Technopits

Polish notation

  The grate polish mathematician came up with a new technique for representation  and calculation of arithmetic expression where operator will be before or after the operand called polish notation.

Normal expression    A+B
Prefix                       +AB
Postfix                       AB+
Infix                          A+N     

Example questions -- 

convert the following expression to prefix & postfix
{[(A+B)/C] *(D-E)}

 

 Prefix

We have to solve above expression according to the  priory of operators
First we solve the brackets

={[(+AB)/C]*(-DE)}

={[/+ABC]*(-DE)}

={*/+ABC-DE}

 Postfix 

={[(AB+)/C]*(DE-)}

={[AB+C/]*(DE-)}

={AB+CD/DE-*}

=AB+CD/DE-*

Algorithms  for converting infix to postfix using stack 

1.  Add a unique symbol # into stack and add it in the end of array infix. 
    A*(B+C^D)-E^F  #
2.  Scan the symbol of array infix one by one from left to right.
3. Symbol is left parenthesis '(' then add it to the array.   
4. Symbol is operand then add it to array postfix.
5. Symbol is operator then pop the operator which have same priority or higher priority then operator which occurred .
6. Add the pop operator to array.
7. Add the scaned symbole into stack.
8. Symbol is right parenthesis ')' then pop all the operator from the stack. 
9. Symbol is # then pop all the symbol from stack & add them to array except #.
10. You ave done it . 

For example .