4.linked list(contd.)

Data Structure & Algorithm
CS 102
Ashok K Turuk

List Traversal
Head Data Link
2

=
Head Data Link
PTR = PTR - > Link
4

List Traversal
Let Head be a pointer to a linked
list in memory. Write an algorithm
to print the contents of each node
of the list
5

List Traversal
Algorithm
1. set PTR = Head
2. Repeat step 3 and 4 while
PTR  NULL
3. Print PTR->DATA
4. Set PTR = PTR -> LINK
5. Stop
6

Search for an ITEM
• Let Head be a pointer to a
linked list in memory. Write an
algorithm that finds the location
LOC of the node where ITEM
first appears in the list, or sets
LOC = NULL if search is
unsuccessful.
7

Search for an ITEM
Algorithm
1. Set PTR = Head
2. Repeat step 3 while PTR  NULL
3. if ITEM == PTR -> DATA, then
Set LOC = PTR, and Exit
else
Set PTR = PTR -> LINK
4. Set LOC = NULL /*search
unsuccessful */
5. Stop
8

Search for an ITEM
Algorithm [Sorted ]
1. Set PTR = Head
3. if ITEM < PTR -> DATA, then
Set PTR = PTR->LINK,
else if ITEM == PTR->DATA, then
Set LOC = PTR, and Exit
else
Set LOC = NULL, and Exit
4. Set LOC = NULL /*search unsuccessful
*/
5. Stop
9

Insertion to a Linked List
Head Data Link
10

Insertion to Beginning
Head Data Link
New NodePTR
11

Head Data Link
New NodePTR
PTR->Link = Head
12

Head Data Link
New NodePTR
PTR->Link = Head , Head = PTR
13

Overflow and Underflow
• Overflow : A new Data to be inserted
into a data structure but there is no
available space.
• Underflow: A situation where one wants
to delete data from a data structure
that is empty.
14

Head Data Link
New NodePTR
Overflow , PTR == NULL
15

Insertion at the Beginning
Let Head be a pointer to a linked list in
memory. Write an algorithm to insert
node PTR at the beginning of the
List.
16

Insertion at the Beginning
Algorithm
1. If PTR == NULL , then Write
Overflow and Exit
2. Set PTR -> DATA = ITEM
3. Set PTR -> LINK = Head -> LINK
4. Set Head = PTR
5. Exit
17

Insertion After a Given Node
Let Head be a pointer to a linked list in
memory. Write an algorithm to insert
ITEM so that ITEM follows the node
with location LOC or insert ITEM as
the first node when LOC == NULL
18

Insertion at a Given Node
Head Data Link
New NodePTR
A BA
LOC
19

Head Data Link
New NodePTR
BA
LOC
PTR->Link = LOC->Link 20

Head Data Link
New NodePTR
BA
LOC
LOC->Link = PTR 21

Insertion After a Given Node
Algorithm
1. If PTR == NULL , then Write
Overflow and Exit
2. Set PTR -> DATA = ITEM
3. If LOC == NULL
Set PTR -> LINK = Head
Set Head = PTR
Else Set PTR->Link = LOC->Link
Set LOC->Link = PTR
4. Exit
22

Insertion into a Sorted Linked
List
Head Data Link
1000 2000 3000 4000 5000
3500
3000 < 3500 < 4000
23

Insertion into a Sorted Linked
List
1000 2000 3000 4000 5000
3000 < 3500 < 4000
BA
To Insert Between Node A and B We have to
Remember the Pointer to Node A which is the
predecessor Node of B
24

Insertion into a Sorted Linked List
Steps to Find the LOC of Insertion
1. If Head == NULL, then Set LOC = NULL and
Return
2. If ITEM < Head ->Data , then Set LOC =
NULL and Return
3. Set SAVE = Head and PTR = Head -> Link
4. Repeat Steps 5 and 6 while PTR  NULL
5. If ITEM < PTR -> Data then
LOC = SAVE and Return
6. Set SAVE = PTR and PTR = PTR->Link
7. Set LOC = SAVE
8. Return
25

