Top MCQs on QuickSort Algorithm with Answers

Question 1

What is recurrence for worst case of QuickSort and what is the time complexity in Worst case?

• Recurrence is T(n) = T(n-2) + O(n) and time complexity is O(n^2)
• Recurrence is T(n) = T(n-1) + O(n) and time complexity is O(n^2)
• Recurrence is T(n) = 2T(n/2) + O(n) and time complexity is O(nLogn)
• Recurrence is T(n) = T(n/10) + T(9n/10) + O(n) and time complexity is O(nLogn)

Question 2

Suppose we have an O(n) time algorithm that finds the median of an unsorted array. Now consider a QuickSort implementation where we first find the median using the above algorithm, then use the median as a pivot. What will be the worst-case time complexity of this modified QuickSort?

• O(n^2 Logn)

• O(n^2)

• O(n Logn Logn)

• O(nLogn)

Question 3

Which of the following is not a stable sorting algorithm in its typical implementation.

• Insertion Sort

• Merge Sort

• Quick Sort

• Bubble Sort

Question 4

Which of the following sorting algorithms in its typical implementation gives best performance when applied on an array which is sorted or almost sorted (maximum 1 or two elements are misplaced).

• Quick Sort

• Heap Sort

• Merge Sort

• Insertion Sort

Question 5

Given an unsorted array. The array has this property that every element in the array is at most k distance from its position in a sorted array where k is a positive integer smaller than the size of an array. Which sorting algorithm can be easily modified for sorting this array and what is the obtainable time complexity?

• Insertion Sort with time complexity O(kn)

• Heap Sort with time complexity O(nLogk)

• Quick Sort with time complexity O(kLogk)

• Merge Sort with time complexity O(kLogk)

Question 6

Suppose we are sorting an array of eight integers using quicksort, and we have just finished the first partitioning with the array looking like this:

2  5  1  7  9  12  11  10 

Which statement is correct?

• The pivot could be either the 7 or the 9.
• The pivot could be the 7, but it is not the 9
• The pivot is not the 7, but it could be the 9
• Neither the 7 nor the 9 is the pivot.

Question 7

You have to sort 1 GB of data with only 100 MB of available main memory. Which sorting technique will be most appropriate?

• Heap sort
• Merge sort
• Quick sort
• Insertion sort

Question 8

In quick sort, for sorting n elements, the (n/4)th smallest element is selected as a pivot using an O(n) time algorithm. What is the worst-case time complexity of the quick sort?

(A) [Tex]\\theta [/Tex](n)

(B) [Tex]\\theta [/Tex](n*log(n))

(C) [Tex]\\theta [/Tex](n²)

(D) [Tex]\\theta [/Tex](n^{2 log n})

• A

• B

• C

• D

Question 9

Consider the Quicksort algorithm. Suppose there is a procedure for finding a pivot element that splits the list into two sub-lists each of which contains at least one-fifth of the elements. Let T(n) be the number of comparisons required to sort n elements. Then

• T(n) <= 2T(n/5) + n

• T(n) <= T(n/5) + T(4n/5) + n

• T(n) <= 2T(4n/5) + n

• T(n) <= 2T(n/2) + n

Question 10

Which sorting algorithms is most efficient to sort string consisting of ASCII characters?

• Quick sort
• Heap sort
• Merge sort
• Counting sort