Convert Infix to postfix

<aside> 💡 Expression Representation Techniques → Expression is a collection of operators and operands that represents a specific value. 1.Infix Expression 2. Prefix Expression 3. Postfix Expression

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Example Note Infix a + b Operator Between Operands Prefix + a b Operator before Operands Postfix a b + Operator after Operands

To evaluate an infix expression, we need to consider Operators’ Priority and Associative property. For example: Expression 3+5*4 evaluate to 32 i.e. (3+5)4 or to 23 i.e. 3+(54).

Generally, postfix expressions are free from Operator Precedence that's why they are preferred in Computer system. Computer System Uses Postfix form to represent expression. Table below show the Priority for operators that needs in conversion method.

Explanation the conversion in steps:

1. Read symbol from expression and it may be – o Alphabet from A-Z or a-Z o Numerical Digit from 0-9 o Operator

   o Opening And Closing Braces ( , )

2. If Entered Character is Alphabet or Digit then Following Action Should be taken: o Print Alphabet and Digit as Output

3. If Entered Character is Opening Bracket then Following Action Should be taken- o Push ‘(‘ onto Stack

   o If any Operator Appears before ‘)’ then Push it onto Stack. o If Corresponding ‘)’ bracket appears then Start Removing Elements [Pop] from Stack till ‘(‘ is removed.

4. If Entered Character is Operator then Following Action Should be taken: o Check Whether There is any Operator Already present in Stack or not. o If Stack is Empty then Push Operator onto Stack. o If Present then Check Whether Priority of Incoming Operator is greater than Priority of Topmost Stack Operator. o If Priority of Incoming Operator is Greater than Push Incoming Operator onto Stack. o Else Pop (Operator that have high Priority or equal) From Stack and push incoming operator to stack, again go to Step 1.

Evaluation of Postfix Expression

Explanation the Evaluation in steps:

1. At first, stack is empty.
2. Read symbol from expression one after another until reach the end of expression: ⇒ If the symbol is operand push into stack. ⇒ If the symbol is operator pop two operands from stack.
3. Perform the operation(operator) between the two operands and push result into stack.
4. Back into step 2, until the end.