DATA STRUCTURES AND ALGORITHMS Lecture Notes 3 Prepared by İnanç TAHRALI

DATA STRUCTURES

ANDALGORITHMS

Lecture Notes 3

Prepared by İnanç TAHRALI

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ROAD MAP Abstract Data Types (ADT)

The List ADT Implementation of Lists

Array implementation of lists Linked list implementation of lists Cursor implementation of lists

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Abstract Data Types (ADT) Definition :

Is a set of operationMathematical abstractionNo implementation detail

Example :Lists, sets, graphs, stacks are examples of ADT along with their operations

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Why ADT ? Modularity

divide program into small functions easy to debug and maintain easy to modify group work

Reuse do some operations only once

Easy to change of implementation transparent to the program

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THE LIST ADT Ordered sequence of data items called

elements A1, A2, A3, …,AN is a list of size N size of an empty list is 0 Ai+1 succeeds Ai Ai-1 preceeds Ai position of Ai is i first element is A1 called “head” last element is AN called “tail”

Operations ?

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THE LIST ADT Operations

PrintList Find FindKth Insert Delete Next Previous MakeEmpty

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THE LIST ADT

Example:the elements of a list are34, 12, 52, 16, 12

Find (52) 3 Insert (20, 3) 34, 12, 52, 20, 16, 12 Delete (52) 34, 12, 20, 16, 12 FindKth (3) 20

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Implementation of Lists

Many Implementations Array Linked List Cursor (linked list using arrays)

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Array Implementation of List ADT Need to define a size for array

High overestimate (waste of space)

Operations Running TimesPrintList O(N)Find

Insert O(N) (on avarage half needs to be moved)Delete

FindKthNext O(1)Previous

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Array Implementation of List ADT

Disadvantages : insertion and deletion is very slow

need to move elements of the list redundant memory space

it is difficult to estimate the size of array

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Array implementation of lists Linked list implementation of lists

Cursor implementation of lists

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Linked List Implementation of Lists

Series of nodes not adjacent in memory contain the element and a pointer to a node containing

its succesor Avoids the linear cost of insertion and deletion !

A1 A4 A2 A3

A1 500 A4 0 A2 400 A3 666

350 500 400 666

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Insertion into a linked list

A2 400

X

A1 500 A4 0 A3 666

350 500 400 666

A2 530 X 400 A1 500 A4 0 A3 666

350 500 400 666530

530

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Deletion from a linked list

A2 400 A1 500 A4 0 A3 666

350 500 400 666

A2 666 A1 500 A4 0

350 500 666

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Need to know where the first node is the rest of the nodes can be accessed

No need to move the list for insertion and deletion operations

No memory waste

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Linked List ArrayPrintList O(N) (traverse the list)

O(N)

Find

FindKth (L,i) O(i) O(1)

Delete O(1) O(N)

Insert

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Programming Details There are 3 special cases for linked lists

Insert an element at the front of the list there is no really obvious way

Delete an element from the front of the list changes the start of the list

Delete an element in general requires to keep track of the node before the deleted

one

How can we solve these three problems ?

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Programming Details

Keep a header node in position 0

A1 A4 A2 A3header

Write a FindPrevious routine returns the predecessor of the cell

To delete the first element FindPrevious routine returns the position

of headerUse of header node is controversial !

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Type decleration for link list nodetemplate <class Object>class List; // Incomplete declaration.

template <class Object>class ListItr; // Incomplete declaration.

template <class Object>class ListNode {

ListNode( const Object & theElement = Object( ), ListNode*n=NULL) :

element(theElement),next(n) {}

Object element; ListNode *next;

friend class List<Object>; friend class ListItr<Object>;};

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Iterator class for linked liststemplate <class Object>class ListItr { public: ListItr( ) : current( NULL ) { } bool isPastEnd( ) const { return current == NULL; }

void advance( ) { if( !isPastEnd( ) ) current = current->next; }

const Object & retrieve( ) const

{ if( isPastEnd( ) ) throw BadIterator( );

return current->element; }

private: ListNode<Object> *current; // Current position ListItr(ListNode<Object> *theNode):current( theNode ) { } friend class List<Object>; // Grant access to constructor};

