Computer Notes - Data Structures - 6

8/3/2019 Computer Notes - Data Structures - 6

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Class No.06

Data Structures

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Stack Using Linked List

We can avoid the size limitation of a stackimplemented with an array by using alinked list to hold the stack elements.

As with array, however, we need to decidewhere to insert elements in the list andwhere to delete them so that push and pop

will run the fastest.

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For a singly-linked list, insert at start or endtakes constant time using the head and currentpointers respectively.

Removing an element at the start is constanttime but removal at the end required traversingthe list to the node one before the last.

Make sense to place stack elements at the startof the list because insert and removal areconstant time.



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No need for the current pointer; head is enough.

top

2

5

7

1

1 7 5 2

head



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Stack Operation: List

int pop(){

int x = head->get();

Node* p = head;

head = head->getNext();

delete p;

return x;}

top

2

5

7

1 7 5 2

head



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void push(int x){

Node* newNode = new Node();

newNode->set(x);

newNode->setNext(head);

head = newNode;}

top

2

5

7

9

7 5 2

head

push(9)

9

newNode



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int top(){

return head->get();}int IsEmpty()

{return ( head == NULL );

}

All four operations take constant time.



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Stack: Array or List

Since both implementations support stackoperations in constant time, any reason tochoose one over the other?

Allocating and deallocating memory for list

nodes does take more time than preallocatedarray.

List uses only as much memory as required bythe nodes; array requires allocation ahead of

time. List pointers (head, next) require extra memory.

Array has an upper limit; List is limited bydynamic memory allocation.

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Use of Stack

Example of use: prefix, infix, postfixexpressions.

Consider the expression A+B: we think of

applying the operator+ to the operandsA and B.

+ is termed a binary operator: it takestwo operands.

Writing the sum as A+B is called the infixform of the expression.



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Prefix, Infix, Postfix

Two other ways of writing the expressionare

+ A B prefixA B + postfix

The prefixes pre and post refer to theposition of the operator with respect to thetwo operands.



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Consider the infix expressionA + B * C

We know that multiplication is done

before addition.

The expression is interpreted asA + ( B * C )

Multiplication has precedenceoveraddition.



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Conversion to postfix

A + ( B * C ) infix form



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A + ( B C * ) convert multiplication



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A ( B C * ) + convert addition



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A ( B C * ) + convert addition

A B C * + postfix form



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(A + B ) * C infix form



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( A B + ) * C convert addition



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( A B + ) C * convert multiplication



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( A B + ) C * convert multiplication

A B + C * postfix form



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Precedence of Operators

The five binary operators are: addition,subtraction, multiplication, division andexponentiation.

The order of precedence is (highest tolowest)

Exponentiation

Multiplication/division *, /

Addition/subtraction +, -



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Precedence of Operators

For operators of same precedence, theleft-to-right rule applies:

A+B+C means (A+B)+C.

For exponentiation, the right-to-left ruleapplies

A B C means A ( B C )



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Infix to Postfix

Infix Postfix

A + B A B +

12 + 60 23 12 60 + 23(A + B)*(C D ) A B + C D *

A B * C D + E/F A B C*D E F/+

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Computer Notes - Data Structures - 6