What Determines Evaluation Order in a Prefix (Polish Notation) Expression?

An online assessment includes this multiple-choice question. Which of the following factors determine the order of evaluation of a prefix expression? - **A.** Precedence of operators - **B.** Associativity of operators - **C.** Both precedence and associativity - **D.** Neither precedence nor associativity Choose one option and justify it with a small example. In a prefix expression (Polish notation), each operator is written before its operands, so the infix expression `2 + 3` is written `+ 2 3`. ```hint Draw the trees Write `* + 2 3 4` and `+ 2 * 3 4` as expression trees, and notice what you relied on to group each one. ``` ```hint Where the rules come from Ask why `2 + 3 * 4` needs a rule before anyone can evaluate it, and whether a prefix string can leave the same question open. ``` ### Clarifying Questions - Does every operator take a fixed number of operands, for example is `-` always binary? - Does "order of evaluation" mean which operator applies to which operands, or the order in which an implementation happens to compute independent subexpressions? - May the expression be assumed to be well formed? ### What a Strong Answer Covers - The correct option, with the reason a prefix expression has only one possible grouping - What precedence and associativity do in infix notation, with an example of each - The assumption that makes prefix notation unambiguous, and what breaks without it - How a prefix expression is evaluated in a single pass, including the operand order for non-commutative operators ### Follow-up Questions - Evaluate `- * 3 4 / 8 2` and describe the procedure you used. - Convert the infix expressions `a - b - c` and `2 ^ 3 ^ 2` (with `^` as exponentiation) to prefix. Where do precedence and associativity come back into play? - If `-` may be either unary negation or binary subtraction, what values can `- - 5 3` have?