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Sorted List CS3240

Sorted List CS3240. 2 Goals Describe the Abstract Data Type Sorted List from three perspectives Implement the following Sorted List operations using an

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Page 1: Sorted List CS3240. 2 Goals Describe the Abstract Data Type Sorted List from three perspectives Implement the following Sorted List operations using an

Sorted List

CS3240

Page 2: Sorted List CS3240. 2 Goals Describe the Abstract Data Type Sorted List from three perspectives Implement the following Sorted List operations using an

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Goals

• Describe the Abstract Data Type Sorted List from three perspectives

• Implement the following Sorted List operations using an array-based implementation

– Create and destroy a list

– Determine whether the list is full

– Insert an element

– Retrieve an element

– Delete an element

Page 3: Sorted List CS3240. 2 Goals Describe the Abstract Data Type Sorted List from three perspectives Implement the following Sorted List operations using an

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Goals

• Implement the list operations outlined above using a linked implementation

• Implement the binary search algorithm

• Compare the two implementations of the ADT Sorted List in terms of Big-O approximations

• Compare the implementations of the Unsorted List ADT and the Sorted List ADT in terms of Big-O Analysis

• Distinguish between bounded and unbounded ADTs at the logical and implementation levels

• Identify and apply the phases of the object-oriented methodology

Page 4: Sorted List CS3240. 2 Goals Describe the Abstract Data Type Sorted List from three perspectives Implement the following Sorted List operations using an

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ADT Sorted List

Remember the difference between an unsorted list and a sorted list?

Remember the definition of a key?

If the list is a sorted list

of names, what would be the key?

of bank balances, what would be the key?

of grades, what would be the key?

Page 5: Sorted List CS3240. 2 Goals Describe the Abstract Data Type Sorted List from three perspectives Implement the following Sorted List operations using an

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ADT Unsorted List Operations

Transformers – MakeEmpty – InsertItem – DeleteItem

Observers – IsFull– GetLength

– RetrieveItem

Iterators – ResetList – GetNextItem

change state

observe state

process all

Page 6: Sorted List CS3240. 2 Goals Describe the Abstract Data Type Sorted List from three perspectives Implement the following Sorted List operations using an

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Which member function specifications and implementations must change to ensure that any instance of the Sorted List ADT remains sorted at all times?

– InsertItem

– DeleteItem

ADT Sorted List

What about the othertransformer MakeEmtpy?

Page 7: Sorted List CS3240. 2 Goals Describe the Abstract Data Type Sorted List from three perspectives Implement the following Sorted List operations using an

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Array Implementation

What do you have to do to insert Clair into the following list?

Anne

Betty

Mary

Susan

Page 8: Sorted List CS3240. 2 Goals Describe the Abstract Data Type Sorted List from three perspectives Implement the following Sorted List operations using an

Array Implementation

• Find proper location for the new element in the sorted list

• Create space for the new element by moving down all the list elements that will follow it

• Put the new element in the list

• Increment length

Page 9: Sorted List CS3240. 2 Goals Describe the Abstract Data Type Sorted List from three perspectives Implement the following Sorted List operations using an

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Array ImplementationInsertItem

Initialize location to position of first item

Set moreToSearch to (have not examined Info(last))

while moreToSearch

switch (item.ComparedTo(Info(location)))

case LESS : Set moreToSearch to false

case EQUAL : // Cannot happen

case GREATER :

Set location to Next(location)

Set moreToSearch to (have not examined Info(last))

for index going from length DOWNTO location + 1

Set Info(index ) to Info(index-1)

Set Info(location) to item

Increment length

Why can't EQUAL happen?

Page 10: Sorted List CS3240. 2 Goals Describe the Abstract Data Type Sorted List from three perspectives Implement the following Sorted List operations using an

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Array Implementation

What were the conversions from notation to array-based code?

info(last)

info(location)

Next(location)

Page 11: Sorted List CS3240. 2 Goals Describe the Abstract Data Type Sorted List from three perspectives Implement the following Sorted List operations using an

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Array ImplementationDeleteItem

Initialize location to position of first itemSet found to falsewhile NOT foundswitch (item.ComparedTo(Info(location)))

case GREATER : Set location to Next(location)case LESS : // Cannot happencase EQUAL : Set found to true

for index going from location +1 TO length -1Set Info(index - 1) to Info(index)

Decrement length

Why can't LESS happen?

