Directions: Please answer the following questions.

1. Write specifications using UML notation for a function that computes the sum of the first five positive integers in an array of n arbitrary integers.

2. What is an abstract data type?

3. What steps should you take when designing an ADT?

4. The following function computes the sum of the first n ≥ 1 integers. Show how this function satisfies the properties of a recursive function.

5. Given an integer n > 0, write a recursive function countDown that writes the integers n, n - 1, . . . , 1. Hint: What task can you do and what task can you ask a friend to do for you?

6. In the previous definition of writeArrayBackward, why does the base case occur when the value of first exceeds the value of last?

7. Write a recursive function that computes and returns the product of the first n ≥ 1 real numbers in an array.

8. What happens to the array items when the method add cannot add another entry to it, because it is already full?

9. If a client of ArrayBag creates a bag aBag and a vector v containing five items, what happens to those items after the statement v = aBag.toVector() executes?

10. What is an advantage and a disadvantage of calling the method getFrequencyOf from contains?

11. Why are only a few changes necessary to reuse the code in Listing 3-2? How would you implement the changes using the "find and replace" functionality of a text editor or IDE?

12. Why is a LinkedBag object not concerned about becoming full?

13. How many assignment operations does the method that you wrote for the previous question require?

14. Consider the language of these character strings: $, cc$d, cccc$dd, cccccc$ddd, and so on. Write a recursive grammar for this language.

15. Write the prefix expression that represents the following infix expression: (a / b) * c - (d + e) * f