Objectives:

Students will gain an experience to evaluate arithmetic expressions by stacks

Students will gain an experience to handle errors using $C++$ exceptions

Problem

Task$1-$ Exercises

Given the following expressions,

$a-(\frac{b}{c}**d)$

$\frac{a}{b}\frac{?}{c}-(d+e)***f$

$a**(\frac{b}{c}\frac{?}{d})+e$

use the algorithm learnt in Chapter $6$ to convert these expression into the equivalent

fpostfix expression. Illustrate the algorithm step by step in the following table:

Task$2$

Consider simple infix expressions that consist of single$-$digit operands; the operators,$+-,$

$*,$ and $/$; and the parentheses. Assume that unary operators are illegal and that the

expression contains no embedded spaces. Design and implement a class of infix

calculators. The class should have the following members:

Private members:

a string to store an infix expression for evaluation.

a private member function that checks if an infix expression is well formed.

a private member function that checks for balanced brackets of an expression

using the algorithm studied in Chapter $6.$

a private member function that converts an infix expression to a postfix

expression using the algorithm studied in Chapter $6.$

a private member function that determines the precedence of an operator

a private member function that evaluates a postfix expression using the algorithm

studied in Chapter $6.$

Public members:

a default constructor.

a function that sets the data member by an infix expression. The function must

first check if the infix expression is well formed and balanced with brackets by

calling private member function $2$ and $3$ before passing it to the data member.

The function returns true if the operation is successfully performed. Otherwise it

returns false to indicate the parameter expression is not valid.a function that evaluates the expression stored in the data member. This function

should not have any parameters. The function should first convert the infix

expression to its postfix form and then evaluate the resulting postfix expression.

Other requirements

Use the link$-$based Stack with exceptions.

Write a main function to test your calculators. Your program should allow the

user to evaluate additional expressions until the user wants to end the program.

You should not assume that the expression is well$-$formed. The user is asked to

reenter an expression if the expression entered is not well formed.

You should not assume that the parentheses in the expression are balanced. The

user is asked to reenter an expression if the expression entered is not balanced.