GATE DA Programming, Data structure and Algorithms Quiz

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Question 1

Let F(n) denote the maximum number of comparisons made while searching for an entry in a sorted array of size 𝑛 using binary search. Which ONE of the following options is TRUE?

  • F(n)=F(⌊n/2⌋)+1

  • F(n)=F(⌊n/2⌋)+F(⌈n/2⌉)

  • F(n)=F(⌊n/2⌋)

  • F(n)=F(n-1)+1

Question 2

Consider the following python code:

Python 
def count(child_dict, i):
       if i not in child_dict.keys():
               return 1
      ans = 1
      for j in child_dict[i]:
                 ans += count(child_dict, j)
      return ans

child_dict = dict()
child_dict[0] = [1,2]
child_dict[1] = [3,4,5]
child_dict[2] = [6,7,8]
print(count(child_dict,0))

Which ONE of the following is the output of this code?

  • 6

  • 1

  • 8

  • 9

Question 3

Consider the following Python function:1

Python 
def fun(D, s1, s2):
 if s1 < s2:
 D[s1], D[s2] = D[s2], D[s1]
 fun(D, s1+1, s2-

What does this Python function fun() do? Select the ONE appropriate option below.
 

  • It finds the smallest element in D from index s1 to s2, both inclusive. 

  • It performs a merge sort in-place on this list D between indices s1 and s2, both inclusive.
     

  • It reverses the list D between indices s1 and s2, both inclusive

  • It swaps the elements in D at indices s1 and s2, and leaves the remaining elements unchanged.
     

Question 4

Match the items in Column 1 with the items in Column 2 in the following tab
 

Column 1Column 2
p. First In First Out
q. Lookup Operation
r. Last In First Out		i. Stacks
ii. Queues
iii. Hash Tables

  • (p) − (ii), (q) − (iii), (r) − (i)

  • (p) − (ii), (q) − (i), (r) − (iii)

  • (p) − (i), (q) − (ii), (r) − (iii)

  • (p) − (i), (q) − (iii), (r) − (ii)

Question 5

Consider the following tree traversals on a full binary tree:

1.PreOrder

2.Inorder

3.PostOrder

Which of the following traversal options is/are suffiecient to uniquely reconstruct the full Binary Tree?

  • (i) and (ii)

  • (ii) and (iii)

  • (i) and (iii)

  • (ii) only 

Question 6

Consider sorting the following array of integers in ascending order using an in-place Quicksort algorithm that uses the last element as the pivot.

60708090100

The minimum number of swaps perfoemed during this quicksort ?

  • 0

  • 1

  • 2

  • 4

Question 7

Consider the following sorting algorithms:

(i) Bubble sort

(ii) Insertion sort

(iii) Selection sort

Which ONE among the following choices of sorting algorithms sorts the numbers in the array [4, 3, 2, 1, 5] in increasing order after exactly two passes over the array?

  • (i) only

  • (iii) only

  • (i) and (iii) only

  • (ii) and (iii) only

Question 8

Consider the directed acyclic graph (DAG) below:

GATE-DA-PYQ-2024-5

Which of the following is/are valid vertex orderings that can be obtained from a topological sort of the DAG?

  • P Q R S T U V

  • P R Q V S U T

  • P Q R S V U T

  • P R Q S V T U

Question 9

Let H,𝐼, 𝐿, and 𝑁 represent height, number of internal nodes, number of leaf nodes, and the total number of nodes respectively in a rooted binary tree. Which of the following statements is/are always TRUE?

  • 𝐿 ≤ 𝐼 + 1

  • 𝐻 + 1 ≤ 𝑁 ≤ 2 𝐻+1 − 1

  • 𝐻 ≤ 𝐼 ≤ 2 𝐻 − 1

  • 𝐻 ≤ 𝐿 ≤ 2 𝐻−1

Question 10

Consider performing uniform hashing on an open address hash table with load factor [Tex]\alpha = \frac{n}{m} < 1[/Tex], where 𝑛 elements are stored in the table with m slots. The expected number of probes in an unsuccessful search is at most [Tex]\frac{1}{1-\alpha}[/Tex]. Inserting an element in this hash table requires at most ______ probes, on average.

  • [Tex]n\frac{1}{1-\alpha}[/Tex]

  • [Tex]\frac{1}{1-\alpha}[/Tex]

  • [Tex]1+\frac{\alpha}{2}[/Tex]

  • [Tex]\frac{1}{1+\alpha}[/Tex]

There are 20 questions to complete.

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