Page 12: Sorted List CS3240. 2 Goals Describe the Abstract Data Type Sorted List from three perspectives Implement the following Sorted List operations using an

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Array Implementation

Can we improve searching in a sorted list?With the Unsorted List ADT we examined each list element beginning with info[ 0 ], until we found a matching key or we examined all the elements

Page 13: Sorted List CS3240. 2 Goals Describe the Abstract Data Type Sorted List from three perspectives Implement the following Sorted List operations using an

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Binary Search Algorithm

Examine the element in the middle of the array– Match item?

• Stop searching

– Middle element too small?• Search second half of array

– Middle element too large?• Search first half of array Is it the sought item?

Repeat the process in half that should be examined next

Stop when item is found or when there is nowhere else to look

Page 14: Sorted List CS3240. 2 Goals Describe the Abstract Data Type Sorted List from three perspectives Implement the following Sorted List operations using an

void SortedType::RetrieveItem ( ItemType& item, bool& found ) // Pre: Key member of item is initialized.// Post: If found, item’s key matches an element’s key and a copy // of element has been stored in item; otherwise, item is // unchanged.

{ int midPoint;int first = 0;

int last = length - 1 bool moreToSearch = ( first <= last );

found = false;while ( moreToSearch && !found ){ midPoint = ( first + last ) / 2; switch ( item.ComparedTo(info[midPoint]) )

{ case LESS : . . . // LOOK IN FIRST HALF NEXT case GREATER : . . . // LOOK IN SECOND HALF NEXT case EQUAL : . . . // ITEM HAS BEEN FOUND

} }}

Binary Search Algorithm

Page 15: Sorted List CS3240. 2 Goals Describe the Abstract Data Type Sorted List from three perspectives Implement the following Sorted List operations using an

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Trace of Binary Search

info[0] [1] [2] [3] [4] [5] [6] [7] [8] [9]

15 26 38 57 62 78 84 91 108 119

item = 45

first midPoint last

info[0] [1] [2] [3] [4] [5] [6] [7] [8] [9]

15 26 38 57 62 78 84 91 108 119

first midPoint last

LESS last = midPoint - 1

GREATER first = midPoint + 1

Page 16: Sorted List CS3240. 2 Goals Describe the Abstract Data Type Sorted List from three perspectives Implement the following Sorted List operations using an

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Trace continued

info[0] [1] [2] [3] [4] [5] [6] [7] [8] [9]

15 26 38 57 62 78 84 91 108 119

item = 45

first, midPoint, last

info[0] [1] [2] [3] [4] [5] [6] [7] [8] [9]

15 26 38 57 62 78 84 91 108 119

first, last midPoint

LESS last = midPoint - 1

GREATER first = midPoint + 1

Page 17: Sorted List CS3240. 2 Goals Describe the Abstract Data Type Sorted List from three perspectives Implement the following Sorted List operations using an

Array-Based Big-O Comparison

OPERATION UnsortedList SortedList

RetrieveItem O(N) O(N) linear search O(log2N) binary search

InsertItemFind O(1) O(N) searchPut O(1) O(N) moving downCombined O(1) O(N)

DeleteItemFind O(N) O(N) searchPut O(1) swap O(N) moving upCombined O(N) O(N)

Page 18: Sorted List CS3240. 2 Goals Describe the Abstract Data Type Sorted List from three perspectives Implement the following Sorted List operations using an

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Dynamically Allocated Arrays{public:SortedType(int max); // max is maximum list sizeSortedType(); // Default size is 500// Rest of the prototypes go here

private: int length; int maxList; // Maximum number of list items

ItemType* info; // Pointer to dynamically // allocated memory int currentPos;

};

What does this structure look like?

Page 19: Sorted List CS3240. 2 Goals Describe the Abstract Data Type Sorted List from three perspectives Implement the following Sorted List operations using an

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Dynamically Allocated Arrays

Howdoyou

accessthe

arrayelements

?

