infixToPostfix

Infix to Postfix Conversion

Course : Data StructuresCourse Code : CSE-203

Infix to Postfix Conversion

Need to handle operator precedence Need to handle parentheses Need to handle left-to-right association Input: Infix with variables, integers,

operators, parentheses (no exponentiation for now)

Output: Postfix form of same expression

Infix Precedence

Parenthesis () Exponentiation ^ Multiplication *, Division / Addition +, Subtraction -

We will use a stack to convert infix expression to its equivalent postfix expression

In computer science, a stack is an abstract data type and data structure based on the principle of

Last In First Out (LIFO).

http://en.wikipedia.org/wiki/Computer_science

http://en.wikipedia.org/wiki/Abstract_data_type

http://en.wikipedia.org/wiki/Data_structure

http://en.wikipedia.org/wiki/LIFO

Psuedocode

Get the input of an infix expression into an array

tos=0 (tos=top of the stack)

for (i=0;i<=arraySize;i++)

{ if array[i]is an operand: Append array[i] to the postfix expression break; if array[i]is an operator: if (tos==0) push array[i] into the stack tos++; if (tos>0) { for(j=tos;j>=0;j--){ compare the precedence of array[i] and stack[j]; if array[i] is an operator of greater or equal precedence pop stack[j] and append it to the postfix expression; tos--; else break; } then push array[i] into the stack tos++; break; }

if array[i] is '(' :

push array[i] into the stack

tos++;

if array[i] is ')' :

for(k=tos;k>=0;k--)

{

if ( stack[k]!=’(’ ) pop stack[k] and append it to the postfix expression;

tos --;

if ( stack==’(’ ) tos --;

break;

}

if array[i]is NULL:

for(l=tos;l>=0;l--)

{

pop stack[l] and append it to the postfix expression;

}

}

Infix input

a*b + (b-c)/g * ( (a+d) * (b-c/f) )

Lets start converting it to its equivalent postfix

form using a stack.

infix expression

postfix expression

a*b + (b-c)/g * ( (a+d) * (b-c/f) )

Infix to postfix conversion

infix expression

postfix expression

*b + (b-c)/g * ( (a+d) * (b-c/f) )

a


infix expression

postfix expression

b + (b-c)/g * ( (a+d) * (b-c/f) )

*

a


infix expression

postfix expression

+ (b-c)/g * ( (a+d) * (b-c/f) )

*

a b


infix expression

postfix expression

(b-c)/g * ( (a+d) * (b-c/f) )

+

a b *


b-c)/g * ( (a+d) * (b-c/f) )

infix expression

postfix expression

+

a b *

(


infix expression

postfix expression

-c)/g * ( (a+d) * (b-c/f) )

+

a b * b

(


infix expression

postfix expression

+

a b * b


c)/g * ( (a+d) * (b-c/f) )

(

-

infix expression

postfix expression

)/g * ( (a+d) * (b-c/f) )

a b * b c

(


-

+

infix expression

postfix expression

/g * ( (a+d) * (b-c/f) )

a b * b c -


+

infix expression

postfix expression

g * ( (a+d) * (b-c/f) )

a b * b c -

/


+

infix expression

postfix expression

* ( (a+d) * (b-c/f) )

a b * b c - g

/


+

infix expression

postfix expression

( (a+d) * (b-c/f) )

a b * b c – g /

*


+

infix expression

postfix expression

(a+d) * (b-c/f) )

a b * b c – g /(


+

*

infix expression

postfix expression

a+d) * (b-c/f) )

a b * b c – g /

(


+

*

(

infix expression

postfix expression

+d) * (b-c/f) )

a b * b c – g / a

(


+

*

(

infix expression

postfix expression

d) * (b-c/f) )

a b * b c – g / a

(


+

*

(

+

infix expression

postfix expression

) * (b-c/f) )

a b * b c – g / a d

(


+

*

(

+

infix expression

postfix expression

* (b-c/f) )

a b * b c – g / a d +


*

(

+

infix expression

postfix expression

(b-c/f) )

a b * b c – g / a d +


*

*

+

(

infix expression

postfix expression

b-c/f) )

a b * b c – g / a d +


*

*

+

(

(

infix expression

postfix expression

-c/f) )

a b * b c – g / a d + b


*

*

+

(

(

infix expression

postfix expression

c/f) )

a b * b c – g / a d + b


*

*

+

-

(

(

infix expression

postfix expression

/f) )

a b * b c – g / a d + b c


*

*

+

-

(

(

infix expression

postfix expression

f) )

a b * b c – g / a d + b c


*

*

+

/

(

(

-

infix expression

postfix expression

) )

a b * b c – g / a d + b c f


*

*

+

/

(

(

-

infix expression

postfix expression

)

a b * b c – g / a d + b c f / -


*

*

+

(

infix expression

postfix expression

a b * b c – g / a d + b c f / - *


*

+

infix expression

postfix expression

a b * b c – g / a d + b c f / - * *


+

infix expression

postfix expression

a b * b c – g / a d + b c f / - * * +


Equivalent postfix expression

a b * b c – g / a d + b c f / - * * +

We have observed When we get any integer or character it goes to the output. The order of the operands in the postfix expression is the same as

the order in the infix expression, and the operands that appear to the left of an operator in the infix expression also appear to its left in the postfix expression.

When we get an operator, it is pushed onto the stack maintaining the following rule

if the stack is empty, the operator is pushed onto the stack. However, if the stack is not empty, at first we pop the operators of greater or equal precedence from the stack and append them to postfix expression. Then the new operator is pushed onto the stack. Thus, this step orders the operators by precedence and in accordance with left-to-right association.

We have observed

After getting a left parenthesis ‘(‘ , 1 & 2 is maintained until we get right parenthesis ‘)’. When ")" is encountered, we pop operators off the stack and append them to the end of postfix expression until we encounter the matching "(".

Within a pair of parentheses, precedence and left-to-right association determine the order of the operators.

When we reach the end of the string, we append the remaining contents of the stack to postfix expression.

And finally we get the postfix expression.

Thanks to……..

Course teacher:Abul Hasan Samee

Made by……

Sabrina Hossain Tonny

Roll : 200614033

CSE-7

MIST

infixToPostfix

Documents

Transcript of infixToPostfix