Question 1) Write a Java Recursion Descent Parser:

Below is a grammar that represents a restricted form of an infix expression. The restriction is that unless you use parenthesis for clarification, you can only have one '+' or '-' per expression. In addition, '*' and/or '/' may not appear consecutively (A/B*C) -- note that A/B+C/D is valid.

= | + | - = | * | / = | () = A | B | C | D | ... | Z

Thus A+B-C is not valid. Similarly, A/B*C is not valid. Note that A+(B-C) is fine, as is (A/B)*C.

Here is some pseudo-code to aid you in construction of your algorithm:

FIND AN EXPRESSION

• Find a term
• if (next symbol is a + or a -)
  • Find a term

FIND A TERM

• Find a factor
• if (next symbol is a * or a /)
  • Find a factor

FIND A FACTOR

• if (the first symbol is a letter)
  • Done
• else if (the first symbol is a '(' )
  • Find an expression starting at character after '('
  • Check for ')'
• else
  • No factor exists

------

Example input/output:

A+B-C A+B*C A/B+C (A+B)-C (A) (A-B-C)

Your program output should be as follows:

A+B-C is NOT Valid A+B*C is Valid A/B+C is Valid (A+B)-C is Valid (A) is Valid (A-B-C) is NOT Valid