Page 20: Sorted List CS3240. 2 Goals Describe the Abstract Data Type Sorted List from three perspectives Implement the following Sorted List operations using an

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Linked Implementation

Does replacing algorithm terms with linked code work for the linked implementation of searching?

Page 21: Sorted List CS3240. 2 Goals Describe the Abstract Data Type Sorted List from three perspectives Implement the following Sorted List operations using an

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Linked Implementation

What about passing spot where item would be if there?

Page 22: Sorted List CS3240. 2 Goals Describe the Abstract Data Type Sorted List from three perspectives Implement the following Sorted List operations using an

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Linked Implementation

Is Inserting as easy? Let's see

Set location to listDataSet moreToSearch to (location != NULL)while moreToSearch

switch (item.ComparedTo(location->info)) case GREATER :

Set location to location->nextSet moreToSearch to (location != NULL)

case LESS : Set moreToSearch to false

Seethe

problem?

Page 23: Sorted List CS3240. 2 Goals Describe the Abstract Data Type Sorted List from three perspectives Implement the following Sorted List operations using an

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Linked Implementation

We need a trailing pointer

Page 24: Sorted List CS3240. 2 Goals Describe the Abstract Data Type Sorted List from three perspectives Implement the following Sorted List operations using an

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Inserting ‘S’ into a Sorted List

‘C’ ‘L’ ‘X’

Private data:

length 3

listData

currentPos ?

predLoc location

moreToSearch

Page 25: Sorted List CS3240. 2 Goals Describe the Abstract Data Type Sorted List from three perspectives Implement the following Sorted List operations using an

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Finding proper position for ‘S’

‘C’ ‘L’ ‘X’

Private data:

length 3

listData

currentPos ?

predLoc location

NULL

moreToSearch true

Page 26: Sorted List CS3240. 2 Goals Describe the Abstract Data Type Sorted List from three perspectives Implement the following Sorted List operations using an

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Finding proper position for ‘S’

‘C’ ‘L’ ‘X’

Private data:

length 3

listData

currentPos ?

predLoc location

moreToSearch true

Page 27: Sorted List CS3240. 2 Goals Describe the Abstract Data Type Sorted List from three perspectives Implement the following Sorted List operations using an

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Finding Proper Position for ‘S’

‘C’ ‘L’ ‘X’

Private data:

length 3

listData

currentPos ?

predLoc location

moreToSearch false

Page 28: Sorted List CS3240. 2 Goals Describe the Abstract Data Type Sorted List from three perspectives Implement the following Sorted List operations using an

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Inserting ‘S’ into Proper Position

‘C’ ‘L’ ‘X’

Private data:

length 4

listData

currentPos

predLoc location

moreToSearch false

‘S’

Page 29: Sorted List CS3240. 2 Goals Describe the Abstract Data Type Sorted List from three perspectives Implement the following Sorted List operations using an

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Linked Implementation

Does DeleteItem have to be changed?

Page 30: Sorted List CS3240. 2 Goals Describe the Abstract Data Type Sorted List from three perspectives Implement the following Sorted List operations using an

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Big-O Comparison

Which array-based operations are O(1)?

Which linked operations are O(1)?

Which array-based operations are O(N)?

Which linked operations are O(N)?

Can you say which implementation is better?

Which sorted operations differ in Big-O from unsorted operations?

Page 31: Sorted List CS3240. 2 Goals Describe the Abstract Data Type Sorted List from three perspectives Implement the following Sorted List operations using an

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Bounded and Unbounded ADTs

Bounded ADT

An ADT for which there is a logical limit on the number of items in the structure

Unbounded ADT

An ADT for which there is no logical limit on the number of items in the structure

How do you relate the logical limit to the physical limit?

