1. Linked Lists Definition of Linked Lists Examples of Linked Lists
Operations on Linked Lists
Linked List as a Class
Linked Lists as Implementations of Stacks, Sets, etc.
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2. Definition of Linked Lists
A linked list is a sequence of items (objects) where every item is linked to the next.
Graphically:
data
head_ptr
tail_ptr
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3. Definition Details
Each item has a data part (one or more data members), and a link that points to the next item
One natural way to implement the link is as a pointer; that is, the link is the address of the next item in the list
It makes good sense to view each item as an object, that is, as an instance of a class.
We call that class: Node
The last item does not point to anything. We set its link member to NULL. This is denoted graphically by a self-loop
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4. Examples of Linked Lists (A Waiting Line)
A waiting line of customers: John, Mary, Dan, Sue (from the head to the tail of the line)
A linked list of strings can represent this line:
John
Mary
Dan
Sue
tail_ptr
head_ptr
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5. Examples of Linked Lists (A Stack of Numbers)
A stack of numbers (from top to bottom): 10, 8, 6, 8, 2
A linked list of ints can represent this stack: 10 8 6 8 2
tail_ptr
head_ptr
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6. Examples of Linked Lists (A Set of Non-redundant Elements)
A set of characters: a, b, d, f, c
A linked list of chars can represent this set: a b d f c
tail_ptr
head_ptr
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7. Examples of Linked Lists (A Sorted Set of Non-redundant Elements)
A set of characters: a, b, d, f, c
The elements must be arranged in sorted order: a, b, c, d, f
A linked list of chars can represent this set: a b c d f
tail_ptr
head_ptr
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8. Examples of Linked Lists (A Polynomial)
A polynomial of degree n is the function Pn(x)=a0+a1x+a2x2+…+anxn. The ai’s are called the coefficients of the polynomial
The polynomial can be represented by a linked list (2 data members and a link per item):
a0,0
a1,1
a2,2
an,n
head_ptr
tail_ptr
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9. Operations on Linked Lists
Insert a new item
At the head of the list, or
At the tail of the list, or
Inside the list, in some designated position
Search for an item in the list
The item can be specified by position, or by some value
Delete an item from the list
Search for and locate the item, then remove the item, and finally adjust the surrounding pointers
size( );
isEmpty( )
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10. Insert– At the Head A Insert a new data A. Call new: newPtr
List before insertion:
After insertion to head:
data
data
data
data
head_ptr
tail_ptr A
data
tail_ptr
head_ptr
The link value in the new item = old head_ptr
The new value of head_ptr = newPtr
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11. Insert – at the Tail A Insert a new data A. Call new: newPtr
List before insertion
After insertion to tail:
data
data
data
data
head_ptr
tail_ptr
data A
tail_ptr
head_ptr
The link value in the new item = NULL
The link value of the old last item = newPtr
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12. Insert – inside the List
data
Insert a new data A. Call new: newPtr
List before insertion:
After insertion in 3rd position:
data
data
data
data
head_ptr
tail_ptr
data
data A
data
data
tail_ptr
head_ptr
The link-value in the new item = link-value of 2nd item
The new link-value of 2nd item = newPtr
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13. Delete – the Head Item List before deletion:
List after deletion of the head item:
data
data
data
data
data
tail_ptr
head_ptr
data
data
data
data
data
head_ptr
tail_ptr
The new value of head_ptr = link-value of the old head item
The old head item is deleted and its memory returned
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14. Delete – the Tail Item List before deletion:
List after deletion of the tail item:
data
data
data
data
data
tail_ptr
head_ptr
data
data
data
data
data
tail_ptr
head_ptr
New value of tail_ptr = link-value of the 3rd from last item
New link-value of new last item = NULL.
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15. Delete – an inside Item List before deletion:
List after deletion of the 2nd item:
data
data
data
data
data
tail_ptr
head_ptr
data
data
data
data
data
tail_ptr
head_ptr
New link-value of the item located before the deleted one =
the link-value of the deleted item
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16. size() and isEmpty()
We need to scan the items in the list from the head_ptr to the last item marked by its link-value being NULL
Count the number of items in the scan, and return the count. This is the size().
Alternatively, keep a counter of the number of item, which gets updated after each insert/delete. The function size( ) returns that counter
If head_ptr is NULL, isEmpty() returns true; else, it returns false.
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17. Searching for an Item
Suppose you want to find the item whose data value is A
You have to search sequentially starting from the head item rightward until the first item whose data member is equal to A is found.
At each item searched, a comparison between the data member and A is performed.
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18. Time of the Operations
Time to search() is O(L) where L is the relative location of the desired item in the List. In the worst case. The time is O(n). In the average case it is O(N/2)=O(n).
Time for remove() is dominated by the time for search, and is thus O(n).
Time for insert at head or at tail is O(1).
Time for insert at other positions is dominated by search time, and thus O(n).
