1. What does time complexity measure in an algorithm?

A . Number of operations executed

B . Amount of memory used

C . Number of lines of code

D . Input size

Answer

2. Which of the following best describes space complexity?

A . The amount of time an algorithm takes to run

B . The amount of memory an algorithm requires to execute

C . The number of inputs an algorithm can handle

D . The number of times an algorithm loops

Answer

3. What is the space complexity of an algorithm that creates a new array of size n?

A . O(1)

B . O(n)

C . O(log n)

D . O(n^2)

Answer

4. What is the time complexity of a binary search algorithm?

A . O(1)

B . O(n)

C . O(log n)

D . O(n^2)

Answer

5. What is the purpose of asymptotic notation in algorithm analysis?

A . To precisely measure the exact number of operations in an algorithm

B . To provide a rough estimate of algorithmic performance

C . To compare algorithms based on their exact execution times

D . To simplify the comparison of algorithms based on their growth rates

Answer

6. Which asymptotic notation represents the worst-case time complexity of an algorithm?

A . Θ(n)

B . O(n)

C . Ω(n)

D . All of the above

Answer

7. Which notation describes an Lower bound on the time complexity of an algorithm?

A . O(n)

B . Ω(n)

C . Θ(n)

D . All of the above

Answer

8. What does Θ(n) represent in asymptotic notation?

A . Best-case time complexity

B . Average-case time complexity

C . Tight bound on the time complexity

D . Worst-case time complexity

Answer

9. Which of the following is true about the relationship between O(n) and Ω(n)?

A . O(n) is always greater than Ω(n)

B . Ω(n) is always greater than O(n)

C . O(n) and Ω(n) are equal

D . There`s no relationship between O(n) and Ω(n)

Answer

10. What is the asymptotic notation for constant time complexity?

A . O(1)

B . O(n)

C . O(log n)

D . O(n^2)

Answer

11. What is a recurrence relation?

A . A relation between two variables that recurs infinitely

B . A relation between two functions that recurs infinitely

C . A mathematical expression that defines a function in terms of its value at smaller inputs

D . A mathematical expression that defines a function in terms of its value at larger inputs

Answer

12. Which of the following is a common notation for a recurrence relation?

A . R(n) = R(n-1) + R(n-2)

B . F(n) = F(n+1) - F(n-1)

C . P(n) = P(n^2)

D . Q(n) = 2 * Q(n/2)

Answer

13. What is the base case in a recurrence relation?

A . The case where the recurrence relation is true for all values of n

B . The case where the recurrence relation is true for some specific value of n

C . The smallest input value(s) for which the recurrence relation is defined directly

D . The largest input value(s) for which the recurrence relation is defined directly

Answer

14. Which method is commonly used to solve recurrence relations?

A . Iterative method

B . Dynamic programming

C . Master theorem

D . All of the above

Answer

15. What is the solution to the recurrence relation T(n) = 2T(n/2) + n?

A . O(n)

B . O(n log n)

C . O(n^2)

D . O(2^n)

Answer

16. In the Master Theorem, what does "a" represent in the form T(n) = aT(n/+ f(n)?

A . The number of subproblems

B . The ratio of subproblem size to original problem size

C . The coefficient of the leading term in the recurrence relation

D . The base case value

Answer

17. Which case of the Master Theorem applies when the work done at each level of recursion is asymptotically equal?

A . Case 1

B . Case 2

C . Case 3

D . None of the above

Answer

18. What is the time complexity of the recurrence relation T(n) = T(n/3) + T(2n/3) + n?

A . O(n)

B . O(n log n)

C . O(n^2)

D . O(n^3)

Answer

19. What is the Master Theorem used for?

A . Solving differential equations

B . Solving recurrence relations

C . Analyzing algorithmic time complexity

D . Finding prime numbers

Answer

20. What is the Master Theorem based on?

A . Divide and conquer strategy

B . Dynamic programming

C . Linear algebra

D . Graph theory

Answer

21. What is the time complexity of the recurrence relation T(n) = 4T(n/2) + n^2 using the Master Theorem?

A . O(n)

B . O(n log n)

C . O(n^2)

D . O(n^2 log n)

Answer

22. When applying the Master Theorem, what is compared to determine the complexity?

A . The number of subproblems and the size of each subproblem

B . The size of the original problem and the size of the subproblems

C . The number of recursive calls and the base case value

D . The coefficients of the leading terms in the recurrence relation

Answer

23. Which case of the Master Theorem applies when the work done at each level of recursion decreases geometrically?

A . Case 1

B . Case 2

C . Case 3

D . None of the above

Answer

24. What is the time complexity of binary search in the worst-case scenario?

A . O(1)

B . O(log n)

C . O(n)

D . O(n^2)

Answer

25. Quick sort is an example of a sorting algorithm based on which strategy?

A . Dynamic programming

B . Greedy approach

C . Divide and conquer

D . Backtracking

Answer

26. What is the worst-case time complexity of quick sort?

A . O(n)

B . O(n log n)

C . O(n^2)

D . O(log n)

Answer

27. What is the time complexity of merge sort in all cases?

A . O(n)

B . O(n log n)

C . O(n^2)

D . O(log n)

Answer

28. Strassen`s matrix multiplication is an algorithm that multiplies two matrices using which approach?

A . Brute force

B . Greedy approach

C . Dynamic programming

D . Divide and conquer

Answer

29. What is the time complexity of Strassen`s matrix multiplication algorithm?

A . O(n)

B . O(n log n)

C . O(n^2)

D . O(n^log7)

Answer

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Relevant Materials :

☞ Design and Analysis of Algorithms MCQs - Unit-1 - [ DAA ]

☞ Design and Analysis of Algorithms MCQs - Unit-2 - [ DAA ]

☞ Design and Analysis of Algorithms MCQs - Unit-3 - [ DAA ]

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