CS210- Lecture 6
Jun 13, 2005
Announcements
 Assignment 2 has been posted.
 Part 1: Programming - Due on 6/19 (Sunday)
 Part 2: Problems – Due on 6/21 (Tuesday)
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Agenda
Linked Lists
Linked List implementation of Stack
Linked List implementation of Queue
Double Ended Queue
Implementing a deque with a doubly linked
list
 Implementing a Stack with doubly linked list
 Vectors





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Singly Linked Lists


A singly linked list is a
concrete data structure
consisting of a sequence
of nodes
Each node stores

head

next
element
link to the next node
node
elem

A
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B
C
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Inserting at the head
 Allocate a new
node
 Insert new
element
 Have new node
point to old head
 Update head to
point to new
node
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Removing at the head


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Update head to
point to next
node in the list
Allow garbage
collector to
reclaim the
former first node
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Inserting at the tail
 Allocate a new
node
 Insert new
element
 Have new node
point to null
 Have old last node
point to new node
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 Update tail to
point to new node
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Removing at tail


Removing at the tail
of a singly linked list
is not efficient!
There is no
constant-time way
to update the tail to
point to the previous
node.
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Analyzing the Singly Linked List
Method
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Time
Inserting at the head
O(1)
Inserting at the tail
O(1)
Deleting at the head
O(1)
Deleting at the tail
O(n)
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Singly Linked List implementation of Stack



We can implement a stack with a singly
linked list by inserting and removing
elements at head.
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.
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Singly Linked List implementation of Stack
top
null
top
push (“A”)
nul
l
“A”
top
null
“B”
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push (“B”)
“A”
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Singly Linked List implementation of Stack
top
null
pop()
“A”
top
pop()
null
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Singly Linked List implementation of Queue

We can implement a queue with a singly
linked list





The front element is stored at the first node
(head)
The rear element is stored at the last node (tail)
We insert at tail and remove at head
Why would it be bad to insert at the head and
remove at the tail ?
The space used is O(n) and each operation of
the Queue ADT takes O(1) time
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Singly Linked List implementation of Queue
head
null
tail
head
enqueue (“A”)
null
tail
“A”
head
null
“A”
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enqueue (“B”)
“B”
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Singly Linked List implementation of Queue
tail
head
null
dequeue ()
“B”
head
null
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dequeue ()
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Double Ended Queues (Deque)


Deque is a queue like data structure
that supports insertion and deletion at
both the front and rear of the queue.
Also known as “deck” to avoid
confusion with the dequeue method of
the regular queue ADT.
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The Deque ADT




insertFirst(o): Insert a new object o at
the beginning of the deque.
insertLast(o): Insert a new object o at
the end of the deque
removeFirst(): Remove and return the
first element of the deque.
removeLast(): Remove and return the
last element of the deque.
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Implementing a Deque with a Doubly Linked List



As deque requires insertion and deletion
at both ends of a list, using a singly
linked list would be inefficient.
There is another kind of linked list that
allows us to insert and remove
elements at both ends in O(1) time –
doubly linked list
Node in a double linked list has two
references – a next link and a prev link.
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Doubly Linked List
prev
next
DLNode
header
trailer
A
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elem
B
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Doubly Linked List



Header and Trailer are dummy or
sentinel nodes. These do not store any
element.
The header has a valid next reference
but a null prev reference.
The trailer has a valid prev reference
but a null next reference.
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Inserting at the head of DLL
header
trailer
A
B
C
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Deleting at the tail of DLL
header
trailer
A
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B
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Insert at the tail of DLL
header
trailer
p
A
B
C
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Deleting at the head of DLL
header
trailer
A
B
Analysis
Method
size, isEmpty
Time
O(1)
first, last
O(1)
insertFirst, insertLast
O(1)
removeFirst, removeLast
O(1)
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Implementing Stack using a DLL
top
null
top
push (“A”)
null
null
“A”
top
null
null
“B”
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push (“B”)
“A”
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Implementing Stack using a DLL
top
null
null
pop ()
“A”
top
pop ()
null
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Vector, List and Sequence ADT



Suppose we have a collection S of n
elements stored in a certain linear
order, so that we can refer to the
elements is S as first, second and third
so on.
Such a collection is generically referred
to as a sequence.
Vector, List and Sequence ADTs are
sequences.
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Vector, List and Sequence ADT



Each represents a collection of linearly
arranged elements and provides methods for
accessing, inserting and removing arbitrary
elements.
These sequences differ in the ways in which
the different operations are defined.
Stacks, Queues and Deques can be viewed as
restricted types of sequences that access only
first and/or last elements.
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Vectors and Array Lists



A vector which is also known as array
list, is an abstraction and extension of
the concrete array data structure.
It provides accessor methods that can
index into the middle of a sequence and
it also provides update methods for
adding and removing elements by their
indices.
We typically use the term rank to refer
to the index of an element in a vector.
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Vectors and Array Lists


We define rank of an element e in S to
be the number of elements that are
before e in S.
First element in S has rank 0 and the
last element has rank n – 1.
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Vector ADT




elemAtRank(r): return the element of S
with rank r. Error occurs if r < 0 and r >
size() - 1 .
replaceAtRank(r, e): Replace with e and
return the element at rank r.
insertAtRank(r, e): Insert a new element
e into S to have rank r. When will error
occur?
removeAtRank(r): Remove from S the
element at rank r.
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Realization of Deque by means of Vector
Deque Method
Vector Method
first()
last()
insertFirst(o)
insertLast(o)
removeFirst()
removeLast()
elemAtRank(0)
?
?
?
?
?
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Simple Array based implementation of Vector
Shifting up for an insertion at rank r ( O(n) )
S
0
1
2
r
n -1
N -1
Shifting down for a removal at rank r ( O(n) )
S
0
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1
2
r
n -1
N -1
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