September 05 Kraemer UGA/CSCI 2720 Lists – Part I CSCI 2720 Eileen Kraemer The University of Georgia

ADTs  ADT = abstract data type  a mathematical specification of a set of data and the set of operations that can be performed on the data.  the focus is on the definitions of the constructor that returns an abstract handle that represents the data, and the various operations with their arguments.  actual implementation is not defined

The List ADT  List = ordered sequence of elements.  Length of the list: |L| –Read “cardinality of L” –| | = n –Can be any non-negative number  L[i] –ith element of list L,  provided 0 <= i <= |L|

Lists  We’ll define several types of lists, each with their own ADT  Common operations: –Access(L,i) –Length(L) –Concat(L 1,L 2 ) –MakeEmptyList() –IsEmptyList(L)

Access(L,i)  Return L[i] –Return error if i out of range  i < 0  i > |L| - 1

Length(L)  return | L |

Concat(L 1,L 2 )  Return the result of concatenating L 1 with L 2  If L 1 = and L 2 =, then Concat (L 1, L 2 ) returns the combined list

MakeEmptyList()  Returns the empty list <>

IsEmptyList(L)  Returns true if |l| == 0  Otherwise returns false

Special Types of Lists  Stack –Can be modified only by adding and removing items at one end  Queue –Can be modified only by adding items at one end and removing them at the other

Stacks  A Stack Applet example A Stack Applet example A Stack Applet example

Stacks  Push – add new item at the top  Pop – remove item from the top  Top – peek at item on the top, but don’t remove it  LIFO lists – last in, first out  used to implement recursion, reversing of strings, bracket- checking, more

Stack ADT  Top(L)  Pop(L)  Push(x,L)  MakeEmptyStack()  IsEmptyStack(L)

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

Pop(L)  Remove and return last element of L  Return Top(L) and replace L with  Return Top(L) and replace L with  Error results if L is empty

Push(x,L)  Add x at the end of L  Replace L by Concat(L, )

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

IsEmptyStack(L)  Return true if |L| == 0  Otherwise return false

UML for Stack Class

Queue ADT  similar to stack, except that the first item to be inserted is the first one to be removed.  This mechanism is called First-In-First-Out (FIFO).  Placing an item in a queue is called “insertion or enqueue”, which is done at the end of the queue called “rear”.  Removing an item from a queue is called “deletion or dequeue”, which is done at the other end of the queue called “front”.  Some of the applications are : printer queue, keystroke queue, etc.

Queue Example  A queue applet A queue applet A queue applet

Queue ADT  Enqueue(x,L)  Dequeue(L)  Front(L)  MakeEmptyQueue()  IsEmptyQueue(L)

Enqueue(x,L)  Add x at the end of L  Replace L by Concat(L, )  O(1)

Dequeue(L)  Remove and return the first element of L  Replace L by and return L[0]  Error results if L is empty

Front(L)  Return the first element of L  Return L[0]  Error results if L is empty

MakeEmptyQueue()  Return the empty list <>

IsEmptyQueue(L)  Return true if |L| ==0  Otherwise return false

UML for Queue class

List representations  Contiguous memory representations –Elements stored in table of fixed size (greater than max_length) –Adjacent items in list are adjacent in storage  Linked representations –Elements can be scattered in memory –Elements carry pointers to next element in list  Pro: easy to insert/delete  Con: need to follow links to access