Time for size() is O(1), and time for isEmpty() is O(1)
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19. Implementation of an Item
Each item is a collection of data and pointer fields, and should be able to support some basic operations such as changing its link value and returning its member data
Therefore, a good implementation of an item is a class
The class will be called Node
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20. Class Node Design for Item
The member variables of Node are:
The data field(s)
The link pointer, which will be called next
The functions are:
Function
Action
Why Needed
getNext( )
returns the link.
for navigation
getData( )
returns the data
for search
setNext(Node *ptr)
sets link to ptr
for insert/delete
setData(type x)
sets data to x.
to modify data contents
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21. Class Node Type class Node { private:
int data; // different data type for other apps
Node *next; // the link pointer to next item
public:
Node(int x=0;Node * ptr=NULL); // constructor
int getData( );
Node *getNext( );
void setData(int x);
void setNext(Node *ptr); };
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22. Class Node Implementation
Node::Node(int x, Node *p){ data=x; next=p;};
int Node::getData( ){return data;};
Node * Node::getNext( ){return next;};
void Node::setData(int x) {data=x;};
void Node::setNext(Node *ptr){next=ptr;};
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23. Implementation of Linked List
A linked list is a collection of Node objects, and must support a number of operations
Therefore, it is sensible to implement a linked list as a class
The class name for it is List
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24. Class Design for List The member variables are: Member functions
Node *head_ptr; Node *tail_ptr;
int numOfItems;
Member functions
Node * search(int x); Node * itemAt(int position);
void removeHead(); void removeTail();
void remove(int x);
void insertHead(int x); void insertTail(int x);
void insert(Node *p, int x) // inserts item after the item // pointed to by p
int size( ); Node *getHead( ); Node getTail( );
bool isEmpty( );
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25. Class List Type class List { private:
Node *head_ptr; Node *tail_ptr; int numOfItems;
public:
List( ); // constructor
int size( ); Node *getHead( ); Node *getTail( );
bool isEmpty( );
Node *search(int x); Node *itemAt(int position);
void removeHead(); void removeTail();
void remove(int x); // delete leftmost item having x
void insertHead(int x); void insertTail(int x);
void insert(Node *p, int x); };
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26. Implementation of Class List
List::List( ){head_ptr= NULL; tail_ptr=NULL; numOfItems=0;};
int List::size( ){return numOfItems;};
Node * List::getHead( ) {return head_ptr;};
Node * List::getTail( ) {return tail_ptr;};
bool List::isEmpty() {return (numOfItem==0);};
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27. Implementation of search( )
Node *List::search(int x){
Node * currentPtr = getHead( );
while (currentPtr != NULL){
if (currentPtr->getData( ) == x)
return currentPtr;
else
currentPtr = currentPtr->getNext(); }
return NULL; // Now x is not, so return NULL };
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28. Implementation of itemAt( )
Node *List::itemAt(int position){
if (position<0 || position>=numOfItems)
return NULL;
Node * currentPtr = getHead( );
for(int k=0;k != position; k++)
currentPtr = currentPtr -> getNext( );
return currentPtr; };
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29. Implementation of removeHead( )
void List::removeHead( ){
if (numOfItems == 0)
return;
Node * currentPtr = getHead( );
head_ptr=head_ptr->getNext( );
delete currentPtr;
numOfItems--; };
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30. Implementation of removeTail( )
void List::removeTail( ){
if (numOfItems == 0)
return;
if (head_ptr == tail_ptr){
head_ptr=NULL; tail_ptr= NULL;
numOfItems=0; return; }
Node * beforeLast = itemAt(numOfItems-2);
beforeLast->setNext(NULL); // beforeLast becomes last
delete tail_ptr; // deletes the last object
tail_ptr=beforeLast;
numOfItems--; };
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31. Implementation of remove( )
void List::remove(int x){
if (numOfItems == 0) return;
if (head_ptr==tail_ptr && head_ptr->getData()==x){
head_ptr=NULL; tail_ptr= NULL; numOfItems=0; return; }
Node * beforePtr=head_ptr; // beforePtr trails currentPtr
Node * currentPtr=head_ptr->getNext();
Node * tail = getTail();
while (currentPtr != tail)
if (currentPtr->getData( ) == x){ // x is found. Do the bypass
beforePtr->setNext(currentPtr->getNext());
delete currentPtr; numOfItems--; }
else { // x is not found yet. Forward beforePtr & currentPtr.
beforePtr = currentPtr;
currentPtr = currentPtr->getNext(); } };
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32. Implementation of insertHead( )
void List::insertHead(int x){
Node * newHead = new Node(x,head_ptr);
head_ptr= newHead;
if (tail_ptr == NULL) // only one item in list
tail_ptr = head_ptr;
numOfItems++; };
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33. Implementation of insertTail( )
void List::insertTail(int x){
if (isEmpty())
insertHead(x);
else{
Node * newTail = new Node(x);
tail_ptr->setNext(newTail);
tail_ptr = newTail; numOfItems++; } };
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34. Implementation of insert( )
// inserts item x after the item pointed to by p
void List::insert(Node *p, int x){
Node *currentPtr = head_ptr;
while(currentPtr !=NULL && currentPtr != p)
currentPtr = currentPtr->getNext();
if (currentPtr != NULL ) { // p is found
Node *newNd=new Node(x,p->getNext());
p->setNext(newNd);
numOfItems++; } };
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35. For your Work in the Lab
Make the necessary modifications to the List class implementations so that no two Nodes have the same data value. This is useful when using linked lists to implement sets.
Make the necessary changes to the List class so that the Nodes are in increasing order of data values. In particular, replace all the insert methods, and replace them with insert(int x), which inserts x in the right position so that the List remains sorted.
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