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List class interfacetemplate <class Object>class List { public: List( ); List( const List & rhs ); ~List( );

bool isEmpty( ) const; void makeEmpty( ); ListItr<Object> zeroth( ) const; ListItr<Object> first( ) const; void insert( const Object & x, const ListItr<Object> & p ); ListItr<Object> find( const Object & x ) const; ListItr<Object> findPrevious( const Object & x ) const; void remove( const Object & x ); const List & operator=( const List & rhs );

private: ListNode<Object> *header;};

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Function to print a listtemplate <class Object>void printList( const List<Object> &the List){

if (theList.isEmpty())cout<< “Empty list” << endl;

else{

ListItr<Object> itr = theList.first();for (; !itr.isPastEnd(); itr.advance())

cout << itr.retrieve() <<“ ”;}cout << endl;

}

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Some list one-liners/* Construct the list */ template <class Object> List<Object>::List( ) {

header = new ListNode<Object>; }

/* Test if the list is logically empty */ template <class Object> bool List<Object>::isEmpty( ) const {

return header->next == NULL; }

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Some list one liners/* Return an iterator representing the header node template <class Object> ListItr<Object> List<Object>::zeroth( ) const { return ListItr<Object>( header ); }

/* Return an iterator representing the first node in the list. This operation is valid for empty lists. */

template <class Object> ListItr<Object> List<Object>::first( ) const { return ListItr<Object>( header->next );

}

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Find routine/* Return iterator corresponding to the first

node containing an item x. Iterator isPastEnd if item is not found. */

template <class Object> ListItr<Object> List<Object>::find( const

Object & x ) const {

ListNode<Object> *itr = header->next;while( itr != NULL && itr->element != x )

itr = itr->next;return ListItr<Object>( itr );

}

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Deletion routine for linked lists/* Remove the first occurrence of an item x. */ template <class Object> void List<Object>::remove( const Object & x ){

ListItr<Object> p = findPrevious( x );

if( p.current->next != NULL ) { ListNode<Object> *oldNode = p.current->next; p.current->next = p.current->next->next; delete oldNode; }}

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findPrevious-the find routine for use with remove

/*Return iterator prior to the first node containing an item x.

template <class Object>ListItr<Object> List<Object>::findPrevious( const Object &

x ) const{

ListNode<Object> *itr = header;

while( itr->next != NULL && itr->next->element != x ) itr = itr->next;

return ListItr<Object>( itr );}

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Insertion routine for linked lists

/* Insert item x after p. */

template <class Object>void List<Object>::insert( const Object & x, const ListItr<Object> & p ){

if( p.current != NULL ) p.current->next = new ListNode<Object>

( x, p.current->next );}

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makeEmpty and List destructor/* Make the list logically empty. */ template <class Object> void List<Object>::makeEmpty( ) { while( !isEmpty( ) ) remove( first( ).retrieve( ) ); }

/* Destructor */ template <class Object> List<Object>::~List( ) {

makeEmpty( ); delete header; }

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List copy routines: operator=/*Deep copy of linked lists.template <class Object>const List<Object> & List<Object>::operator=( const

List<Object> & rhs ){

ListItr<Object> ritr = rhs.first( );ListItr<Object> itr = zeroth( );

if( this != &rhs ) { makeEmpty( ); for( ; !ritr.isPastEnd( );

ritr.advance( ),itr.advance( )) insert( ritr.retrieve( ), itr ); } return *this;}

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List copy routines : copy constructor

/* Copy constructor

template <class Object>

List<Object>::List( const List<Object> & rhs )

{

header = new ListNode<Object>;

*this = rhs;

}

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Doubly Linked List

Traversing list backwards not easy with regular lists

Insertion and deletion more pointer fixing Deletion is easier

Previous node is easy to find

A1 A2 A3

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Circulary Linked List Last node points the first

A1 A2 A3

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Cursor Implementation of Linked List

Problems with linked list implementation:

Same language do not support pointers ! Then how can you use linked lists ?

new and free operations are slow Actually not constant time

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SOLUTION: Implement linked list on an arraycalled CURSOR

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Cursor operation simulates the features Collection of structures

uses array for nodes Array index is pointer

new and delete operation Keep a free list

new returns an element from freelist delete place the node in freelist

Freelist Use cell 0 as header All nodes are free initially 0 is a NULL pointer

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If L = 5, then L represents list (A, B, E)If M = 3, then M represents list (C, D, F)

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Iterator for cursor implementation of linked liststemplate <class Object>class ListItr{ public:

