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Lecture - 6 �On�Data Structures

Linked list

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Lecture Outline

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          • Inserting into a sorted linked list
          • Finding a Node
          • Inserting into a sorted linked list
          • Deletion from a Linked List
          • Variations of Linked Lists:
          • (a) Circular linked lists
          • (b) Doubly linked lists
          • Array versus Linked Lists

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Inserting into a sorted linked list

  • ITEM must be inserted between nodes A and B so that
  • INFO(A)<ITEM<=INFO(B)
  • Traverse the list using a pointer variable PTR
  • Comparing the ITEM with INFO[PTR] at each node.
  • Keep track the location of the preceding node by a pointer variable SAVE, as in fig 5-20
  • SAVE and PTR are updated by the assignments

SAVE : =PTR and PTR : =LINK[PTR]

​

START

Node A

Node B

Fig :5-20

SAVE

PTR

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Finding a Node

FINDA(INFO, LINK, START, ITEM, LOC)

This procedure finds the location LOC of the last node in a sorted list such that

INFO[LOC] < ITEM or sets LOC= NULL

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  1. [List Empty?] If START = NULL then:

Set LOC = NULL and return.

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  • [special case?] If ITEM < INFO[START], then:

Set LOC = NULL and return.

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  • Set SAVE=START and PTR = LINK[START] [initialize pointer]

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  • Repeat step 5 and 6 while PTR ≠ NULL.

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  • If ITEM < INFO[PTR] then:

Set LOC= SAVE and Return.

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  • Set SAVE = PTR and PTR= LINK[PTR] [update pointer]

(End of step 4)

​

  1. Set LOC= SAVE
  2. Exit.

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Inserting into a sorted linked list

Algorithm 5.7: INSSRT(INFO, LINK, START, AVAIL, ITEM)

This algorithm inserts an item into a sorted linked list.

  1. [Use Procedure 5.6 to find the location of the node preceding ITEM] Call FINDA(INFO, LINK, START, ITEM, LOC).
  2. [Use algorithm 5.5 to insert ITEM after the node with location LOC] Call INSLOC(INFO, LINK, START, AVAIL, LOC, ITEM).
  3. Exit

​

​

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Deletion from a Linked List

  • The next pointer field of node-A now points to node-B, where node-N previously pointed
  • The next pointer field of N now points to the original first node in the free pool, where AVAIL previously pointed.
  • AVAIL now points to the deleted node-N

START

Node A

Node N

(a) Before deletion

Node B

Node A

Node B

After deletion

AVAIL

Free storage list

START

Node N

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Deleting a node

  • DELETE(INFO, LINK, START, AVAIL, ITEM)
    • Delete a node with the value equal to INFO from the list.
    • If such a node is found, return its position. Otherwise, return NULL.
  • Steps
    • Find the desirable node (similar to FINDB)
    • Release the memory occupied by the found node
    • Set the pointer of the predecessor of the found node to the successor of the found node
  • Like INSLOC, there are two special cases
    • Delete first node
    • Delete the node in middle or at the end of the list

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Finding a Node

FINDB(INFO, LINK, START, ITEM, LOC, LOCP)

This procedure finds the location LOC of the first node N which contains ITEM and the location LOCP of the node preceding node N.

  • If ITEM does not appear in the list, then sets LOC=NULL
  • If ITEM appear in the first node, then sets LOCP=NULL

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  1. [List Empty?] If START = NULL then:

Set LOC = NULL and LOCP = NULL and return.

  • [ITEM in the first node?] If INFO[START] = ITEM, then:

Set LOC = START and LOCP = NULL and return.

  • Set SAVE=START and PTR = LINK[START] [initialize pointer]
  • Repeat step 5 and 6 while PTR ≠ NULL.
  • If INFO[PTR] = ITEM then:

Set LOC= PTR and LOCP = SAVE and Return.

  • Set SAVE = PTR and PTR= LINK[PTR] [update pointer]
  • Set LOC= NULL[SEARCH UNSUCCESSFUL]
  • Exit.

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Deleting a node

DELETE(INFO, LINK, START, AVAIL, ITEM)

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  1. Call FINDB(INFO, LINK, START, ITEM, LOC, LOCP)

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  • IF LOC = NULL then: ITEM not in the list and exit.

