Calculator Case Study

A Scala / functional programming case study based.

Overview

1. Define a data type Expr representing expressions containing +, -, *, and /.

2. Define a method eval that:

   • accepts a parameter of type Expr;
   • returns the result of running the calculation.

3. Define a method prettyPrint that:

   • accepts a parameter of type Expr;
   • returns a pretty printed String representing Expr (make sure to add parentheses in the right places).

4. Update your eval method to account for division by zero:

   • return Some(result) if the calculation is successful;
   • return None if a division by zero occurs;
   • don't use exceptions or nulls!

5. Write a method parsePostfix that:

   • accepts a parameter of type String representing a postfix expression;
   • returns the expression as an Expr;
   • handles parse errors gracefully;
   • doesn't use exceptions or nulls!

Tips for the postfix parser

Postfix expressions put the parameters first and the operators last. They are interesting because you don't need parentheses to show precedence (like you do with normal infix expressions). For example:

POSTFIX                   INFIX
1 2 +                     1 + 2
1 2 * 3 4 * +             1 * 2 + 3 * 4
1 2 + 3 4 + *             (1 + 2) * (3 + 4)

You can parse postfix expressions easily using an expression stack:

• parse the text word-by-word from left to right;
• every time you pass a number:
  • push it onto the stack;
• every time you pass an operator:
  • pop two expressions from the stack;
  • combine them;
  • push the resulting expression onto the stack.
• when you come to the end, you should have exactly one expression on the stack: your final result.