Quiz 4 Solutions

Wed Nov 15

You have up to 25 minutes. You may use a standard calculator if necessary, but no text book, notes, or computer.

1. Evaluate the following prefix expression. What result does it produce?

   (- (* 3 (+ 1 7)) (+ 9 4))

   ⇒ (- (* 3 (+ 1 7)) (+ 9 4))
   ⇒ (- (* 3 8) (+ 9 4))
   ⇒ (- 24 (+ 9 4))
   ⇒ (- 24 13)
   ⇒ 11

2. Evaluate the following postfix expression. What result does it produce?

   2 5 2 + 4 * 1 - *

   Evaluate the operators left to right. Each one refers to the previous two things in the list.

   2 5 2 + 4 * 1 - *
   2 7 4 * 1 - *
   2 28 1 - *
   2 27 *
   54

4. Above is a tree representing an arithmetic expression. Write the corresponding expression in:

• Prefix notation: (* (* 2 5) (+ 7 2))

• Infix notation: 2 * 5 * (7 + 2)

3. Convert the following infix expression to postfix notation:

   3 * (2 + 8) - (6 + 1)

   The postfix expression is:

   3 2 8 + * 6 1 + -

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