Info2: Exercise 06: Reverse Polish Notation

Pre-Lab

P1. Make sure that you understand postfix evaluation. If you do the complete Pre-Lab you will be able to understand the algorithms given in the hand out.

P2. What is the order of precedence for the operators “+”, “-”, “*”, “/”, “^”? If we wanted to include “(” and “)” in this order, where would each of them be?

P3. Łukasiewicz was a Polish logician, so his notation for parentheses-free expressions is often called Reverse Polish Notation. To get your brain in gear, convert the following expressions to RPN! What are the values of the expressions?

1. 1 * 2 + 3
2. 1 + 2 * 3
3. 1 + 2 - 3 ^ 4
4. 1 ^ 2 - 3 * 4
5. 1 + 2 * 3 - 4 ^ 5 + 6
6. ( 1 + 2 ) * 3 + ( 4 ^ ( 5 - 6 ) )
7. 1 + 2 + 3 / 4 + 5 + 6 * ( 7 + 8 )
8. 9 - 1 - 2 - 3 * 2 - 1

P4. For the infix expression a + b ^ c * d ^ e ^ f - g - h / ( i + j ), do the following:

1. Show how to generate the corresponding postfix expression.
2. Show how to evaluate the resulting postfix expression.

P5. Explain, in general terms, how unary operators can be incorporated into the expression evaluators. Assume that the unary operators precede their operands and have high precedence.

Assignment

Read through all of the exercises before starting. This is a lot of work, so I suggest that your group works on exercise 1 and exercise 2 in parallel. Then you exchange code and get back together to do the third exercise.

You can use this eclipse project Lab06_ReversePolishNotation as a scaffold for your solution - it already includes a lot of test cases as well as the interfaces.

Part 1: Stack Class

Implement a class Stack.java as discussed in the lecture, using a linked list of objects that you implement yourself.
Your class should include both an exception on stack underflow as well as stack overflow.
Override the toString()method to provide a useful way of printing a stack.
Now make it generic, so it can take values of any type. Coordinate your interface with your partner.

Attention:

Don’t use the Stack or LinkedList that is already available in the Java Collections Library.
Try and type it in yourself, not just copy the handout.

Part 2: Postfix Class

Implement a class Postfix.javathat has a method public int evaluate (String pfx){…} that takes a String representing a postfix expression and determines the value represented by that expression. You will need to access the individual characters of the string and store them in a stack. This is necessary for the evaluation, luckily your partner is currently in the process of making a stack.
Build a testclass and check the postfix expressions you did in the finger exercises. If there is a difference between the value computed and the value expected, either you were wrong, or the implementation is wrong or both.

Do not go on before you are sure that this is working correctly!

Part 3: Infix to Postfix

Now add another method to the Postfix.javaclass: public String infixToPostfix (String ifx){...} that converts an infix expression which is presented as a Stringto a Stringrepresenting a postfix expression. Throw an exception if your input is not well-formed.

Part 4: UI

Now add another method that reads a string from the console, evaluates the result and prints the result to the console.

For the bored

Once this works for digits, go on and parse multidigit Integers out of the String. Can you do it for double values as well? If you are still bored, parse mixed expressions (doubles and ints in the same expression).
How can you convert prefix to postfix? Find an algorithm and implement it. Can you handle unary operators like - or ! as well?

Lab Report / What to turn in

All info on the lab reports can be found on the Labs page.

Also answer the following questions in your report.

Additional questions for part 1:

Will you really need both exceptions? Why or why not?

Please do not put answers for the pre-lab into the lab report. I will not look at them. The lab hangout is for discussing the pre-lab.