You are to design a simple calculator using the ArrayStack implementation in Q1 to perform additions, subtractions, multiplications and divisions. The user may enter an arithmetic expression in infix using numbers (0 to 9), parentheses and arithmetic operations (+, -, *, /). The first step to do so is to create a utility class MyCalculator that will have the following methods:

a) Input of an expression and checking Balanced Parenthesis:

public static Boolean isBalanced(String expression);

This is a static method that will read a string representing an infix mathematical expression with parentheses from left to right and decide whether the brackets are balanced or not. To discover whether a string is balanced each character is read in turn. The character is categorized as an opening parenthesis, a closing parenthesis, or another type of character. Values of the third category are ignored for now. When a value of the first category is encountered, the corresponding close parenthesis is stored in the stack. For example, when a ( is read, the character ) is pushed on the stack. When a { is encountered, the character pushed is }. The topmost element of the stack is therefore the closing value we expect to see in a well balanced expression.

When a closing character is encountered, it is compared to the topmost item in the stack. If they match, the top of the stack is popped and execution continues with the next character. If they do not match an error is reported. An error is also reported if a closing character is read and the stack is empty. If the stack is empty when the end of the expression is reached then the expression is well balanced.

For this application a parenthesis can be one of the following:

parantheses: ( ) curly braces: { } square brackets: [ ] angle brackets: < >

These must be defined as constants in the class.

b) Infix to Postfix conversion

Write a method that converts Infix expressions to postfix expressions using your stack implementation: public static String infixToPostfix(String infix)

c) Evaluating a Postfix expression

Write a method thatevaluates a postfix expression: public static double evaluate(string postfix);

d) Your main class QuestionTwo

To evaluate your methods create the class QuestionTwo It must contain a public static void main(String[] args) method to run your code. This main method should ask the user to input

one infix expression per line until the user types q or Q. After every input, it should first test if the expression has balanced paranthesis and tells the user if the expression is balanced or not.

If the expression is balanced it will convert it into a postfix expression, displays the expression and then evaluates it and outputs the results and then ask for the next input.

If the expression is not balanced it tells the user that and asks for a new input.

Some rules:

-You should assume no whitespace in the infix expression provided by the user. For example, your code should work for inputs like 2+(32). The postfix that you will print, however, should have tokens separated by whitespace. For example, 321 should have the postfix

3 21 , and not 321.