

Andrew

Ben

Stelhan

James

These names will be added to the Binary Tree

ABCDEFGHIJKLMNOPQRSTUVWXYZ

Jack

Stephen

Alex

Janine

Andrew

Ben

Stelhan

James

ABCDEFGHIJKLMNOPQRSTUVWXYZ

Jack

Stephen

Alex

Janine

Andrew

Ben

Stelhan

James

ABCDEFGHIJKLMNOPQRSTUVWXYZ

Jack

Stephen

Alex

Janine

Andrew

Ben

Stelhan

James

Stelhan comes after James in the alphabet so goes right

ABCDEFGHIJKLMNOPQRSTUVWXYZ

Jack

Stephen

Alex

Janine

Andrew

Ben Stelhan

James

Ben is before James in the alphabet so goes left

ABCDEFGHIJKLMNOPQRSTUVWXYZ

Jack

Stephen

Alex

Janine

Andrew

Ben Stelhan

James

Andrew is before James so goes left, he is also before Ben so goes left again

ABCDEFGHIJKLMNOPQRSTUVWXYZ

Jack

Stephen

Alex

JanineAndrew

Ben Stelhan

James

Janine is after James but before Stelhan

ABCDEFGHIJKLMNOPQRSTUVWXYZ

Jack

Stephen

Alex

JanineAndrew

Ben Stelhan

James

Alex comes before James, Ben and Andrew

ABCDEFGHIJKLMNOPQRSTUVWXYZ

Jack

Stephen

Alex

JanineAndrew

Ben Stelhan

James

Stephen comes after James and Stelhan

ABCDEFGHIJKLMNOPQRSTUVWXYZ

Jack Stephen

Alex

JanineAndrew

Ben Stelhan

James

Jack is before James and after Ben

Jack Stephen

Alex

JanineAndrew

Ben Stelhan

JamesRoot Node Parent Child Node

Leaf Node

Left Subtree Right Subtree

Traversing a binary Tree

• Preorder Traversal

• Inorder Traversal

• Postorder Traversal

Preorder Traversal

• Start at root node• Traverse the left hand subtree• Traverse the right hand subtree• D B A C F E G

C

B F

A E G

D

Inorder Traversal

• Traverse the left hand subtree• Visit the root node• Traverse the right hand subtree• A B C D E F G

C

B F

A E G

D

Postorder Traversal

• Traverse the left hand subtree• Traverse the right hand subtree• Return to the root node• A C B E G F D

C

B F

A E G

D

Questions

• What is meant by the term ‘pushing’ and ‘popping’

• The name ‘Robert’ is pushed onto an empty stack, followed by ‘Felicity’, ‘Martin’ and ‘Sam’. What data will be on the stack after the following operations? Pop stack, push ‘Henry’, push ‘George’, pop stack.

• Explain the purpose of the stack pointer

Tasks

• Create a binary tree for the following people:

Jim, Tom, Bob, Bill, Percy, Toby, John, Jack and Terry

• Create your own notes to explain a stack

• Create your own notes to explain a queue