September 05September 05KraemerKraemer

UGA/CSCI 2720UGA/CSCI 2720

Lists – Part ILists – Part ICSCI 2720CSCI 2720

Eileen KraemerEileen Kraemer

The University of GeorgiaThe University of Georgia

ADTsADTs

ADT = abstract data typeADT = abstract data type a mathematical specification of a set of a mathematical specification of a set of

data and the set of operations that can be data and the set of operations that can be performed on the data. performed on the data.

the focus is on the definitions of the the focus is on the definitions of the constructor that returns an abstract constructor that returns an abstract handle that represents the data, and the handle that represents the data, and the various operations with their arguments.various operations with their arguments.

actual implementation is not definedactual implementation is not defined

The List ADTThe List ADT

List = ordered sequence of elements List = ordered sequence of elements <x<x00, …, x, …, xn-1n-1>.>.

Length of the list: |L| Length of the list: |L| – Read “cardinality of L”Read “cardinality of L”– | <x| <x00, …, x, …, xn-1n-1>| = n>| = n– Can be any non-negative numberCan be any non-negative number

L[i]L[i]– ith element of list L, ith element of list L,

provided 0 <= i <= |L|provided 0 <= i <= |L|

ListsLists

We’ll define several types of lists, We’ll define several types of lists, each with their own ADTeach with their own ADT

Common operations:Common operations:– Access(L,i)Access(L,i)– Length(L)Length(L)

– Concat(LConcat(L11,L,L22))

– MakeEmptyList()MakeEmptyList()– IsEmptyList(L)IsEmptyList(L)

Access(L,i)Access(L,i)

Return L[i]Return L[i]– Return error if i out of rangeReturn error if i out of range

i < 0i < 0 i > |L| - 1i > |L| - 1

Length(L)Length(L)

return | L |return | L |

Concat(LConcat(L11,L,L22))

Return the result of concatenating LReturn the result of concatenating L11 with Lwith L22

If LIf L11 = <x = <x00, …, x, …, xn-1n-1> and L> and L22 = <y = <y00, …, , …, yym-1m-1>, then Concat (L>, then Concat (L1, 1, LL22) returns the ) returns the combined listcombined list

<x<x00, …, x, …, xn-1,n-1,yy00, …, y, …, ym-1m-1>>

MakeEmptyList()MakeEmptyList()

Returns the empty list <>Returns the empty list <>

IsEmptyList(L)IsEmptyList(L)

Returns Returns truetrue if |l| == 0 if |l| == 0 Otherwise returns Otherwise returns falsefalse

Special Types of ListsSpecial Types of Lists

StackStack– Can be modified only by adding and Can be modified only by adding and

removing items at one endremoving items at one end QueueQueue

– Can be modified only by adding items at Can be modified only by adding items at one end and removing them at the otherone end and removing them at the other

StacksStacks

A Stack Applet exampleA Stack Applet example

StacksStacks

Push – add new item at the topPush – add new item at the top Pop – remove item from the topPop – remove item from the top Top – peek at item on the top, but Top – peek at item on the top, but

don’t remove itdon’t remove it

LIFO lists – last in, first outLIFO lists – last in, first out used to implement recursion, used to implement recursion,

reversing of strings, bracket-reversing of strings, bracket-checking, morechecking, more

Stack ADTStack ADT

Top(L)Top(L) Pop(L)Pop(L) Push(x,L)Push(x,L) MakeEmptyStack()MakeEmptyStack() IsEmptyStack(L)IsEmptyStack(L)

Top(L)Top(L)

Return last element of LReturn last element of L Same as Access(L, |L| -1)Same as Access(L, |L| -1) Error results if L is emptyError results if L is empty

Pop(L)Pop(L)

Remove and return last element of LRemove and return last element of L Return Top(L) and replace L with Return Top(L) and replace L with

<L[0], ….L[|L| -2]><L[0], ….L[|L| -2]> Error results if L is emptyError results if L is empty

Push(x,L)Push(x,L)

Add x at the end of LAdd x at the end of L Replace L by Concat(L,<x>)Replace L by Concat(L,<x>)

MakeEmptyStack()MakeEmptyStack()

Return the empty list <>Return the empty list <> O(1)O(1)

IsEmptyStack(L)IsEmptyStack(L)

Return Return truetrue if |L| == 0 if |L| == 0 Otherwise return Otherwise return falsefalse

UML for Stack ClassUML for Stack Class

Queue ADTQueue ADT similar to stack, except that the first item to be similar to stack, except that the first item to be

inserted is the first one to be removed.inserted is the first one to be removed. This mechanism is called First-In-First-Out (FIFO). This mechanism is called First-In-First-Out (FIFO). Placing an item in a queue is called “insertion or Placing an item in a queue is called “insertion or

enqueue”, which is done at the end of the queue enqueue”, which is done at the end of the queue called “rear”.called “rear”.

Removing an item from a queue is called Removing an item from a queue is called “deletion or dequeue”, which is done at the other “deletion or dequeue”, which is done at the other end of the queue called “front”.end of the queue called “front”.

Some of the applications are : printer queue, Some of the applications are : printer queue, keystroke queue, etc.keystroke queue, etc.

Queue ExampleQueue Example

A queue appletA queue applet

Queue ADTQueue ADT

Enqueue(x,L)Enqueue(x,L) Dequeue(L)Dequeue(L) Front(L)Front(L) MakeEmptyQueue()MakeEmptyQueue() IsEmptyQueue(L)IsEmptyQueue(L)

Enqueue(x,L)Enqueue(x,L)

Add x at the end of LAdd x at the end of L Replace L by Concat(L,<x>)Replace L by Concat(L,<x>) O(1)O(1)

Dequeue(L)Dequeue(L)

Remove and return the first element Remove and return the first element of Lof L

Replace L by <L[1] … L[|L|-1]> and Replace L by <L[1] … L[|L|-1]> and return L[0]return L[0]

Error results if L is emptyError results if L is empty

Front(L)Front(L)

Return the first element of LReturn the first element of L Return L[0]Return L[0] Error results if L is emptyError results if L is empty

MakeEmptyQueue()MakeEmptyQueue()

Return the empty list <>Return the empty list <>

IsEmptyQueue(L)IsEmptyQueue(L)

Return Return truetrue if |L| ==0 if |L| ==0 Otherwise return Otherwise return falsefalse

UML for Queue classUML for Queue class

+Queue()+insert() : void+remove() : long+peekFront() : long+isEmpty() : bool+isFull() : bool+size() : int

-maxSize : int-queueArray [] : long-front : int-rear : int-nItems : int

Queue

QueueApp

Interface1

List representationsList representations

Contiguous memory representationsContiguous memory representations– Elements stored in table of fixed size (greater Elements stored in table of fixed size (greater

than max_length)than max_length)– Adjacent items in list are adjacent in storageAdjacent items in list are adjacent in storage

Linked representationsLinked representations– Elements can be scattered in memoryElements can be scattered in memory– Elements carry pointers to next element in listElements carry pointers to next element in list

Pro: easy to insert/deletePro: easy to insert/delete Con: need to follow links to accessCon: need to follow links to access