Problem 8.1: A simple calculator

Postfix notation, also called reverse Polish notation, can be used to write arithmetic expressions without parentheses. Instead of writing (3+5)*7, in postfix notation we write

  3 5 + 7 *

Postfix expressions can be evaluated using a stack. The steps in evaluating the expression above are: Push 3, push 5; pop top two values, add them, and push the result; push 7; pop top two values, multiply them, and push the result. (Other operations like subtraction work similarly).

You will construct a program that reads a postfix expression from the keyboard and executes it. In addition to positive integers and arithmetic operators, the postfix expression can contain a few other commands:

argument	action	example input	example output
(positive integer)	push integer on stack	88 =	88
=	print top value on stack on a line by itself (without changing the stack)	88 = 7 3 + =	88 10
C	clear stack (returns to initial, empty state)	88 35 C =	No current value!
+	addition	5 4 + 3 + =	12
-	subtraction	15 5 - 4 - =	6
*	multiplication	3 7 * =	21
/	integer division	7 3 / =	2
%	modulus (like % in Java)	7 3 % =	1
Q	Quit the calculator program	Q

You can start the calculator from TextPad - just make sure that you do not have capture output checked in "Run Java Application" preferences. You can also start from a command prompt by

> java Calculator

3 5 + 7 * =
56
C
15 5 - 4 - =
6
82 + = 7 3 + =
88
10
Q

This calculator does not crash or print an error message when the expression is illegal. It uses a slightly odd stack, which can be popped even when it is empty. Popping the empty stack returns zero. Therefore, if you evaluate this malformed expression:

  4 2 - 7 + + + + + =

Constraints

You should check for the possibility of division by zero and make sure that no exception is generated. You can either ignore division by zero or have it result in a value of zero.

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