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Data Structures and Algorithms Design Week 2 NPTEL Assignment Answers 2025

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NPTEL Data Structures and Algorithms Design Week 2 Assignment Answers 2025

1. What is the worst-case time complexity of Bubble Sort?

  • O(n2)
  • O(nlogn)
  • O(n)
  • O(logn)
Answer : See Answers

2. What is the best time complexity of the following subroutine as a
function of n? Assume each instruction takes O(1) time only.

sum = 0;
for (i = 1; i < n; i = i*2)
for(j = 0; j < i; j = j+1)
sum = sum + 1;

  • O(n)
  • O(nlogn)
  • O(n2)
  • O(n2logn)
Answer :

3. Arrange the following in increasing order of growth: O(nlogn) O(n2) O(2n) O(n!)

  • O(nlogn)<O(n2)<O(2n)<O(n!)
  • O(nlogn)<O(2n)<O(n2)<O(n!)
  • O(n2)<O(nlogn)<O(n!)<O(2n)
  • O(2n)<O(n!)<O(n2)<O(nlogn)
Answer :

4. If f(n)=nlogn and g(n)=n(logn)2, which is true?

  • f(n)=o(g(n))
  • f(n)=ω(g(n))
  • f(n)=Θ(g(n))
  • g(n)=o(f(n))
Answer :

5. Let f(n)=2logn√, g(n)=(logn)5. Which of the following is true?

  • g(n)=o(f(n))
  • f(n)=o(g(n))
  • f(n)=Θ(g(n))
  • f(n)=ω(n)
Answer :

6. Arrange the following functions in increasing order of asymptotic growth:
1.n1.5
2.nlog2n
3.n−−√logn
4.n0.75

  • 3<4<2<1
  • 2<3<4<1
  • 3<2<4<1
  • 4<3<2<1
Answer : See Answers

7. Consider the following pseudocode:

for i = 1 to n:
j = i
while j > 1:
j = j / 2

What is the time complexity?

  • O(nlogn)
  • O(n)
  • O(logn)
  • O(n2)
Answer :

8. Consider the following pseudocode:

i = 2
while i <= n:
j = 2
while j <= \log i:
j = j * j
i = i * 2

What is the time complexity?

  • O(lognâ‹…logloglogn)
  • O(lognâ‹…loglogn)
  • O(logn)
  • O(n)
Answer :

9. At each index i, the O(n) maximum subarray sum algorithm updates the running sum by:

  • Taking the maximum of the current element and the sum so far plus the current element
  • Taking the minimum of the current element and the sum so far plus the current element
  • Always adding the current element to the sum
  • Comparing the current element to the maximum sum found so far
Answer :

10. What is the time complexity of a brute-force solution that checks all possible subarrays and computes their sums individually?

  • O(n3)
  • O(n2)
  • O(nlogn)
  • O(n!)
Answer : See Answers

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