Top MCQs on Complexity Analysis of Algorithms with Answers

Question 111

The following statement is valid. log(n!) = [Tex]\\theta [/Tex](n log n).

• True

• False

Question 112

Which of the following is not true about comparison-based sorting algorithms?

• The minimum possible time complexity of a comparison-based sorting algorithm is O(n(log(n)) for a random input array

• Any comparison based sorting algorithm can be made stable by using position as a criteria when two elements are compared

• Counting Sort is not a comparison based sorting algorithm

• Heap Sort is not a comparison based sorting algorithm.

Question 113

Which of the following is not O(n²)?

• (15) * n²

• n^1.98

• n³/(sqrt(n))

• (20) * n²

Question 114

If we use Radix Sort to sort n integers in the range (n^k/2,n^k], for some k>0 which is independent of n, the time taken would be?

• Θ(n)

• Θ(kn)

• Θ(nlogn)

• Θ(n²)

Question 115

A problem in NP is NP-complete if  

• It can be reduced to the 3-SAT problem in polynomial time

• The 3-SAT problem can be reduced to it in polynomial time

• It can be reduced to any other problem in NP in polynomial time

• Some problem in NP can be reduced to it in polynomial time

Question 116

Which one of the following statements is TRUE for all positive functions f (n)?

• [Tex]f(n^{2}) = \theta (f(n^{2}))  [/Tex], when f (n) is a polynomial

• [Tex]f(n^{2}) = o (f(n^{2}))[/Tex]

• [Tex]f(n^{2}) = O(f(n^{2}))  [/Tex], when f (n) is an exponential function

• [Tex]f(n^{2}) = Ω(f(n^{2}))[/Tex]

Question 117

What is the time complexity of the following function?

void A (int n)
{
         int i, j, k;
         for (i=1; i<=n; i++)
             {
                  for (j =1; j <=i; j++)
                        {
                              for (k =1; k< = 133; k++)
                                       {
                                             X=Y+Z;
                                        }
                         }
               }
}

• n^3

• nlogn

• n^2

• loglogn

Question 118

O(n) is the worst case time complexity, so among the given options it can represent :-

• O(n^2)

• O(1)

• O(nlogn)

• None of the above