Write a JAVA program that will take a string, parse it, and then calculate the value in post-fix (reverse polish) notation. To understand this mostly every expression youve seen in math is called in-fix notation.

In-fix Example:

3 + 2

However in post-fix notation the operator is at the end of the expression.

Post-fix Example:

3 2 +

A stack is used to calculate values in post-fix notation. Numbers are pushed onto the stack, and when an operator is reached it pops off the last two numbers and then pushes the resulting value back on the stack.

This program must:

Calculate values using the algorithm mentioned above and in the slides for addition, subtraction, multiplication, and division (+,-,*,/)

Error message if the user tries to divide by zero

Take in a string and process each digit and operator one at a time assuming white space delimits each

Make sure to check if theres at least two items on the stack before when an operator is encountered or else its not a properly formatted post-fix expression

Finish when the program reaches the end of the string and it has only one value left on the stack, then that value is popped off and returned. Otherwise it was not properly formatted

Use your own created stack and not javas built in stack

You may use any implementation so either an array or a linked structure.

HINTS! First when youre processing the inputted string you can use a Scanner and call the method next() to get each token. From there you can evaluate if that token is an operator, numeric value, or an error. If its a numeric value then you may parse that string using Integer.parseInt() to get the integer value. You may also call Integer.parseInt() in a try-catch block. If the token is not an integer an exception will be raised and should be immediately halted.

Example Dialog:

Enter a reverse polish expression or "quit" to quit

3 2 +

5

Enter a reverse polish expression or "quit" to quit

5 1 2 + 4 * + 3 -

14

Enter a reverse polish expression or "quit" to quit

2 3 4 +

This was not properly formatted

0

Enter a reverse polish expression or "quit" to quit

quit

Goodbye