Infix Arithmetic Expression Problem

I have gotten this question in an interview before and wanted to work through it to get it right. Let me know if you find a better way!

Question

Write a function that given an infix arithmetic expression, outputs a prefix version (the output order is unimportant as long as it evaluates to the same result).

For example: 3 becomes 3 1 + 2 becomes (+ 1 2) 3 + 1 - 2 becomes (- (+ 3 1) 2)

1 + 2 * 5 becomes (+ 1 (* 2 5)) 2 + 3 * 4 / 5 becomes (+ 2 (/ (* 3 4) 5) 1 + 3 * 4 - 8 becomes (- (+ 1 (* 3 4) 8)

Quick notes:

• Parentheses in the output are not important - they are only in the examples for readability.
• You can assume input and output are given as arrays of strings, e.g. [“3”, “+”, “1”, … etc.]
• You can assume there are convenience functions such as isOperator.