Review:
programmer-defined data type that
specifies a set of data values and a
collection of well defined operations
Review:
A way to store and organize data in order
to facilitate access and modification
Definition
Array:
Contiguous array of memory
Definition
Array:
Contiguous array of memory consisting
of equal-size elements
Definition
Array:
Contiguous array of memory consisting
of equal-size elements indexed by
contiguous integers.
1
2
3
4
5
6
7
8
Constant-time access
array_addr + elem_size x (i – first_index)
1
2
3
4
5
6
7
8
(1,1)
(3,4)
(3,4)
(3-1) x 6
(3,4)
(3-1) x 6 + (4-1)
(3,4)
elem_size * ((3-1) x 6 + (4-1))
(3,4)
array_addr + elem_size * ((3-1) x 6 + (4-1))
Add
Remove
Beginning
End
Middle
5 8
3 12
Add
Remove
Beginning
End
Middle
5 8
3 12 4
Add
Remove
Beginning
End O(1)
Middle
5 8
3 12 4
Add
Remove
Beginning
End O(1)
Middle
5 8
3 12
Add
Remove
Beginning
End O(1)
O(1)
Middle
5 8
3 12
Add
Remove
Beginning
End O(1)
O(1)
Middle
8
3 12
Add
Remove
Beginning
End O(1)
O(1)
Middle
8
3 12
Add
Remove
Beginning
End O(1)
O(1)
Middle
8
3
12
Add
Beginning
Remove
O(n)
End O(1)
O(1)
Middle
8
3 12
Add
Remove
Beginning O(n)
O(n)
End O(1)
O(1)
Middle
8
3 12
Add
Remove
Beginning O(n)
O(n)
End O(1)
O(1)
Middle O(n)
8
O(n)
3 12
Stores a set of elements in a particular order
Stack principle: LAST IN FIRST OUT = LIFO
It means: the last element inserted is the first
one to be removed
Example
Which is the first element to pick up?
A
top
B
A
top
C
B
A
top
D
C
B
A
top
E
D
C
B
A
top
D
C
B
A
top
▪push(key): inserts key to collection
▪Key pop(): removes and returns the
last inserted element
▪top(): returns most recently added element
without removing it
▪size(): returns the number of elements stored
▪isEmpty(): indicates whether no elements are
stored
▪Delimiter matching
() {} [] <>
▪Undo sequence in a text editor
▪Web browser history
▪A simple way of implementing the Stack ADT
uses an array
▪We add elements from left to right
…
S
0
1
2
t
▪A variable keeps track of the index of the top
element
▪The array storing the stack elements may
become full
…
S
0
1
2
t
numElements: 0
Push(a)
numElements: 1
a
Push(a)
numElements: 1
a
Push(b)
numElements: 2
a
b
Push(b)
numElements: 2
a
b
Top() → b
numElements: 2
a
b
Push(c)
numElements: 3
a
b
c
Push(c)
numElements: 3
a
b
c
Pop()
numElements: 2
a
b
Pop() → c
numElements: 3
a
b
d
Push(d)
numElements: 4
a
b
d
Push(e)
e
numElements: 5
a
b
d
Push(f)
e
f
numElements: 5
a
b
d
e
f
Push(g) → error
numElements: 5
a
b
d
e
f
Empty() → False
numElements: 4
a
b
d
e
Pop() → f
numElements: 3
a
b
d
Pop() → e
numElements: 2
a
b
Pop() → d
numElements: 1
a
Pop() → b
numElements: 0
Pop() → a
numElements: 0
Empty() → True
▪ Stores a set of elements in a particular order in
which Insertions and deletions follow the first-in
first-out(FIFO) scheme
▪ Insertions are at the rear of the queue and
removals are at the front of the queue
▪enqueue(object): inserts an element at the
end of the queue
▪object dequeue(): removes and returns the
element at the front of the queue
▪ object front(): returns the element at the front without
removing it
▪ integer size(): returns the number of elements stored
▪ boolean isEmpty(): indicates whether no elements are
stored
▪ Naïve way
▪ When enqueuing, the front index is always fixed and the rear index
moves forward in the array.
rear
rear
3
3
front
front
Enqueue(3)
6
Enqueue(6)
▪ Naïve way
▪ When dequeuing, the element at the front the queue is
removed. Move all the elements after it by one position.
(Inefficient!!!)
rear
rear
3
3
front
front
Enqueue(3)
6
Enqueue(6)
rear
6
front
Dequeue()
0
0
read
write
Enqueue(a)
0
1
read
write
a
Enqueue(b)
0
2
read
write
a b
isEmpty() → False
0
3
read
write
a b c
Enqueue(c)
1
3
read
write
b c
Dequeue() → a
2
3
read
write
c
Dequeue() → b
4
2
write
read
c d
Enqueue(d)
0
2
write
read
c d e
Enqueue(e)
1
2
write
read
f
c d e
Enqueue(f)
1
2
write
read
f
c d e
Enqueue(g)
Error!!!
1
3
write
read
f
d e
Dequeue → c
1
4
write
read
f
e
Dequeue → d
1
0
write
read
f
Dequeue → e
1
read
1
write
isEmpty() → True
▪ Running times
Running time
Enqueue(obj)
O(1)
Dequeue()
O(1)
isEmpty()
O(1)
▪ Waiting lists, bureaucracy
▪ Access to shared resources (e.g., printer)
▪ Multiprogramming
▪ Attempting the execution of dequeue or front on an
empty queue throws an EmptyQueueException