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Data Structures and Algorithms MCQ - Performance Analysis of Algorithms and Recurrences

116 For merging two sorted lists of sizes m and n into a sorted list of size m+n, we required comparisons of

We use merge sorting and finally we get comparison O (m + n)

117 If one uses straight two-way merge sort algorithm to sort the following elements in ascending order:
20, 47, 15, 8, 9, 4, 40, 30, 12, 17
then the order of these elements after second pass of the algorithm is?

118 Assume that a mergesort algorithm in the worst case takes 30 seconds for an input of size 64. Which of the following most closely approximates the maximum input size of a problem that can be solved in 6 minutes?

Time complexty is O (nlogn)
C * 64 log 64 = 30
(C = 5/14)
for 6 minuts
5/64 * n log n 6 * 60 ⇒ [n = 512]

119 Match the pairs in the following:

List-I		List-II
A.	Straseen's matrix multiplication algorithm	P.	Greedymethod
B.	Kruskal's minimum spanning tree algorithm	Q.	Dynamic programming
C.	Biconnected components algorithm	R.	Divide and Conquer
D.	Floyd's shortest path algorithm	S.	Depth first search

A – R, B–P, C–S, D–Q

120 The minimum number of comparisons required to sort 5 elements is

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Question:

The time complexity of computing the transitive closure of a binary relation on a set of n elements is known to be

A. O(n)
B. O(nlogn)
C. O(n^3/2)
D. O(n³)

Correct answer: D

Explanation:

The time complexity of computing the transitive closure of binary relation on a set of n elements is O (n3).

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