Writing a simple equation parser

Question

What sorts of algorithms would be used to do this (as in, this is a string, and I want to find the answer):

((5 + (3 + (7 * 2))) - (8 * 9)) / 72

Answer 1

You could use either a state machine parser (yacc LALR, etc.), or a recursive descent parser.

The parser could emit RPN tokens to evaluate or compile later. Or, in an immediate interpreter implementation, a recursive descent parser could calculate subexpressions on the fly as it returns from the leaf tokens, and end up with the result.