[justinmeiners]

Doesn't shunting yard solve this pretty simply? Once you have an expression in RPN, building expression trees is pretty easy.

[rbtprograms]

I recently did this same project in Javascript and you're correct, shunting yard is perfect for this.

[MH15]

I did a project with Shunting-Yard in Golang and yes, that's the proper way to do this.