Quiznetik

Design and Analysis of Algorithms | Set 1

1. Recursion is similar to which of the following?

Correct : B. loop

2. Recursion is a method in which the solution of a problem depends on

Correct : C. smaller instances of the same problem

3. Which of the following problems can’t be solved using recursion?

Correct : D. problems without base case

4. In general, which of the following methods isn’t used to find the factorial of a number?

Correct : A. recursion

5. Which of the following recursive formula can be used to find the factorial of a number?

Correct : C. fact(n) = n * fact(n-1)

6. Suppose the first fibonnaci number is 0 and the second is 1. What is the sixth fibonnaci number?

Correct : A. 5

7. Which of the following is not a fibonnaci number?

Correct : D. 14

8. Which of the following option is wrong?

Correct : D. no method is defined to calculate fibonacci number

9. Which of the following recurrence relations can be used to find the nth fibonacci number?

Correct : D. f(n) = f(n – 1) + f(n – 2)

10. Which of the following gives the sum of the first n natural numbers?

Correct : C. (n+1)c2

11. If GCD of two number is 8 and LCM is 144, then what is the second number if first number is 72?

Correct : D. 16

12. Which of the following is also known as GCD?

Correct : A. highest common divisor

13. Which of the following is coprime number?

Correct : D. 9 and 28

14. In terms of Venn Diagram, which of the following expression gives GCD (Given A ꓵ B ≠ Ø)?

Correct : B. multiplication of a ꓵ b terms

15. What is the GCD according to the given Venn Diagram?

Correct : C. 5

16. What is the GCD of a and b?

Correct : B. gcd (a-b, b) if a>b

17. What is the GCD of 48, 18, 0?

Correct : D. 6

18. Is 9 and 28 coprime number?

Correct : A. true

19. If gcd (a, b) is defined by the expression, d=a*p + b*q where d, p, q are positive integers and a, b is both not zero, then what is the expression called?

Correct : A. bezout’s identity

20. Is gcd an associative function.

Correct : A. true

21. Who gave the expression for the probability and expected value of gcd?

Correct : A. james e. nymann

22. What is the computational complexity of Binary GCD algorithm where a and b are integers?

Correct : A. o (log a + log b)2)

23. LCM is also called as

Correct : B. scm

24. What is the LCM of 8 and 13?

Correct : D. 104

25. Which is the smallest number of 3 digits that is divisible by 2, 4, 8?

Correct : D. 104

26. Which of the following is also known as LCM?

Correct : A. lowest common divisor

27. What is the LCM of two coprime numbers?

Correct : D. multiplication of two coprime numbers

28. In terms of Venn Diagram, which of the following expression gives LCM (Given A ꓵ B ≠ Ø)?

Correct : A. multiplication of a u b terms

29. What is the LCM according to the given Venn Diagram?

Correct : C. 180

30. What is the lcm (a, b)?

Correct : C. lcm (b, a)

31. Is 9 and 28 coprime number.

Correct : A. true

32. What is the following expression, lcm (a, lcm (b, c) equal to?

Correct : D. lcm (lcm (a, b), c)

33. Is lcm an associative function.

Correct : A. true

34. What is the following expression, lcm (a, gcd (a, b)) equal to?

Correct : A. a

35. Which algorithm is the most efficient numerical algorithm to obtain lcm?

Correct : B. euclid’s algorithm

36. Which of the following methods can be used to find the sum of digits of a number?

Correct : D. both recursion and iteration

37. What can be the maximum sum of digits for a 4 digit number?

Correct : C. 36

38. What can be the minimum sum of digits for a 4 digit number?

Correct : B. 1

39. What is the time complexity of the above code used to reverse a string?

Correct : D. checks if a string is a palindrome

40. Which of the following is the binary representation of 100?

Correct : C. 1100100

41. What is the time complexity of the above recursive implementation used to reverse a string?

Correct : B. o(n)

42. What is the time complexity of matrix multiplied recursively by Divide and Conquer Method?

Correct : C. o(n3)

43. How many recursive calls are there in Recursive matrix multiplication by Strassen’s Method?

Correct : B. 7

44. Matrix A is of order 3*4 and Matrix B is of order 4*5. How many elements will be there in a matrix A*B multiplied recursively.

Correct : B. 15

45. If Matrix X is of order A*B and Matrix Y is of order C*D, and B=C then the order of the Matrix X*Y is A*D?

Correct : A. true

46. Is Coppersmith-Winograd algorithm better than Strassen’s algorithm in terms of time complexity?

Correct : A. true

47. Which of the following statement is true about stack?

Correct : A. pop operation removes the top most element

48. What is the space complexity of program to reverse stack recursively?

Correct : C. o(n)

49. Stack can be reversed without using extra space by

Correct : B. using linked list to implement stack

50. Which of the following is considered as the top of the stack in the linked list implementation of the stack?

Correct : B. first node

51. What is the time complexity of the program to reverse stack when linked list is used for its implementation?

Correct : A. o(n)

