Algebraic expressions are character strings, but since String is a final class, you cannot derive a class of expressions from String. Instead, define an abstract class Expression that can be the basis of other classes of algebraic expressions. Provide methods such as character At, is Operator, and is identifier. Next design and implement a class Infix Expression derived from the class Expression.
Programming Problem 9 of Chapter 6 describes a grammar and a recognition algorithm for infix algebraic expressions. That grammar makes left-to-right association illegal when consecutive operators have the same precedence. Thus, a/b•c is illegal, but both a/ (b* c) and (a/b) * c is legal. Programming Problem 8 of Chapter 7 describes an algorithm to evaluate an infix expression that is syntactically correct by using two stacks.
Include in the class Infix Expression an is Legal method-based on the rec-ognition algorithm given in Chapter 6-and an evaluate method-based on the evaluation algorithm given in Chapter 7. Use one of the ADT stack implementations presented in Chapter 7
