Exam 1 Ch 2

22. For an array containing 2, 3, 5, 6, 9, 13, 16, and 19, what value does a recursive binary search algorithm return when it searches for 10? a) -1 b) 0 c) 1 d) 10

a.

23. In a sorted array having SIZE locations, the kth smallest item is given by ______. a) anArray[k-1] b) anArray[k] c) anArray[SIZE-k] d) anArray[SIZE+k]

a.

25. A recursive solution that finds the factorial of n always reduces the problem size by ______ at each recursive call. a) 1 b) 2 c) half d) one-third

a.

27. In the recursive solution to the Towers of Hanoi problem, the number of disks to move ______ at each recursive call. a) decreases by 1 b) increases by 1 c) decreases by half d) increases by half

a.

9. In the box trace for a recursive function, a new box is created each time ______. a) the function is called b) the function returns a value c) an object is created d) an object is initialized

a.

12. Which of the following is a precondition for a method that accepts a number n and computes the nth Fibonacci number? a) n is a negative integer b) n is a positive integer c) n is greater than 1 d) n is an even integer

b.

21. For an array containing 2, 3, 5, 6, 9, 13, 16, and 19, what value does a recursive binary search algorithm return when it searches for 6? a) 1 b) 3 c) 4 d) none of the above

b.

26. In the recursive solution to finding the kth smallest item in an array, the problem size decreases by ______ at each recursive call. a) 1 b) at least 1 c) half d) at least half

b.

28. A recursive solution that finds the factorial of n generates ______ recursive calls. a) n - 1 b) n c) n + 1 d) n * 2

b.

30. Which of the following is a base case for a recursive binary search algorithm? (first is the index of the first item in the array, last is the index of the last item in the array, and mid is the midpoint of the array). a) last > first b) first > last c) 0 <= first d) last <= SIZE-1

b.

5. The base case for a recursive definition of the factorial of n is ______. a) factorial (-1) b) factorial (0) c) factorial (n) d) factorial (n - 1)

b.

7. In the box trace, each box roughly corresponds to a(n) ______. a) recursive relation b) activation record c) base case d) pivot item

b.

1. In a recursive solution, the ______ terminates the recursive processing. a) local environment b) pivot item c) base case d) recurrence relation

c.

13. How many bases cases does a recursive binary search of a sorted array have? a) 0 b) 1 c) 2 d) 3

c.

14. The number of ways to choose k out of n things is ______. a) the number of ways to choose k - 1 out of n - 1 things b) the number of ways to choose k out of n - 1 things c) the sum of the number of ways to choose k - 1 out of n - 1 things and the number of ways to choose k out of n - 1 things d) the product of the number of ways to choose k - 1 out of n - 1 things and the number of ways to choose k out of n - 1 things

c.

16. A recursive method that computes the number of groups of k out of n things has the precondition that ______. a) n is a positive number and k is a nonnegative number b) n is a nonnegative number and k is a positive number c) n and k are nonnegative numbers d) n and k are positive numbers

c.

17. The midpoint of a sorted array has the index ______, where first is the index of the first item in the array, and last is the index of the last item in the array. a) first / 2 + last / 2 b) first / 2 - last / 2 c) (first + last) / 2 d) (first - last) / 2

c.

2. A binary search uses a ______ strategy. a) divide-and-conquer b) sequential c) determine-the-pivot d) smallest-to-largest

a.

11. In a recursive method that writes a string of characters in reverse order, the base case is ______. a) a string with a length of 0 b) a string whose length is a negative number c) a string with a length of 3 d) a string that is a palindrome

a.

15. When you solve a problem by solving two or more smaller problems, each of the smaller problems must be ______ the base case than the original problem. a) closer to b) farther to c) either closer to or the same "distance" from d) either farther to or the same "distance" from

a.

19. Which of the following is NOT a precondition for an array that is to be searched by a recursive binary search algorithm? (first is the index of the first item in the array, last is the index of the last item in the array, and SIZE is size of the array) a) SIZE <= first b) 0 <= first c) last <= SIZE - 1 d) anArray[first] <= anArray[first + 1] <= ... <= anArray[last]

a.

20. What does the following recursive algorithm display? writeBack(in s:string) if (s is empty) return else { Write the first character of s writeBack(the string beginning at the second character of s) } a) nothing b) the first character of s a number of times equal to the length of s c) the string s d) the string s backward

c.

24. A recursive binary search algorithm always reduces the problem size by ______ at each recursive call. a) 1 b) 2 c) half d) one-third

c.

29. In the Fibonacci sequence, which of the following integers comes after the sequence 1, 1, 2, 3? a) 3 b) 4 c) 5 d) 6

c.

6. What is fundamentally wrong with computing the Fibonacci sequence recursively? a) it has two base cases b) each call to the function results in two recursive calls c) it computes the same values over and over d) nothing

c.

8. In the box trace, each box contains all of the following EXCEPT ______. a) the values the function's arguments b) the function's local variables c) the function's execution time d) a placeholder for the value returned by each recursive call from the current box e) the value returned by the function itself

c.

10. What happens if a recursive function never reaches a base case? a) the function returns the correct value b) the function returns an incorrect value c) the function terminates immediately d) an infinite sequence of recursive calls occurs

d.

18. If the value sought by a recursive binary search algorithm is in the array, which of the following is true? a) the algorithm makes the same comparisons as a sequential search b) the algorithm is successful without reaching a base case c) the algorithm searches the entire array d) the algorithm searches only the array half containing the value

d.

3. A ______ is a mathematical formula that generates the terms in a sequence from previous terms. a) local environment b) pivot item c) base case d) recurrence relation

d.

4. The factorial of n is equal to ______. a) n - 1 b) n - factorial (n-1) c) factorial (n-1) d) n * factorial (n-1)

d.