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Lists and Sequences
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Sequences
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Outline and Reading
Singly linked list
Position ADT and List ADT (§5.2.1)
Doubly linked list (§ 5.2.3)
Sequence ADT (§5.3.1)
Implementations of the sequence ADT
(§5.3.3)
Iterators (§5.5)
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Singly Linked List
A singly linked list is a
concrete data structure
consisting of a sequence
of nodes
Each node stores


next
element
link to the next node
node
elem

A
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B
C
Sequences
D
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Stack with a Singly Linked List
We can implement a stack with a singly linked list
The top element is stored at the first node of the list
The space used is O(n) and each operation of the
Stack ADT takes O(1) time
nodes

t
elements
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Queue with a Singly Linked List
We can implement a queue with a singly linked list


The front element is stored at the first node
The rear element is stored at the last node
The space used is O(n) and each operation of the
Queue ADT takes O(1) time
r
nodes
f

elements
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Position ADT
The Position ADT models the notion of place
within a data structure where a single object
is stored
A special null position refers to no object.
Positions provide a unified view of diverse
ways of storing data, such as


a cell of an array
a node of a linked list
Member functions:


Object& element(): returns the element stored at
this position
bool isNull(): returns true if this is a null position
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List ADT
The List ADT models a
sequence of positions
storing arbitrary objects
It establishes a
before/after relation
between positions
Generic methods:

Accessor methods:
size(), isEmpty()
isFirst(p), isLast(p)
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



Sequences
first(), last()
before(p), after(p)
Update methods:

Query methods:


replaceElement(p, o),
swapElements(p, q)
insertBefore(p, o),
insertAfter(p, o),
insertFirst(o),
insertLast(o)
remove(p)
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Example 5.4
(page 219)
P1, P2, P3,..., Pi are variables representing positions
Operation
Output
S
insertFirst (8)
P1 (8)
(8)
insertAfter (P1 ,5 )
P2 (5)
(8,5)
insertBefore (P2 ,3 )
P3 (3)
(8,3,5)
insertFirst (9)
p4 (9)
(9,8,3,5)
before (p3 )
P1 (8)
(9,8,3,5)
last ()
P2 (5)
(9,8,3,5)
remove (p4)
-
(8,3,5)
swapElements (P1 ,P2)
-
(5,3,8)
replaceElement (P3,7)
-
(5,7,8)
insertAfter(first(),2)
P5 (2)
(5,2,7,8)
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Doubly Linked List
A doubly linked list provides a natural
implementation of the List ADT
Nodes implement Position and store:



element
link to the previous node
link to the next node
prev
next
elem
node
Special trailer and header nodes
nodes/positions
header
trailer
elements
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Insertion
We visualize operation insertAfter(p, X), which returns position q
p
A
B
C
p
A
q
B
C
X
p
A
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q
B
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X
C
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Deletion
We visualize remove(p), where p = last()
A
B
C
A
B
C
p
D
p
D
A
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B
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Performance
In the implementation of the List ADT
by means of a doubly linked list




The space used by a list with n elements is
O(n)
The space used by each position of the list
is O(1)
All the operations of the List ADT run in
O(1) time
Operation element() of the
Position ADT runs in O(1) time
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Sequence ADT
The Sequence ADT is the
union of the Vector and
List ADTs
Elements accessed by


List-based methods:

Rank, or
Position
Generic methods:

size(), isEmpty()
Vector-based methods:

elemAtRank(r),
replaceAtRank(r, o),
insertAtRank(r, o),
removeAtRank(r)
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first(), last(),
before(p), after(p),
replaceElement(p, o),
swapElements(p, q),
insertBefore(p, o),
insertAfter(p, o),
insertFirst(o),
insertLast(o),
remove(p)
Bridge methods:

Sequences
atRank(r), rankOf(p)
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Applications of Sequences
The Sequence ADT is a basic, generalpurpose, data structure for storing an ordered
collection of elements
Direct applications:


Generic replacement for stack, queue, vector, or
list
small database (e.g., address book)
Indirect applications:

Building block of more complex data structures
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Array-based Implementation
elements
We use a
circular array
storing
positions
A position
object stores:


Element
Rank
Indices f and l
keep track of
first and last
positions
0
1
3
positions
S
f
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Sequences
l
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Sequence Implementations
Operation
size, isEmpty
atRank, rankOf, elemAtRank
first, last, before, after
replaceElement, swapElements
replaceAtRank
insertAtRank, removeAtRank
insertFirst, insertLast
insertAfter, insertBefore
remove
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Array
1
1
1
1
1
n
1
n
n
List
1
n
1
1
n
n
1
1
1
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Iterators
An iterator abstracts the
process of scanning through
a collection of elements
Methods of the ObjectIterator
ADT:



boolean hasNext()
object next()
reset()

ObjectIterator elements()
Two notions of iterator:
Extends the concept of
position by adding a traversal
capability
May be implemented with an
array or singly linked list
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An iterator is typically
associated with an another
data structure
We can augment the Stack,
Queue, Vector, List and
Sequence ADTs with method:
Sequences


snapshot: freezes the
contents of the data
structure at a given time
dynamic: follows changes to
the data structure
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