52. Which of the following takes O(n) time in worst case in array implementation of stack?

Correct : D. pop, push and isempty takes constant time

53. What will be the time complexity of the code to reverse stack recursively?

Correct : D. o(n2)

54. Which of the following sorting algorithm has best case time complexity of O(n2)?

Correct : B. selection sort

55. Which of the following is the biggest advantage of selection sort?

Correct : D. it requires only n swaps under any condition

56. What will be the recurrence relation of the code of recursive selection sort?

Correct : C. t(n) = t(n-1) + n

57. Which of the following sorting algorithm is NOT stable?

Correct : A. selection sort

58. What will be the best case time complexity of recursive selection sort?

Correct : B. o(n2)

59. Recursive selection sort is a comparison based sort.

Correct : A. true

60. What is the average case time complexity of recursive selection sort?

Correct : C. o(n2)

61. What is the bidirectional variant of selection sort?

Correct : A. cocktail sort

62. Which of the following methods can be used to find the largest and smallest element in an array?

Correct : C. both recursion and iteration

63. What is the number of swaps required to sort the array arr={5,3,2,4,1} using recursive selection sort?

Correct : C. 2

64. Which of the following methods can be used to find the largest and smallest number in a linked list?

Correct : C. both recursion and iteration

65. Which of the following techniques can be used to search an element in an unsorted array?

Correct : A. iterative linear search

66. Consider the array {1,1,1,1,1}. Select the wrong option?

Correct : D. no method is defined to search for an element in the given array

67. What is the time complexity of the above recursive implementation of binary search?

Correct : C. o(logn)

68. Which of the following methods can be used to search an element in a linked list?

Correct : A. iterative linear search

69. Can binary search be applied on a sorted linked list in O(Logn) time?

Correct : A. no

70. Recursive program to raise an integer x to power y uses which of the following algorithm?

Correct : C. divide and conquer

71. What is the least time in which we can raise a number x to power y?

Correct : D. o(log y)

72. What is the advantage of iterative code for finding power of number over recursive code?

Correct : B. iterative code requires less space

73. Recursive approach to find power of a number is preferred over iterative approach.

Correct : B. false

74. What is the objective of tower of hanoi puzzle?

Correct : A. to move all disks to some other rod by following rules

75. Recurrence equation formed for the tower of hanoi problem is given by

Correct : C. t(n) = 2t(n-1)+c

76. Tower of hanoi problem can be solved iteratively.

Correct : A. true

77. Minimum time required to solve tower of hanoi puzzle with 4 disks assuming one move takes 2 seconds, will be

Correct : B. 30 seconds

78. Master’s theorem is used for?

Correct : A. solving recurrences

79. How many cases are there under Master’s theorem?

Correct : B. 3

80. What is the result of the recurrences which fall under second case of Master’s theorem (let the recurrence be given by T(n)=aT(n/b)+f(n) and f(n)=nc?

Correct : B. t(n) = o(nc log n)

81. What is the result of the recurrences which fall under third case of Master’s theorem (let the recurrence be given by T(n)=aT(n/b)+f(n) and f(n)=nc?

Correct : C. t(n) = o(f(n))

82. We can solve any recurrence by using Master’s theorem.

Correct : B. false

83. Under what case of Master’s theorem will the recurrence relation of merge sort fall?

Correct : B. 2

84. Under what case of Master’s theorem will the recurrence relation of stooge sort fall?

Correct : A. 1

85. Which case of master’s theorem can be extended further?

Correct : B. 2

86. What is the result of the recurrences which fall under the extended second case of Master’s theorem (let the recurrence be given by T(n)=aT(n/b)+f(n) and f(n)=nc(log n)k?

Correct : C. t(n)= o(nc (log n)k+1

87. Under what case of Master’s theorem will the recurrence relation of binary search fall?

Correct : B. 2

88. 7 T (n/2) + 1/n

Correct : D. cannot be solved using master’s theorem

89. What is the worst case time complexity of KMP algorithm for pattern searching (m = length of text, n = length of pattern)?

Correct : C. o(m)

90. What is the time complexity of Z algorithm for pattern searching (m = length of text, n = length of pattern)?

Correct : A. o(n + m)

91. What is the auxiliary space complexity of Z algorithm for pattern searching (m = length of text, n = length of pattern)?

Correct : B. o(m)

92. The naive pattern searching algorithm is an in place algorithm.

Correct : A. true

93. Rabin Karp algorithm and naive pattern searching algorithm have the same worst case time complexity.

Correct : A. true

94. Which of the following sorting algorithms is the fastest?

Correct : B. quick sort

95. Quick sort follows Divide-and-Conquer strategy.

Correct : A. true

96. What is the worst case time complexity of a quick sort algorithm?

Correct : C. o(n2)

97. Which of the following methods is the most effective for picking the pivot element?

Correct : C. median-of-three partitioning

98. Which is the safest method to choose a pivot element?

Correct : A. choosing a random element as pivot

99. What is the average running time of a quick sort algorithm?

Correct : C. o(n log n)

100. Which of the following sorting algorithms is used along with quick sort to sort the sub arrays?

Correct : C. insertion sort