Ha ha, for my parsers I’ve reinvented the wheel and created modification of this algorithm with combined operand/operation stack. In my stack I have operands (A) or operands with incomplete operation (A+). Each stack element have ‘level’ which corresponds to operator precedence and incoming operator combines stack elements with level higher than operator level. At the end of expression I put dummy operator with lowest level.

For example, parsing token sequence A * B + C * D [end]

```
A
A*
A* B
(A*B)+ <- A* and B have higher level than +
(A*B)+ C
(A*B)+ C*
(A*B)+ C* D
((A*B)+(C*D))= <- (A*B)+, C* and D have higher level than [end]
```

If someone decides to use my version instead of original I can give additional details.

I wrote an article about an algorithm that doesn’t seem to be very widely known, but should be! It’s called the “shunting-yard algorithm” and is used to parse arithmetic expressions in infix notation. Check out the article here: http://www.reedbeta.com/blog/2011/12/11/the-shunting-yard-algorithm/