Recursive Descent Parser

Write a program in Java where you consider the following expression BNF:

< expression> ::= < term> + < expression> | < term> - < expression> | < term>
< term> ::= < factor> * < term> | < factor> / < term> | < factor>
< factor> ::= < digit> | ( < expression> )
< digit> ::= 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9

Using recursive descent, and only recursive descent, scan expressions that adhere to this BNF to build their expression tree; write an integer valued function that scans the tree to evaluate the expression represented by the tree.

Input:

  • A numeric expression adhering to this BNF.

Output:

  • Some representation of the expression tree.
  • The result of evaluating the expression.
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