ListItr( ) : current( 0 ) { } bool isPastEnd( ) const {return current == 0; } void advance( ){

if( !isPastEnd( ) ) current =

List<Object>::cursorSpace[ current ].next; } const Object & retrieve( ) const {

if( isPastEnd( ) ) throw BadIterator( ); return List<Object>::cursorSpace[ current ].element; }

private: int current; // Current position friend class List<Object>;

ListItr( int theNode ) : current( theNode ) { }};

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Class skeleton for cursor-based Listtemplate <class Object>class ListItr; // Incomplete declaration.

template <class Object>class List{ public:

List( );List( const List & rhs );

~List( );

bool isEmpty( ) const; void makeEmpty( ); ListItr<Object> zeroth( ) const; ListItr<Object> first( ) const; void insert( const Object & x, const ListItr<Object> & p ); ListItr<Object> find( const Object & x ) const; ListItr<Object> findPrevious( const Object & x ) const; void remove( const Object & x );

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Class skeleton for cursor-based Listpublic: struct CursorNode { CursorNode( ) : next( 0 ) { }

private: CursorNode( const Object & theElement, int n ) : element( theElement ), next( n ) {}

Object element; int next;

friend class List<Object>; friend class ListItr<Object>; };

const List & operator=( const List & rhs );

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Class skeleton for cursor-based List

private: int header;

static vector<CursorNode> cursorSpace;

static void initializeCursorSpace( ); static int alloc( ); static void free( int p ); friend class ListItr<Object>;};

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cursorSpace initialization/* Routine to initialize the cursorSpace. */

template <class Object>void List<Object>::initializeCursorSpace( ){

static int cursorSpaceIsInitialized = false;

if( !cursorSpaceIsInitialized ) { cursorSpace.resize( 100 ); for( int i = 0; i < cursorSpace.size( ); i++ ) cursorSpace[ i ].next = i + 1; cursorSpace[ cursorSpace.size( ) - 1 ].next = 0; cursorSpaceIsInitialized = true; }}

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Routines : alloc and free/* Allocate a CursorNodetemplate <class Object>int List<Object>::alloc( ){

int p = cursorSpace[ 0 ].next; cursorSpace[ 0 ].next = cursorSpace[ p ].next; return p;}

/* Free a CursorNodetemplate <class Object>void List<Object>::free( int p ){

cursorSpace[ p ].next = cursorSpace[ 0 ].next;cursorSpace[ 0 ].next = p;

}

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Short routines for cursor-based lists

/* Construct the listtemplate <class Object>List<Object>::List( ){

initializeCursorSpace( ); header = alloc( ); cursorSpace[ header ].next = 0;}

/* Destroy the listtemplate <class Object>List<Object>::~List( ){

makeEmpty( ); free( header );}

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Short routines for cursor-based lists

/* Test if the list is logically empty. return true if empty

template <class Object>bool List<Object>::isEmpty( ) const{

return cursorSpace[ header ].next == 0;}

/* Return an iterator representing the first node in the list. This operation is valid for empty lists.

template <class Object>ListItr<Object> List<Object>::first( ) const{

return ListItr<Object>( cursorSpace[ header ].next );}

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find routine - cursor implementation

/*Return iterator corresponding to the first node containing an item x. Iterator isPastEnd if item is not found.

template <class Object>ListItr<Object> List<Object>::find( const Object & x ) const{

int itr = cursorSpace[ header ].next;

while( itr != 0 && cursorSpace[ itr ].element != x ) itr = cursorSpace[ itr ].next;

return ListItr<Object>( itr );}

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insertion routine-cursor implementation

/* Insert item x after p.template <class Object>void List<Object>::insert(const Object & x,const ListItr<Object> & p){ if( p.current != 0 ) {

int pos = p.current; int tmp = alloc( );

cursorSpace[ tmp ] = CursorNode( x, cursorSpace[ pos ].next ); cursorSpace[ pos ].next = tmp; }}

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deletion routine - cursor implementation

/* Remove the first occurrence of an item x.template <class Object>void List<Object>::remove( const Object & x ){

ListItr<Object> p = findPrevious( x );int pos = p.current;

if( cursorSpace[ pos ].next != 0 ){

int tmp = cursorSpace[ pos ].next; cursorSpace[ pos ].next = cursorSpace[ tmp ].next; free ( tmp ); }}

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DATA STRUCTURES AND ALGORITHMS Lecture Notes 3 Prepared by İnanç TAHRALI