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  • [Delete node]

IF LOCP = NULL then:

Set START= = LINK[START] [Delete first node]

Else:

Set LINK[LOCP] = LINK [LOC]

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  1. Return deleted node to the AVAIL list

Set LINK[LOC] = AVAIL and AVAIL = LOC

​

  1. Exit.

​

​

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Deleting a node

LOC

START

DELETE(INFO, LINK, START, AVAIL, ITEM)

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  1. Call FINDB(INFO, LINK, START, ITEM, LOC, LOCP)

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  • IF LOC = NULL then: ITEM not in the list and exit.

​

  • [Delete node]

IF LOCP = NULL then:

Set START= = LINK[START] [Delete first node]

Else:

Set LINK[LOCP] = LINK [LOC]

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  1. Return deleted node to the AVAIL list

Set LINK[LOC] = AVAIL and AVAIL = LOC

​

  1. Exit.

​

​

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Deleting a node

LOC

LOCP

DELETE(INFO, LINK, START, AVAIL, ITEM)

​

  1. Call FINDB(INFO, LINK, START, ITEM, LOC, LOCP)

​

  • IF LOC = NULL then: ITEM not in the list and exit.

​

  • [Delete node]

IF LOCP = NULL then:

Set START= = LINK[START] [Delete first node]

Else:

Set LINK[LOCP] = LINK [LOC]

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  1. Return deleted node to the AVAIL list

Set LINK[LOC] = AVAIL and AVAIL = LOC

​

  1. Exit.

​

​

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  • 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.)

Variations of Linked Lists

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Variations of Linked Lists�

circular linked list:

  • In a circular linked list there are two methods to know if a node is the first node or not.

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    • Either a external pointer, list, points the first node or
    • A header node is placed as the first node of the circular list.

​

  • The header node can be separated from the others by either heaving a sentinel value as the info part or
  • having a dedicated flag variable to specify if the node is a header node or not.

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CIRCULAR LIST with header node

  • The header node in a circular list can be specified by a sentinel value or a dedicated flag:
  • Header Node with Sentinel: Assume that info part contains positive integers. Therefore the info part of a header node can be -1.

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CIRCULAR LIST with header node

  • Header Node with Flag: In this case a extra variable called flag can be used to represent the header node.
  • For example flag in the header node can be 1, where the flag is 0 for the other nodes.

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Example of application of circular linked list

  • A good example of an application where circular linked list should be used is a timesharing problem solved by the operating system.
  •   In a timesharing environment, the operating system must maintain a list of present users and must alternately allow each user to use a small slice of CPU time, one user at a time. 
  • The operating system will pick a user, let him/her use a small amount of CPU time and then move on to the next user, etc.
  •   For this application, there should be no NIL pointers unless there is absolutely no one requesting CPU time.

​

  • - polygon clipping
  • - round robin situations
  • - when you need to rotate the list, rather than the reference.

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Advantages

  • Each node is accessible from any node.
  • Address of the first node is not needed.
  • Certain operations, such as concatenation and splitting of string, is more efficient with circular linked list.
  • Disadvantage:
  • Danger of an infinite loop !

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Linear linked list vs Circular Linked Lists

  • In linear linked lists if a list is traversed (all the elements visited) an external pointer to the list must be preserved in order to be able to reference the list again.
  • Circular linked lists can be used to help the traverse the same list again and again if needed. A circular list is very similar to the linear list where in the circular list the pointer of the last node points not NULL but the first node.

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Variations of Linked Lists

  • Doubly linked lists
  • A linked list in which each node has three parts :one information and 2 pointers:
  • An information field which contains the data of node.
  • a forward pointer (a pointer to the next node in the list) and
  • a backward pointer (a pointer to the node preceding the current node in the list) is called a doubly linked list.  Here is a picture:

A

Head

B

∅

C

∅

The primary disadvantage of doubly linked lists are that

  1. Each node requires an extra pointer, requiring more space, and
  2. The insertion or deletion of a node takes a bit longer (more pointer operations).
    • Advantage: given a node, it is easy to visit its predecessor. Convenient to traverse lists backwards.

Each node points to not only successor but the predecessor

There are two NULL: at the first and last nodes in the list

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Example :Doubly linked lists�

​

  • A doubly linked list of lines in a document that may be kept by a text editor.  The following denotes how each node should appear:
  • To move backward and forward through the document (as it appears on the screen ) and insert or delete lines, a doubly linked list is ideal. 
  • With the cursor on the current line (stored in a pointer "current"),
  • it is easy to move up one line (current = current->prev) or
  • down one line (current = current->next). 
  • With a singly linked list this is possible but probably too slow. �

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Array versus Linked Lists

    • Linked lists are more complex to code and manage than arrays, but they have some distinct advantages.

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    • 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.

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    • 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.