The prefix expression is *−+abc+d*ef. Evaluate the expression for a = 10, b =…

Concept

In a valid binary prefix expression, every operator precedes exactly two operands or complete subexpressions. Therefore, an expression with n operands requires n − 1 binary operators.

A reliable evaluation method is to scan from right to left: push operands, and whenever an operator appears, combine the next two available values in their original left-to-right order.

Application

1. Count the tokens: the operands are a, b, c, d, e, and f (six operands), while the operators are *, −, +, +, and * (five operators). Thus, no operator is missing.

2. The prefix parse is * (− (+ a b) c) (+ d (* e f)).

3. Evaluate + a b = 10 + 2 = 12.

4. Then evaluate − 12 c = 12 − 5 = 7.

5. Evaluate * e f = 4 × 1 = 4.

6. Then evaluate + d 4 = 3 + 4 = 7.

7. Finally, the outer multiplication gives 7 × 7 = 49.

Cross-check

The parse consumes all six operands and all five operators exactly once. It also leaves a single value on the evaluation stack, confirming that the prefix expression is complete and its value is 49.