Delete the Node Following a Given
Node
• Write an Algorithm that deletes the
Node N with location LOC. LOCP is the
location of the node which precedes N
or when N is the first node LOCP =
NULL
28

Delete the Node Following a
Given Node
• Algorithm: Delete(Head, LOC, LOCP)
1 If LOCP = NULL then
Set Head = Head ->Link. [Deletes the 1st
Node]
Else
Set LOCP->Link = LOC->Link [Deletes Node
N]
2. Exit
29

Delete an Item
Let Head be a pointer to a linked
list in memory that contains integer
data. Write an algorithm to delete
node which contains ITEM.
30

Delete an Item
1000 2000 3000 4000 5000
4000
BA
To delete a Node [Node B] We have to
Remember the Pointer to its predecessor
[Node A]
31

Deletion of an ITEM
Algorithm
1. Set PTR=Head and TEMP = Head
3. If PTR->DATA == ITEM, then
Set TEMP->LINK = PTR -> LINK, exit
else
TEMP = PTR
PTR = PTR -> LINK
4. Stop
32

Deletion of an ITEM
Algorithm
1. If Head == NULL , then
Write ITEM is not in the
List, Exit
2. If Head ->Data == Item
Head = Head -> Link
3. Set PTR=Head and TEMP =
Head
33

Deletion of an ITEM
Algorithm
If PTR->DATA == ITEM, then
Set TEMP->LINK = PTR -> LINK, exit
else
TEMP = PTR
PTR = PTR -> LINK
5. Stop
34

Header Linked Lists
• A header linked list is a linked list
which always contains a special node
called header node
• Grounded Header List: A header list
where the last node contains the NULL
pointer.
Header Node
35

Header Linked Lists
• Circular Header List: A header list
where the last node points back to the
header node.
Header Node
36

Header Linked Lists
• Pointer Head always points to the
header node.
• Head->Link == NULL indicates that a
grounded header list is empty
• Head->Link == Head indicates that a
circular header list is empty
37

Header Linked Lists
• The first node in a header list is the
node following the header node
• Circular Header list are frequently used
instead of ordinary linked list
– Null pointer are not used, hence all pointer
contain valid addresses
– Every node has a predecessor, so the first
node may not require a special case.
38

Traversing a Circular Header List
• Let Head be a circular header list in
memory. Write an algorithm to print
Data in each node in the list.
39

Traversing a Circular Header List
Algorithm
1. Set PTR = Head->Link;
2. Repeat Steps 3 and 4 while PTR  Head
3. Print PTR->Data
4. Set PTR = PTR ->Link
5. Exit
40

Locating an ITEM
• Let Head be a circular header list in
memory. Write an algorithm to find the
location LOC of the first node in Head
which contains ITEM or return LOC =
NULL when the item is not present.
41

Locating an ITEM
Algorithm
1. Set PTR = Head->Link
2. Repeat while PTR ->Data  ITEM and
PTR  Head
Set PTR = PTR ->Link
3. If PTR->Data == ITEM then
Set LOC = PTR
else
Set LOC = NULL
4. Exit
42

Other variation of Linked List
• A linked list whose last node points back
to the first node instead of containing a
NULL pointer called a circular list
43

Other variation of Linked List
• A linked list which contains both a
special header node at the beginning of
the list and a special trailer node at the
end of list
44
Header Node Trailer Node

Applications of Linked Lists
1. Polynomial Representation and operation on
Polynomials
Ex: 10 X 6 +20 X 3 + 55
2. Sparse Matrix Representation
0 0 11
22 0 0
0 0 66

