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## Count Inversion MCQs

**1. What is the time complexity of the code that uses merge sort for determining the number of inversions in an array?**

a) O(n2)

b) O(n)

c) O(log n)

d) O(n log n)

**Answer: **O(n log n)

**2. What is the time complexity of the code that uses self balancing BST for determining the number of inversions in an array?**

a) O(n2)

b) O(n)

c) O(log n)

d) O(n log n)

**Answer: **O(n log n)

**3. What is the space complexity of the code that uses merge sort for determining the number of inversions in an array?**

a) O(n)

b) O(log n)

c) O(1)

d) O(n log n)

**Answer: **O(n)

**4. Under what condition the number of inversions in an array are maximum?**

a) when the array is sorted

b) when the array is reverse sorted

c) when the array is half sorted

d) depends on the given array

**Answer: **when the array is reverse sorted

**5. Under what condition the number of inversions in an array are minimum?**

a) when the array is sorted

b) when the array is reverse sorted

c) when the array is half sorted

d) depends on the given array

**Answer: **when the array is sorted

**6. How many inversions are there in the array arr = {1,5,4,2,3}?**

a) 0

b) 3

c) 4

d) 5

**Answer: **5

**7. Which of the following form inversion in the array arr = {1,5,4,2}?**

a) (5,4), (5,2)

b) (5,4), (5,2), (4,2)

c) (1,5), (1,4), (1,2)

d) (1,5)

**Answer: **(5,4), (5,2), (4,2)

**8. What does the number of inversions in an array indicate?**

a) mean value of the elements of array

b) measure of how close or far the array is from being sorted

c) the distribution of values in the array

d) median value of the elements of array

**Answer: **measure of how close or far the array is from being sorted

**9. How many inversions does a sorted array have?**

a) 0

b) 1

c) 2

d) cannot be determined

**Answer: **0

**10. What is the condition for two elements arr[i] and arr[j] to form an inversion?**

a) arr[i]<arr[j]

b) i < j

c) arr[i] < arr[j] and i < j

d) arr[i] > arr[j] and i < j

**Answer: **arr[i] > arr[j] and i < j