1 linked lists (lec 6). 2 introduction singly linked lists circularly linked lists doubly linked...
TRANSCRIPT
1
Linked Lists
(Lec 6)
2
Introduction
Singly Linked Lists
Circularly Linked Lists
Doubly Linked Lists
Multiply Linked Lists
Applications
ADT for links
ADT for singly linked lists
Outline
3
Sequential data structures in general, suffer from the following drawbacks:
• Inefficient implementation of insertion and deletion operations
• Inefficient use of storage memory
4
Linked Lists
• A linked list is a series of connected nodes• Each node contains at least– A piece of data (any type)– Pointer to the next node in the list
• Head: pointer to the first node• The last node points to NULL
A
Head
B C
A
data pointer
node
5
A linked representation serves to counteract the drawbacks of sequential representation by exhibiting the following merits:
Efficient implementation of insertion and deletion
operations. Unlike sequential data structures, there is complete
absence of data movement of neighbouring elements during the execution of these operations.
Efficient use of storage memory. The operation and management of linked data
structures are less prone to instigate memory fragmentation.
6
A linked representation of data structure known as a linked list is a collection of nodes.
Each node is a collection of fields categorized as data items and links.
The data item fields hold the information content or data to be represented by the node.
The link fields hold the addresses of the neighbouring nodes or of those nodes which are associated with the given node as dictated by the application.
7
Implementation of linked lists
• to frame chunks of memory into nodes with the desired number of data items and fields
• to determine which nodes are free and which have been allotted for use
• to obtain nodes from the free storage area or storage pool for use GETNODE(X)
• to return or dispose nodes from the reserved area or pool to the free area after use RETURN(X)
8
Linked Lists 8
Singly Linked Lists
• A singly linked list is a concrete data structure consisting of a sequence of nodes
• Each node stores– element– link to the next node
next
elem node
A B C D
9
Singly Linked Lists
• A singly linked list is a linear data structure each node of which has one or more data item fields (DATA) but only a single link field (LINK)
LINK
DATA
10
Linked Lists 10
Inserting at the Head
1. Allocate a new node2. Insert new element3. Make new node
point to old head4. Update head to point
to new node
11
Linked Lists 11
Removing at the Head
1. Update head to point to next node in the list
2. Allow garbage collector to reclaim the former first node
12
Linked Lists 12
Singly linked list with ‘tail’ sentinel
public class SLinkedListWithTail { protected Node head; // head node of the list protected Node tail; // tail node of the list /** Default constructor that creates an empty list */ public SLinkedListWithTail() {
head = null; tail = null;
}// ... update and search methods would go here ...
}
13
Linked Lists 13
Inserting at the Tail
1. Allocate a new node
2. Insert new element
3. Have new node point to null
4. Have old last node point to new node
5. Update tail to point to new node
14
Linked Lists 14
Removing at the Tail
• Removing at the tail of a singly linked list cannot be efficient!
• There is no constant-time way to update the tail to point to the previous node
15
Insertion in a singly linked list
Algorithm 6.1 : To insert a data element ITEM in a non empty singly liked list START, to the right of node NODE.
Procedure INSERT_SL(START, ITEM, NODE)/* Insert ITEM to the right of node NODE in the list START */
Call GETNODE(X);DATA(X) = ITEM;LINK(X) = LINK(NODE); Node X points to the original right neighbour of node NODE */LINK(NODE) = X;
end INSERT_SL.
16
Algorithm 6.3 : Deletion of a node which is to the right of node NODEX in a singly linked list START
Procedure DELETE_SL(START, NODEX)
if (START = NIL) then Call ABANDON_DELETE; /*ABANDON_DELETE terminates the delete operation */ else
{TEMP = LINK(NODEX); LINK(NODEX) = LINK(TEMP);
Call RETURN(TEMP); }end DELETE_SL.
Deletion in a singly linked list
17
Linked Lists 17
Doubly Linked List• A doubly linked list is often more
convenient! • Nodes store:
– element– link to the previous node– link to the next node
• Special trailer and header nodes
prev next
elem
trailerheader nodes/positions
elements
node
18
Linked Lists 18
Insertion• We visualize operation insertAfter(p, X), which returns position q
A B X C
A B C
p
A B C
p
X
q
p q
19
Linked Lists 19
Insertion AlgorithmAlgorithm insertAfter(p,e):
Create a new node vv.setElement(e)v.setPrev(p) {link v to its predecessor}v.setNext(p.getNext()) {link v to its successor}(p.getNext()).setPrev(v) {link p’s old successor to v}p.setNext(v) {link p to its new successor, v}return v {the position for the element e}
20
Linked Lists 20
Deletion• We visualize remove(p), where p == last()
A B C D
p
A B C
D
p
A B C
21
Linked Lists 21
Deletion Algorithm
Algorithm remove(p):t = p.element {a temporary variable to hold the
return value}(p.getPrev()).setNext(p.getNext()) {linking out p}(p.getNext()).setPrev(p.getPrev())p.setPrev(null){invalidating the position p}p.setNext(null)return t
22
Circularly Linked Lists• For further improvement in processing of a singly
linked list one may replace the null pointer in the last node with the address of the first node in the list.
