Generate syntax tree for simple math operations

Question

I am trying to generate a syntax tree, for a given string with simple math operators (+, -, *, /, and parenthesis). Given the string \"1 + 2 * 3\":

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Answer 1

I built a fun little calculator once and had the same problem as you, which I solved by building the syntax tree without keeping the order precedence in mind,firstly. Each node has a precedence value, and when eval'ing non-constants, I'd check the left node: if it has lower precedence, I'd rotate the tree clockwise: bring it into evaluation and evaluate that first, likewise for the right node. then I'd just try to evaluate again. It seemed to work well enough for me.