stacks - imranihsan.comimranihsan.com/upload/lecture/dsaf1708.pdf · 08 stacks implementation &...

DATA STRUCTURES AND ALGORITHMS

IMRAN IHSANASSISTANT PROFESSOR, AIR UNIVERSITY, ISLAMABADWWW.IMRANIHSAN.COM

LECTURES ADAPTED FROM:DANIEL KANE, NEIL RHODESDEPARTMENT OF CS & ENGINEERINGUNIVERSITY OF CALIFORNIA, SAN DIEGO

08STACKSIMPLEMENTATION & APPLICATIONS

STACK

2

ABSTRACT DATA TYPE

• An Abstract Stack (Stack ADT) is an abstract data type which emphasizes specific operations:• Uses a explicit linear ordering• Insertions and removals are performed individually• Inserted objects are pushed onto the stack• The top of the stack is the most recently object pushed onto the stack• When an object is popped from the stack, the current top is erased

• Also called a last-in–first-out (LIFO) behavior• Graphically, we may view these operations as follows:

• There are two exceptions associated with abstract stacks:• It is an undefined operation to call either pop or top on an empty stack

STACK

3

APPLICATIONS

• Numerous applications:• Parsing code:

• Matching parenthesis• XML (e.g., XHTML)

• Tracking function calls• Dealing with undo/redo operations• Reverse-Polish calculators• Assembly language

• The stack is a very simple data structure• Given any problem, if it is possible to use a stack,

this significantly simplifies the solution

• Problem solving:• Solving one problem may lead to subsequent problems• These problems may result in further problems• As problems are solved, your focus shifts back to the problem which lead to

the solved problem

• Notice that function calls behave similarly:• A function is a collection of code which solves a problem

STACK

4

DEFINITION

• Abstract data type with the following operations:

Push(Key): adds key to collection

Key Top(): returns most recently-added key

Key Pop(): removes and returns most recently-added key

Boolean Empty(): are there any elements?

BALANCED BRACKETS

5

• Input:

• A string str consisting of ‘(‘, ‘)’, ‘[‘,‘]’ characters.

• Output:

• Return whether or not the string’s parentheses and square brackets are balanced.

Balanced: Unbalanced:

“([])[]()”, “([]]()”

“((([([])]))())” “][”

BALANCED BRACKETS

6

IsBalanced(str )

Stack stack

for char in str:

if char in [‘(‘, ‘[‘]:

stack.Push(char)

else:

if stack.Empty():

return False

top ← stack.Pop()

if (top = ‘[‘ and char != ‘]’) or

(top = ‘(‘ and char != ‘)’):

return False

return stack.Empty()

STACK IMPLEMENTATION WITH ARRAY

7

numElements: 0


8

numElements: 0

Push(a)


9

numElements: 1

Push(a)

a


10

numElements: 2

Push(b)

a b


11

numElements: 2

Top() b

a B


12

numElements: 3

Push(c)

a b c


13

numElements: 2

Pop() c

a b


14

numElements: 3

Push(d)

a b d


15

numElements: 4

Push(e)

a b d e


16

numElements: 5

Push(f)

a b d e f


17

numElements: 5

Push(g) ERROR

a b d e f


18

numElements: 5

Empty() False

a b d e f


19

numElements: 4

Pop() f

a b d e


20

numElements: 3

Pop() e

a b d


21

numElements: 2

Pop() d

a b


22

numElements: 1

Pop() b

a


23

numElements: 0

Pop() a


24

numElements: 0

Empty() True

STACK IMPLEMENTATION WITH LINKED LIST

25

Empty Linked List/

head


26

Push(a)

a

/

head


27

Push(b)

a

/

head

b


28

Top() b

a

/

head

b


29

Push(c)

a

/

head

bc


30

Pop() c

a

/

head

b


31

Push(d)

a

/

head

bd


32

Push(e)

a

/

head

bde


33

Push(f)

a

/

head

bdef


34

Empty() False

a

/

head

bdef


35

Pop() f

a

/

head

bde


36

Pop() e

a

/

head

bd


37

Pop() d

a

/

head

b


38

Pop() b

a

/

head


39

Pop() a

/

head


40

Empty() True

/

head

PARSING XHTML

41

STACK APPLICATIONS

<html>

<head><title>Hello</title></head>

<body><p>This appears in the <i>browser</i>.</p></body>

</html>

PARSING XHTML

42

STACK APPLICATIONS

<html>



</html>

PARSING XHTML

43

STACK APPLICATIONS

<html>



</html>

PARSING XHTML

44

STACK APPLICATIONS

<html>



</html>

PARSING XHTML

45

STACK APPLICATIONS

<html>



</html>

PARSING XHTML

46

STACK APPLICATIONS

<html>



</html>

PARSING XHTML

47

STACK APPLICATIONS

<html>



</html>

PARSING XHTML

48

STACK APPLICATIONS

<html>



</html>

PARSING XHTML

49

STACK APPLICATIONS

<html>



</html>

PARSING XHTML

50

STACK APPLICATIONS

<html>



</html>

PARSING XHTML

51

STACK APPLICATIONS

<html>



</html>

PARSING XHTML

52

STACK APPLICATIONS

<html>



</html>

SUMMARY

53

• Stacks can be implemented with either an array or a linked list.

• Each stack operation is O(1):

• Push, Pop, Top, Empty.

• Stacks are occasionally known as LIFO queues.

stacks - imranihsan.comimranihsan.com/upload/lecture/dsaf1708.pdf · 08 stacks implementation &...

Documents