Objectives

• Use the Stack ADT
• Practice with postfix expressions
• Practice using Java interfaces and object casting
• Learn how to enforce the design goal of robustness

Your Mission

(6-2)*8

1. Exponents are evaluated first from left to right
2. Multiplication and division operations are performed next, from left to right
3. Addition and subtraction operations are performed last, from left to right

24/2^3-1

On the other hand, a mathematical expression written in postfix notation doesn't need an order of operations or parentheses. Postfix expressions are never ambiguous. In postfix notation, the operator is written after the operands. Here are some examples (make sure you understand these before you try to implement the project):

infix	postfix
7+1	7 1 +
(6-2)*8	6 2 - 8 *
24/2^3-1	24 2 3 ^ / 1 -

Your assignment is to write a computer program that will convert parenthesized or unparenthesized infix expressions into their equivalent postfix expressions. You will be reading a list of infix expressions from a data file. You should display (to System.out) each infix expression along with its equivalent postfix expression.

The Algorithm

1. Read each token (each operand, operator, or parenthesis) from left to right. Only one pass is required.
2. If the next token is an operand (represented by a capital letter), immediately append it to the postfix string.
3. If the next token is an operator, pop and append to the postfix string every operator on the stack until one of the following conditions occurs:
   1. the stack is empty
   2. the top of the stack is a left parenthesis (which stays on the stack)
   3. the operator on top of the stack has a lower precedence than the current operator
   Then push the current operator onto the stack.
4. If the next token is a left parenthesis, push it onto the stack.
5. If the next token is a right parenthesis, pop and append to the postfix string all operators on the stack down to the most recently scanned left parenthesis. Then discard this pair of parentheses.
6. If the next token is a semicolon, then the infix expression has been completely scanned. However, the stack may still contain some operators. (Why?) All remaining operators should be popped and appended to the postfix string.

Next token	Stack	Postfix string	Rule
(	(		4
A	(	A	2
+	( +	A	3
B	( +	AB	2
*	( + *	AB	3
(	( + * (	AB	4
C	( + * (	ABC	2
-	( + * ( -	ABC	3
D	( + * ( -	ABCD	2
)	( + *	ABCD-	5
)		ABCD-*+	5
/	/	ABCD-*+	3
E	/	ABCD-*+E	2
;		ABCD-*+E/	6

The Details

To help you get started, I'm supplying several files for you to download:

1. input.txt. This text file contains some infix expressions to help you get started. The expressions are delimited by semicolons. Of course, you should be testing your code on your own input too! Perform the algorithm on these by hand so you understand how it is supposed to work.
2. FileReader.java. This lets you read tokens from an input file. Read the javadocs in the file to see how it works. You should test it with the sample input file above to be sure you understand how to use it.
3. Token.java. This is a Java interface from which you will implement classes that represent various tokens. (The token classes are listed below). Each implementing class will have a toString() method to return the Token in String format and a handle() method to dictate how to process the token when it is encountered. See the javadocs in the file for more explanation.
4. Semicolon.java. This is a sample of a class that implements the interface above. Only the method prototypes are listed. You'll have to fill in the code yourself.

You are free to alter the code in the above files, but you are required to use them. You are also required to use Javadoc format for all of your documentation for this project.

Here are the classes you'll need to write:

• A Stack class that will hold tokens to be processed. You may use either an array-based or linked-list-based implementation. If you use the code in the book, note that you'll have to alter it a bit since instead of working with generic Objects, you'll want to limit the stack to be able to handle just Tokens. You must write your own Stack class. You may not use Java's built-in version.

• One class for each of the tokens to be processed. Each of these classes will implement the Token interface described above. There are eight tokens that need to be processed: "+", "-", "*", "/", "^", "(", ")", and ";" so you'll be making eight new classes. I've already started one of them for you; namely, the Semicolon class. As mentioned above, each of these classes represents a token whose handle() method will describe how it should be processed according to the rules given above.

• A class named Converter that contains a method, convert(), that performs the algorithm detailed at the top of this document. That is, it reads in a token, identifies it, makes a new Token type from it, and then calls the item's handle() method to take care of it. It repeats this process until all tokens have been read and processed. Having each item's behavior internalized via a method like this is called encapsulation, another object-oriented design goal.

• And, of course, there should be a Client containing your main() method. All main() should need to do is create a new Converter and tell it to convert().

Feel free to add other methods to any of the classes above.

A word about precedence

• Exponent: 3
• Multiplication and Division: 2
• Addition and Subtraction: 1

Why do it this way???

It also allows for the individual tokens to encapsulate their own behavior within their own classes. That way, if you want to modify the program by, say, adding the modulo operator (%), it can be done without touching the code for how division works.

Where do I start???

1. I'm giving you a bunch of code to begin with. So studying and testing the existing code should be your first priority. Understand the interface. Check out the input. Process the input on paper first so you'll (1) know what the right answers are and (2) have a better grasp on how the algorithm works. Test the FileReader class to be sure it's giving you tokens correctly. Try to simply read the input file and then print it to System.out.

2. The primary algorithm at the top of this document is handled by Converter. Get a good understanding on exactly what this class is doing on its own and what tasks it is subcontracting out to other methods. Converter is the one that's repeatedly getting tokens, figuring out which one it is, and calling the appropriate handle() method. Think of handle() this way: instead of you writing all of the code in Converter (which would be very messy), you'll simply let each token "handle" itself. So once you've determined that a token is, say, "+", you'll turn it into a Plus object, and tell it to handle() itself. And it will be each token's version of handle() that does the work of pushing on the stack, popping it, or whatever. That makes each token responsible for doing the right thing and makes your code much more modular. This is a key part of the algorithm so you should make sure you understand what this means before going on (and come see me if you don't).

3. Do one Token at a time. Don't try to take care of all the tokens all at once. Concentrate on being able to read a "+" and get it on the stack. Now can you pop it off and get it back? Can you correctly convert an infix expression that just uses "+" like A+B+C?

Grading

• 20 points for correct output.
• 30 points for program design. This includes:
  • good modularity. It's up to you to decide what methods you should have in what classes.
  • correct use of the interface
  • coherent code. Don't make things overly-complicated. Make sure your code reflects the logic of the assignment.
  • good understandability, including Javadoc format for all documentation. The @param and @returns tags should be used for all parameters and return values.

• Use good comments and variables names
• Test each method individually
• Use good debugging skills: tracing and checkpointing. Use the debugger. It is your friend.

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