# Infix to Postfix in C using Stacks

## Infix to Postfix

Any operation can be expressed in Infix, postfix and prefix, we shall see how to convert infix to prefix operation via manual calculation and via code. Lets have a look at Infix to postfix conversion using stack in C

## Infix to Postfix in C

• Infix – Any operation of format `a op b` format example `a + b` is called an infix operation
• Postfix – An operation or expression can also be written in the format of `a b op` i.e. `a b +` which is similar to writing `a + b` in infix. All we are doing is shifting operator to the right of operands

### Why we need postfix operator?

For a compiler, it is easier to read postfix or prefix operation. As a compiler either reads from right to left or left to right. Let us understand this with the help of an example –
`Imagine the following - a + b * c + d`
• Let us assume compiler starts reading from right to left
• It reads `c + d` the operation first and it would be efficient if it could’ve implemented it, but, it can’t as next operation is `c * b` which has higher precedence and must be implemented first.
• Thus, if the compiler reads a notation in which, it can keep on implementing operations as soon as it sees them right!
`The corresponding Postfix would be: abc*+d+`

## Steps to convert

• Any infix `op1 oper op2` can be written as `op1 op2 oper`
• Where op1 = Operand 1
• op2 = Operand2
• oper = Operation
• Example `a + b` can be written as `ab+` in postfix

#### Problem

• Infix: `a + b * c + d` can be written as `a + (b * c) + d`
• Now, for all + – / * associativity is left to right we will write it as
• `(a + (b * c)) + d` and thus further `((a + (b * c)) + d)`
• Solving and converting innermost bracket to postfix
• Step 1 –`((a + bc*)+ d)`
• Step 2 – Consider `bc*` as separate operand `x` the innermost bracket now looks like `((a + x)+ d)`
• Applying postfix it looks like – `(ax+ + d)`replacing x here `(abc*+ + d)`
• Step 3 – Considering`abc*+`as separate operand z, the final bracket looks like – `(z + d)`the result would be `zd+`
• replacing z value = `abc*+d+`

### Algorithm

1. First Start scanning the expression from left to right
2. If the scanned character is an operand, output it, i.e. print it
3. Else
• If the precedence of the scanned operator is higher than the precedence of the operator in the stack(or stack is empty or has'(‘), then push operator in the stack
• Else, Pop all the operators, that have greater or equal precedence than the scanned operator. Once you pop them push this scanned operator. (If we see a parenthesis while popping then stop and push scanned operator in the stack)
4. If the scanned character is an ‘(‘, push it to the stack.
5. If the scanned character is an ‘)’, pop the stack and output it until a ‘(‘ is encountered, and discard both the parenthesis.
6. Now, we should repeat the steps 2 – 6 until the whole infix i.e. whole characters are scanned.
7. Print output
8. Do the pop and output (print) until stack is not empty

## Program for Infix to Postfix in C

We will discuss two methods –

• Method 1: Using array-based stack approach
• Method 2: Using struct based stack approach

#### Output

`abc*+d-`

## Handling all the cases

In the above program, we assumed that expression will only contain alphabets as operands and ‘(‘ or ‘)’ as brackets.

The below program will handle the cases

• Operands: alphabets or digits
• Example – a-z or A-Z or 0 – 9
• Brackets: { } or [ ] or ( )

`a35*d-`

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