september 05 kraemer uga/csci 2720 lists – part i csci 2720 eileen kraemer the university of...
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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
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