Page 32: Sorted List CS3240. 2 Goals Describe the Abstract Data Type Sorted List from three perspectives Implement the following Sorted List operations using an

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Object-Oriented Design Methodology

Object-oriented design decomposes a problem into classes

Four stages to the decomposition process

– Brainstorming

– Filtering

– Scenarios

– Responsibility algorithms

Page 33: Sorted List CS3240. 2 Goals Describe the Abstract Data Type Sorted List from three perspectives Implement the following Sorted List operations using an

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Object-Oriented Design Methodology

BrainstormingA group problem-solving technique that involves the spontaneous contribution of ideas from all members of the group

– All ideas are potential good ideas– Think fast and furiously first, and ponder later– A little humor can be a powerful force

Brainstorming is designed to produce a list of candidate classes

Page 34: Sorted List CS3240. 2 Goals Describe the Abstract Data Type Sorted List from three perspectives Implement the following Sorted List operations using an

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Object-Oriented Design Methodology

Filtering

Determine which are the core classes in the problem solution

– There may be two classes in the list that have many common attributes and behaviors

– There may be classes that really don’t belong in the problem solution

Page 35: Sorted List CS3240. 2 Goals Describe the Abstract Data Type Sorted List from three perspectives Implement the following Sorted List operations using an

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Object-Oriented Design Methodology

ScenariosSequences of steps that describe an interaction between a client and an application or program

– Simulate class interactions– Ask “What if?” questions– Assign responsibilities to each class

– There are two types of responsibilities• What a class must know about itself (knowledge) • What a class must be able to do (behavior)

Use caseA collection of scenarios related to a common goal

Page 36: Sorted List CS3240. 2 Goals Describe the Abstract Data Type Sorted List from three perspectives Implement the following Sorted List operations using an

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Object-Oriented Design Methodology

Roleplaying

Page 37: Sorted List CS3240. 2 Goals Describe the Abstract Data Type Sorted List from three perspectives Implement the following Sorted List operations using an

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Object-Oriented Design Methodology

Responsibility AlgorithmsThe algorithms must be written for the responsibilities

– Knowledge responsibilities usually just return the contents of one of an object’s variables

– Action responsibilities are a little more complicated, often involving calculations

Responsibilities algorithms are often decomposed using top-down design

Page 38: Sorted List CS3240. 2 Goals Describe the Abstract Data Type Sorted List from three perspectives Implement the following Sorted List operations using an

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Relationships Between Classes

Containment– “part-of” – An address class may be part of the definition of a

student class

Inheritance– Classes can inherit data and behavior from other

classes– “is-a”

Page 39: Sorted List CS3240. 2 Goals Describe the Abstract Data Type Sorted List from three perspectives Implement the following Sorted List operations using an

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Computer Example

Let’s work through this problem-solving process by creating an address listBrainstorming and filtering

– Circling the nouns and underlining the verbs is a good way to begin

Page 40: Sorted List CS3240. 2 Goals Describe the Abstract Data Type Sorted List from three perspectives Implement the following Sorted List operations using an

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Computer Example

First pass at a list of classeslistnametelephone numberemail addresslistorder nameslistscrapspapercards

Filtered List

list, name, telephone number, email address

Page 41: Sorted List CS3240. 2 Goals Describe the Abstract Data Type Sorted List from three perspectives Implement the following Sorted List operations using an

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CRC Cards

Can you think of any other useful responsibilities?

Page 42: Sorted List CS3240. 2 Goals Describe the Abstract Data Type Sorted List from three perspectives Implement the following Sorted List operations using an

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CRC Cards

Can you think of any other useful responsibilities?

Page 43: Sorted List CS3240. 2 Goals Describe the Abstract Data Type Sorted List from three perspectives Implement the following Sorted List operations using an

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CRC Cards

How is this class different from Name and Person?

Page 44: Sorted List CS3240. 2 Goals Describe the Abstract Data Type Sorted List from three perspectives Implement the following Sorted List operations using an

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Responsibility Algorithms

Person Class

Initialize

name.initialize()Write "Enter phone number; press return."Get telephone numberWrite "Enter email address; press return."Get email address

Print

name.print() Write "Telephone number: " + telephoneNumberWrite "Email address: " + emailAddress

Tells name to initialize itself

Tells name to print itself

Page 45: Sorted List CS3240. 2 Goals Describe the Abstract Data Type Sorted List from three perspectives Implement the following Sorted List operations using an

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Responsibility Algorithms

Name Class

Initialize

"Enter the first name; press return."Read firstName"Enter the last name; press return."Read lastName

Print

Print "First name: " + firstNamePrint "Last name: " + lastName