• Such a list is called as a circularly linked list or a circular linked list or simply a circular list.
23
Advantages of circularly linked list• accessibility of a node • delete operations • relative efficiency in the implementation of
list based operations
Disadvantages of circularly linked lists getting into an infinite loop owing to the
circular nature of pointers in the list solution to this problem is to designate a special node to act as the head of the list, known as list head or head node
24
• headed circularly linked list or circularly linked list with head node.
HEAD NODE
25
• To enhance greater flexibility of movement, the linked representation could include two links in every node, each of which points to the nodes on either side of the given node
• Such a linked representation known as doubly linked list• Each node has one or more data fields but only two link
fields termed left link (LLINK) and right link (RLINK). • The LLINK field of a given node points to the node on its
left and its RLINK field points to the one on its right. • A doubly linked list may or may not have a head node.
Again, it may or may not be circular.
Doubly Linked Lists
26
Advantages of a doubly linked list
The availability of two links LLINK and RLINK permit forward and backward movement during the processing of the list.
The deletion of a node X from the list calls only for the value X to be known.
Disadvantages of a doubly linked list
memory requirement
LLINK RLINK
DATA
27
Insertion in a doubly linked list
Algorithm 6.4 : To insert node X to the right of node Y in a headed circular doubly linked list P
Procedure INSERT_DL(X, Y)LLINK(X) = Y;RLINK(X) = RLINK(Y);LLINK(RLINK(Y)) = X;RLINK(Y) = X;
end INSERT_DL.
28
Deletion in a doubly linked list
Algorithm 6.5 : Delete node X from a headed circular doubly linked list P
procedure DELETE_DL(P, X)if (X = P) then ABANDON_DELETE;else
{RLINK(LLINK(X)) = RLINK(X); LLINK(RLINK(X)) = LLINK(X);
Call RETURN(X); } end DELETE_DL.
29
Multiply Linked Lists
• A multiply linked list as its name suggests is a linked representation with multiple data and link fields
30
Applications
• Addition of polynomials • Representation of a sparse matrix
31
ADT for Links
Data objects: Addresses of the nodes holding data and null links
Operations:
Allocate node (address X) from Available Space to accommodate data
GETNODE ( X)
Return node (address X) after use to Available Space
RETURN(X)
Store a value of one link variable LINK1 to another link variable LINK2
STORE_LINK ( LINK1, LINK2)
Store ITEM into a node whose address is X
STORE_DATA (X, ITEM)
Retrieve ITEM from a node whose address is X
RETRIEVE_DATA (X, ITEM)
32
ADT for Singly Linked Lists
Data objects: A list of nodes each holding one (or more) data field(s) DATA and a single link field LINK. LIST points to the start node of the list. Operations:
Check if list LIST is empty CHECK_LIST_EMPTY ( LIST) (Boolean function)
Insert ITEM into the list LIST as the first element INSERT_FIRST (LIST, ITEM)
Insert ITEM into the list LIST as the last element INSERT_LAST (LIST, ITEM) Insert ITEM into the list LIST in order INSERT_ORDER (LIST, ITEM)
33
Delete the first node from the list LIST DELETE_FIRST(LIST)
Delete the last node from the list LIST DELETE_LAST(LIST)
Delete ITEM from the list LIST DELETE_ELEMENT
(LIST, ITEM)
Advance Link to traverse down the list
ADVANCE_LINK (LINK)
Store ITEM into a node whose address is X
STORE_DATA(X, ITEM)
Retrieve data of a node whose address is X and return it in ITEM
RETRIEVE_DATA(X, ITEM)
Retrieve link of a node whose address is X and return the value in LINK1
RETRIEVE_LINK (X, LINK1)
34
Variations of Linked Lists
• Circular linked lists– The last node points to the first node of the list
– How do we know when we have finished traversing the list? (Tip: check if the pointer of the current node is equal to the head.)
A
Head
B C
35
Variations of Linked Lists• Doubly linked lists– Each node points to not only successor but the
predecessor– There are two NULL: at the first and last nodes in
the list– Advantage: given a node, it is easy to visit its
predecessor. Convenient to traverse lists backwards
A
Head
B C
36
Array versus Linked Lists
• Linked lists are more complex to code and manage than arrays, but they have some distinct advantages.– Dynamic: a linked list can easily grow and shrink in size.
• We don’t need to know how many nodes will be in the list. They are created in memory as needed.
• In contrast, the size of a C++ array is fixed at compilation time.
– Easy and fast insertions and deletions• To insert or delete an element in an array, we need to copy to
temporary variables to make room for new elements or close the gap caused by deleted elements.
• With a linked list, no need to move other nodes. Only need to reset some pointers.