BARC CS 2018 Nuclear Quiz -1 (Algo)

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Question 1

A machine needs a minimum of 100 sec to sort 1000 names by quick sort. The minimum time needed to sort 100 names will be approximately _____ sec

• A4.6
• B6.64
• C2
• D7

Question 2

Consider the hashing table with ‘m’ slots and ‘n’ keys. If the expected number of probes in unsuccessful search is 3 then find the expected number of probes in a successful search.

• A1.647
• B1.234
• C1.511
• D1.434

Question 3

Consider the vertices and that are simultaneously on the function call stack at some point during the execution of depth-first search from vertex s in a digraph. Which of the following must be true?
I. There exist directed path from s to and directed path from s to .
II. There exist both a directed path from to and a directed path from to
III. If there is no directed path from to then there exist a directed path from to
Which of the above statements is/are true?

• AI only
• BI and II only
• CI and III only
• DI, II and III

Question 4

In tower of Hanoi we need 3 needles and 6 disks, how many total no of moves to solve this problem?

• A63
• B49
• C21
• D58

Question 5

Which of the following statement is false?

• AThere exists a function f(n) such that f(n) is Ω(n²) and is O(n³) but is neither θ(n²) nor θ(n³).
• BThere exist undirected graphs on which BFS traversal takes time θ(|v|).
• CWe can compute the strongly connected components of a DAG in time O(|v|).
• DLet G be a digraph with ‘n’ nodes and ‘s’ one of its nodes. The discovery edges found by DFS starting from ‘s’ always form a tree with (n – 1) edges.

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