021
021 ...)( ee
m
e
m xaxaxaxA mm
 

Representation of Node
Polynomials
coef expon link

3 14 2 8 1 0
a
8 14 -3 10 10 6
b
123 814
 xxa
61014
1038 xxxb 
null
null
Example

Polynomial Operation
1. Addition
2. Subtraction
3. Multiplication
4. Scalar Division

3 14 2 8 1 0
a
-3 108 14 10 6
b
11 14
d
a->expon == b->expon
a
b
d
a->expon < b->expon
-3 10
Polynomial Addition
3 14 2 8 1 0
-3 108 14 10 6
11 14

3 14 2 8 1 0
a
8 14 -3 10 10 6
b
11 14
a->expon > b->expon
-3 10
d
2 8
Polynomial Addition

3 14 2 8
1 0
a
8 14 -3 10 10 6
b
11 14
a->expon > b->expon
-3 10
d
2 8
Polynomial Addition (cont’d)
10 6
1 0

3 14 2 8 1 0
a
-3 108 14 10 6
b
-5 14
d
a->expon == b->expon
a
b
d
a->expon < b->expon
3 10
Polynomial Subtraction
3 14 2 8 1 0
-3 108 14 10 6
-5 14

3 14 2 8 1 0
a
8 14 -3 10 10 6
b
-5 14
a->expon > b->expon
3 10
d
2 8
Polynomial Subtraction (cont’d)

3 14 2 8
1 0
a
8 14 -3 10 10 6
b
-5 14
a->expon > b->expon
3 10
d
2 8
Polynomial Addition (cont’d)
-10 6
1 0

Sparse Matrix
A sparse matrix is a very large
matrix that contains lot of zero’s.
In order to save storage space, a
sparse matrix stores only the
nonzero elements.

Linked list representation
Sparse Matrix
m n -- i j val i j val Null













0830
0000
9072
0500
A
4 4 -- 0 2 5 3 2 8 Null

Sparse Matrix
aij
i j
ROWLINK
COLLINK

Sparse Matrix













0830
0000
9072
0500
A
0
1
2
3
2 5
0 2 1 7 3 9
1 3 2 8

Two-Way List
• What we have discussed till now is a
one-way list [ Only one way we can
traversed the list]
• Two-way List : Can be traversed in two
direction
– Forward : From beginning of the list to end
– Backward: From end to beginning of the list
59

Two-Way List
• A two-way list is a linear collection of
data element called nodes where each
node N is divided into three parts:
– A information field INFO which contains
the data of N
– A pointer field FORW which contains the
location of the next node in the list
– A pointer field BACK which contains the
location of the preceding node in the list
60

Two-Way List
• List requires two pointer variables:
– FIRST: which points to the first node in
the list
– LAST: which points to the last node in the
list
61
INFO field
BACK pointer
FORW pointer

Two-Way List
63
Suppose LOCA and LOCB are the locations
of nodes A and B respectively in a two-way
list.
The statement that node B follows node A
is equivalent to the statement that node A
precedes node B
Pointer Property: LOCA->FORW = LOCB if
and only if LOCB->BACK = LOCA

Two-Way List
64
FIRST LAST
A B
Forward Pointer
Node A Backward Pointer
Node A

Two-Way List
65
FIRST LAST
A B
LOCA LOCB
LOCA->FORW = LOCB if and only if
LOCB->BACK = LOCA

Operation in two-way list
• Traversing
• Searching
• Deleting
• Inserting
66

Deletion in Two-Way List
67
FIRST LAST
A B
LOCB
DELETE NODE B
C
LOCB->BACK->FORW LOCB->FORW=

Deletion in Two-Way List
68
FIRST LAST
A B
LOCB
DELETE NODE B
C
LOCB->FORW->BACK LOCB->BACK=

Insertion in Two-Way List
69
FIRST LAST
A B
LOCA
INSERT NODE NEW
C
NEW
LOCA->FORW->BACK = NEW
NEW->FORW = LOCA->FORW
LOCA->FORW = NEW
NEW->BACK = LOCA

4.linked list(contd.)

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