I remember there's some Knuth coverage of this topic where it's referred to as a 'shunting' problem, but I didn't try that approach. Instead, I tried to write code that remembered where the operators were by allocating 4 arrays of the same length, one for each of the operators +. -. * and /. My code went through the input string once and marked the locations of the operators. Then it processed the operator arrays in order of precedence. I started to bobble here because I couldn't think through how to manage the temporary results and ran out of time, handwaving some potential solutions.