How to parse mathematical expressions involving parentheses

@Rising Star [I hoped to add this as a comment, but the formatting failed]

It may seem counterintuitive, but a binary tree is both simpler and more flexible. A node, in this case, would be either a constant (number) or an operator. A binary tree makes life somewhat easier when you decide to extend the language with elements like control flow, and functions.

Example:

((3 + 4 - 1) * 5 + 6 * -7) / 2

                  '/'
                /     \
              +        2
           /     \
         *         *
       /   \     /   \
      -     5   6     -7
    /   \
   +     1
 /   \
3     4

In the case above the scanner has been programmed to read '-' followed by a series of digits as a single number, so "-7" gets returned as the value component of the "number" token. '-' followed by whitespace is retured as a "minus" token. This makes the parser somewhat easier to write. It fails on the case where you want "-(x * y)", but you can easily change the expression to "0 - exp"

Ages ago when working on a simple graphing app, I used this algorithm (which is reasonably easy to understand and works great for simple math expressions like these) to first turn the expression into RPN and then calculated the result. RPN was nice and fast to execute for different variable values.

Of course, language parsing is a very wide topic and there are many other ways of going about it (and pre-made tools for it too)