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CSC130 Data Structures
and Algorithm Analysis
Spring 2017, Lecture 4
Instructor: Dr. Yuan Cheng
Session Plan

Review: Theoretical Analysis of Algorithm

Arrays and Lists
Abstract Data Type


Data Types vs. Data Structures

A data type is a well-defined collection of data with a well-defined set of operations
on it.

A data structure is an actual implementation of a particular abstract data type.
Abstract data type (ADT) specifies:

Types of data stored

Operations and their parameters supported on the data

ADT specifies what each operation does, not how it does.
Array

An array stores a sequence of values that are all of the same type.

Contiguous area of memory consisting of equal-size elements indexed by
contiguous integers.
0
1
2
3
4
5
6
7
8
9
What’s Special About Arrays?

Constant-time access

array_addr + elem_size × (i – first_index)
0
1
2
3
4
5
6
7
8
9
Quiz


Given an array whose:
•
Address is 1000,
•
Element size is 8,
•
First index is 0
What is the address of the element at index 6?
1)
40
2)
48
3)
1005
4)
1048
5)
1006
6)
1040
Quiz


Given an array whose:
•
Address is 1000,
•
Element size is 8,
•
First index is 0
What is the address of the element at index 6?
1)
40
2)
48
3)
1005
4)
1048
5)
1006
6)
1040
Multi-Dimensional Arrays
Multi-Dimensional Arrays
(1,1)
(3, 4)
Multi-Dimensional Arrays
(1,1)
(3, 4)

array_addr + elem_size × (( i – firstrow_index) × row_size + (j – firstcol_index))
Time for Common Operations
Add
Beginning
End
Middle
Remove
Access
Time for Common Operations
Add
Remove
Access
Beginning
O(n)
O(n)
O(1)
End
O(1)
O(1)
O(1)
Middle
O(n)
O(n)
O(1)
List

An ordered series of objects

We can do:

Insert an object to a list (at location k)

Remove an object from a list

Access an object from a list (at location k)
Applications for List

To-Do List: insert tasks, remove when done.

Word Processor:


Typing text inserts to list,

Deleting text removes (simple array won’t work)
Shopping: insert needed items, remove when bought
Array Implementation of List

1st hurdle: inserting object anywhere but the end


Shift all entries forward one. O(n)
2nd hurdle: arrays have fixed sizes

Create bigger array when we run out of space, copy old array to big array
Linked List Implementation of List

Store list objects anywhere in memory

A linked list is made up of nodes, each of which contains:

An item

A reference to its next node
APIs for Singly-Linked List

Insert at the beginning

Remove from the beginning

Insert at the end

Remove from the end

Insert/Remove at other positions

Remove a given node

Insert a new node before a given node
Time for Common Operations
Singly-Linked List
No tail
PushFront(Key)
O(1)
PopFront()
O(1)
PushBack(Key)
O(n)
PopBack()
O(n)
Find(Key)
O(n)
IsEmpty()
O(1)
AddBefore(Node, Key)
O(n)
AddAfter(Node, Key)
O(1)
With tail
O(1)
Linked List vs. Array List
Linked List
Array List
No additional penalty on size
Need to estimate size/grow array
Insert/remove at front O(1)
Insert/remove at front O(n)
Get kth costs O(n)
Get kth costs O(1)
Need some extra memory for links
Arrays are compact in memory
Doubly-linked List
Time for Common Operations
Doubly-Linked List
No tail
With tail
PushFront(Key)
O(1)
PopFront()
O(1)
PushBack(Key)
O(n)
O(1)
PopBack()
O(n)
O(1)
Find(Key)
O(n)
IsEmpty()
O(1)
AddBefore(Node, Key)
O(n)
AddAfter(Node, Key)
O(1)
O(1)
List in Java

Collection Interface extends Iterable

A Collection stores a group of objects

We can add and remove from a Collection

Iterator objects let us iterate over objects in a Collection

Built in LinkedList and ArrayList implementations of Collection
List: Summary

Constant time to insert at or remove from the front.

With tail and doubly-linked list, constant time to insert at or remove from the
back.

O(n) time to find arbitrary element.

List elements need not be contiguous.

With doubly-linked list, constant time to insert between nodes or remove a
node.
Next class


Topics covered:

Stacks

Queues
Reading assignment:

Sedgewick: Chapter 1.3

Lafore: Chapter 4

Weiss: Chapter 3