Postfix, Infix and Prefix calculators are a way of calculating answers to mathematical problems, without brackets (hence relying purely on order of operations).

## Postfix Calculators

Postfix takes two numbers and an operation in the format:

3 4 +

and applies the operation to them.

This can get quite complicated, for instance:

(1)The algorithm is explained clearly on wikipedia, however it boils down to the following:

One stack - add numbers to it.

When you hit an operation:

- Pop the previous two numbers off
- Apply the operation to them
- Push the result back on

## Infix Calculators

Infix takes two numbers and an operation in the format:

3 + 4

and applies the operation to them.

Two stacks - numbers and operations. Inputs are allocated accordingly.

Whenever a '*' or '/' is encountered:

- Pop the previous element off the stack
- Read in the next number
- Apply the operation to the two numbers
- Push the result back onto the stack

Once all inputs are read in:

- Pop off each '+' or '-'
- Pop the first two elements we read in off (as in, the bottom of the stack, not the top)
- Apply the operation to the first two elements
- Push their result back on

## Prefix Calculators

Prefix takes two numbers and an operation in the format:

+ 3 4

and applies the operation to them.

Read the input right to left and then apply postfix to it.