Algorithms MCQ Quiz in मल्याळम - Objective Question with Answer for Algorithms - സൗജന്യ PDF ഡൗൺലോഡ് ചെയ്യുക

Answer: 1.6 to 1.65

Explanation:

The worst-case happens for the recursive calls on the longer route.

There are 6 such recursive calls to A(n/3) in the worst case.

So, recurrence relation will become like this:

F (n) = 6F(n/3) + O(1)

where O(1) is constant

By using master’s theorem,

a = 6, b =3

λ = 1.63

Answer:3 to 3

Concept:

A minimum spanning tree (MST) or minimum weight spanning tree is a subset of the edges(V – 1 ) of a connected, edge-weighted undirected graph G(V, E) that connects all the vertices together, without any cycles and with the minimum possible total edge weight.

Explanation:

The minimum weight in the graph is 0.1 choosing this we get.

Suppose we get two trees T₁ and T_2.

To connect to those two trees we got 3 possible edges of weight 0.9.

Hence we can choose any one of those 3 edges.

No of Minimum weight spanning tree is 3.

We have to check how many times inner loop will be executed here.

For i=1,

j will run 1 + 2 + 3 + …………. (n times)

For i=2

j will run for 1,3,5, 7, 9, 11,………..(n/2 times)

For i=3

j will run for 1,4,7,10, 13…………… (n/3 times)

So, in this way,

So, Time complexity of given program = Θ (n log n)

The correct answer is Unsupervised Learning.

Key Points 

1. Supervised Learning:

• In supervised learning, the algorithm is trained on a labeled dataset, where the input data is paired with corresponding output labels.
• The goal is to learn a mapping function from input to output so that the algorithm can make predictions or classifications on new, unseen data.

2. Unsupervised Learning:

• In unsupervised learning, the algorithm is given data without explicit instructions on what to do with it.
• The algorithm tries to find patterns, relationships, or structures within the data on its own.
• Clustering algorithms, like k-Means, fall under unsupervised learning because they group similar data points together without using labeled output information.

3. Semi-supervised Learning:

• Semi-supervised learning is a combination of supervised and unsupervised learning.
• It involves a dataset that contains both labeled and unlabeled examples.
• The algorithm is trained on the labeled data, and then it tries to make predictions on the unlabeled data by leveraging the patterns learned from the labeled data.

4. Reinforcement Learning:

• Reinforcement learning involves an agent interacting with an environment and learning to make decisions by receiving feedback in the form of rewards or punishments.
• The agent learns to take actions that maximize the cumulative reward over time.
• Unlike supervised learning, where the algorithm is provided with explicit labeled examples, in reinforcement learning, the algorithm learns by trial and error.

In the case of the k-Means algorithm, it is unsupervised learning because it doesn't rely on labeled output data. Instead, it aims to partition the input data into clusters based on similarity, without using predefined class labels.

Concept:

External sorting is sorting the lists that are so large that the whole list cannot be contained in the internal memory of a computer.

Explanation:

All heap sort, quick sort and insertion sort uses the concept of internal sorting. In internal sorting, data that has to be stored will be in main memory always and it implies faster access.

Important Point:

Example of external sorting is merge sort algorithm

External merge sort algorithm steps:

→ Data is stored in intermediate files

→ intermediate files are sorted and merged.

External sorting algorithms by external memory model in which a cache or internal memory is considered and an unbounded external memory is divided into blocks and time complexity is the number of memory transfers between internal and external memory.

Data:

K₅ is a complete graph with 5 vertex, that is, n = 5

Formula:

maximum number of spanning tree possible = nn - 2

Calculation:

maximum number of spanning tree = 5^5-2 = 125

Concept:

Sin function value ranges from -1 to + 1. (-1, 0, 1)

Explanation:

Case 1: when sin(n) is -1,

g(n) = n^{(1 - 1)} = n⁰ = 1

so, for this case f(n) > g(n) i.e. g(n) = O (f(n))

So, statement 1 is incorrect.

Case 2: when sin(n) is +1,

g(n) = n^{(1 + 1)} = n²

so, for this case f(n)

but for this, second statement i.e. f(n) = Ω(g(n)) is incorrect.

Both statements are not true for all values of sin(n).

Hence, option 4 is correct answer.

The optimal algorithm always selects the smallest sequences for merging.

Given sequence: 41, 30, 15, 80, 25, 50

Ascending order: 15, 25, 30, 41, 50, 80

Merge(15, 25) → new size (40)

Number of comparisons = 25 + 15 – 1 = 39  

Merge(30, 40) → new size (70)

Number of comparisons = 30 + 40 – 1 = 69  

Merge(41, 50) → new size (91)

Number of comparisons = 41 + 50 – 1 = 90

Merge(70, 80) → new size (150)

Number of comparisons = 70 + 80 – 1 = 149  

Merge(91, 150) → new size (241)

Number of comparisons = 91 + 150 – 1 = 240

Therefore, total number of comparisons, 39 + 69 + 90 + 149 + 240 = 587

The correct answer is option 3.

Concept

• A flowchart is a diagrammatic representation that illustrates a solution model to a given problem. It is used to depict the process of an operation or task, from startups to completion. It's a useful tool for visualizing a process, which can help to better understand, analyze, or improve it.​

Key Points