Paper 2

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MCQs on Sorting

1. Which of the following is not a stable sorting algorithm?

a) Insertion sort
b) Selection sort
c) Bubble sort
d) Merge sort

ANSWER: B

2. Which of the following is a stable sorting algorithm?

a) Merge sort
b) Typical in-place quick sort
c) Heap sort
d) Selection sort

ANSWER: A

3. Which of the following is not an in-place sorting algorithm?

a) Selection sort
b) Heap sort
c) Quick sort
d) Merge sort

ANSWER: D

4. Running merge sort on an array of size n which is already sorted is

a) O(n)
b) O(nlogn)
c) O(n²)
d) None

ANSWER: B

5. The time complexity of a quick sort algorithm which makes use of median, found by an O(n) algorithm, as pivot element is

a) O(n²)
b) O(nlogn)
c) O(nloglogn)
d) O(n)

ANSWER: B

6. Which of the following is not a noncomparison sort?

a) Counting sort
b) Bucket sort
c) Radix sort
d) Shell sort

ANSWER: D

7. The time complexity of heap sort in worst case is

a) O(logn)
b) O(n)
c) O(nlogn)
d) O(n²)

ANSWER: C

8. If the given input array is sorted or nearly sorted, which of the following algorithm gives the best performance?

a) Insertion sort
b) Selection sort
c) Quick sort
d) Merge sort

ANSWER: A

9. Which of the following algorithm pays the least attention to the ordering of the elements in the input list?

a) Insertion sort
b) Selection sort
c) Quick sort
d) None

ANSWER: B

10. Consider the situation in which assignment operation is very costly. Which of the following sorting algorithm should be performed so that the number of assignment operations is minimized in general?

a) Insertion sort
b) Selection sort
c) Heap sort
d) None

ANSWER: B

11. Time complexity of bubble sort in best case is

a) θ (n)
b) θ (nlogn)
c) θ (n²) 
d) θ (n(logn) ²)

ANSWER: A

12. Given a number of elements in the range [0….n³]. which of the following sorting algorithms can sort them in O(n) time?

a) Counting sort
b) Bucket sort
c) Radix sort
d) Quick sort

ANSWER: C

13. Which of the following algorithms has lowest worst case time complexity?

a) Insertion sort
b) Selection sort
c) Quick sort
d) Heap sort

ANSWER: D

14. Which of the following sorting algorithms is/are stable

a) Counting sort
b) Bucket sort
c) Radix sort
d) All of the above

ANSWER: D

15. Counting sort performs …………. Numbers of comparisons between input elements.

a) 0
b) n
c) nlogn
d) n² 

ANSWER: A

16. The running time of radix sort on an array of n integers in the range [0……..n⁵ -1] when using base 10 representation is

a) θ (n)
b) θ (nlogn)
c) θ (n²)
d) none

ANSWER: B

17. The running time of radix sort on an array of n integers in the range [0……..n⁵ -1] when using base n representation is

a) θ (n)
b) θ (nlogn)
c) θ (n²)
d) None

ANSWER: A

18. Which of the following sorting algorithm is in-place

a) Counting sort
b) Radix sort
c) Bucket sort
d) None

ANSWER: B

19. The radix sort does not work correctly if each individual digit is sorted using

a) Insertion sort
b) Counting sort
c) Selection sort
d) Bubble sort

ANSWER: C

20. Which of the following sorting algorithm has the running time that is least dependant on the initial ordering of the input?

a) Insertion sort
b) Quick sort
c) Merge sort
d) Selection sort

ANSWER: D

21. Time complexity to sort elements of binary search tree is

a) O(n)
b) O(nlogn)
c) O(n²)
d) O(n²logn)

ANSWER: A

22. The lower bound on the number of comparisons performed by comparison-based sorting algorithm is 

a) Ω (1)
b) Ω (n)
c) Ω (nlogn)
d) Ω (n²)

ANSWER: C

23. Which of the following algorithm(s) can be used to sort n integers in range [1…..n³] in O(n) time?

a) Heap sort
b) Quick sort
c) Merge sort
d) Radix sort



24. Which of the following algorithm design technique is used in the quick sort algorithm?

a) Dynamic programming
b) Backtracking
c) Divide-and-conquer
d) Greedy method

ANSWER: C

25. Merge sort uses

a) Divide-and-conquer
b) Backtracking
c) Heuristic approach
d) Greedy approach

ANSWER: A

26. For merging two sorted lists of size m and n into sorted list of size m+n, we require comparisons of

a) O(m)
b) O(n)
c) O(m+n)
d) O(logm + logn)

ANSWER: C

27. A sorting technique is called stable if it

a) Takes O(nlogn) times
b) Maintains the relative order of occurrence of non-distinct elements
c) Uses divide-and-conquer paradigm
d) Takes O(n) space

ANSWER: B

28. In a heap with n elements with the smallest element at the root, the seventh smallest element can be found in time

a) θ (nlogn)
b) θ (n)
c) θ (logn)
d) θ (1)

ANSWER: A

29. What would be the worst case time complexity of the insertion sort algorithm, if the inputs are restricted to permutation of 1…..n with at most n inversion?

a) θ (n²)
b) θ (nlogn)
c) θ (n^1.5)
d) θ (n)

ANSWER: D

30. In a binary max heap containing n numbers, the smallest element can be found in time

a) θ (n)
b) θ (logn)
c) θ (loglogn)
d) θ (1)

ANSWER: A