Time Complexity Analysis: Master Algorithm Efficiency

Question 1

Which sorting algorithm has a time complexity of O(n^2), where n is the size of the input?

Accepted Answer

Bubble sort

Answer

Binary search

Answer

Merge sort

Answer

Quick sort

Question 2

What is the most efficient time complexity an algorithm can have?

Accepted Answer

O(1)

Answer

O(n)

Answer

O(log n)

Answer

O(n^2)

Question 3

An algorithm has a time complexity of O(n). What does this indicate?

Accepted Answer

The algorithm's execution time increases linearly as the input size increases.

Answer

The algorithm's execution time remains constant regardless of the input size.

Answer

The algorithm's execution time decreases as the input size increases.

Answer

The algorithm's execution time is unpredictable.

Question 4

Which Big-O notation accurately represents the time complexity of an algorithm with a time complexity of O(n^2 + 2n)?

Accepted Answer

O(n^2)

Answer

O(n)

Answer

O(2n)

Answer

O(n^3)

Question 5

Which of the following best describes the time complexity of the linear search algorithm?

Accepted Answer

O(n)

Answer

O(1)

Answer

O(log n)

Answer

O(n^2)

Question 6

Determine the asymptotic behavior of f(n) = 2n^3 + 5n^2 - 3n + 1.

Accepted Answer

O(n^3)

Answer

O(n)

Answer

O(n^2)

Answer

O(n^4)

Question 7

Consider the following algorithm: For i = 1 to n, for j = 1 to n, print(i, j). What is its time complexity?

Accepted Answer

O(n^2)

Answer

O(n)

Answer

O(n^3)

Answer

O(n^4)

Question 8

Determine the best-case time complexity of f(n) = n log n.

Accepted Answer

O(log n)

Answer

O(1)

Answer

O(n)

Answer

O(n log n)

Question 9

Which sorting algorithm exhibits a worst-case time complexity of O(n log n)?

Accepted Answer

Merge sort

Answer

Bubble sort

Answer

Insertion sort

Answer

Selection sort

Question 10

What is the space complexity of an algorithm that creates an array of size n?

Accepted Answer

O(n)

Answer

O(1)

Answer

O(log n)

Answer

O(n^2)

Question 11

Which of the following is the correct Big-O notation for an algorithm with a time complexity of n squared?

Accepted Answer

O(n^2)

Answer

O(n)

Answer

O(log n)

Answer

O(1)

Question 12

An algorithm has a time complexity of O(2^n). What does this indicate about its efficiency?

Accepted Answer

Very inefficient for large inputs

Answer

Very efficient for large inputs

Answer

Moderately efficient for large inputs

Answer

Moderately efficient for small inputs

Question 13

Which of the following best describes the best-case time complexity of an algorithm?

Accepted Answer

O(1)

Answer

O(n)

Answer

O(n^2)

Answer

O(log n)

Question 14

Consider the following code: for(int i = 0; i < n; i++) { for(int j = 0; j < i; j++) { ... } }. What is the time complexity of this code?

Accepted Answer

O(n^2)

Answer

O(n)

Answer

O(log n)

Answer

O(1)

Question 15

Consider the following algorithm: function my_algo(n) { if(n == 0) { return 0; } else { return my_algo(n-1) + my_algo(n-2); } }. What is the time complexity of this algorithm?

Accepted Answer

O(2^n)

Answer

O(log n)

Answer

O(n)

Answer

O(n^2)

Question 16

Given two algorithms with time complexities O(n) and O(n^2), for large inputs, which is more efficient?

Accepted Answer

Algorithm with O(n) time complexity

Answer

Algorithm with O(n^2) time complexity

Answer

Both algorithms are equally efficient

Answer

Cannot be determined without additional information

Question 17

Which algorithm is more efficient, binary search or linear search? Explain your reasoning using Big-O notation.

Accepted Answer

Binary search has a time complexity of O(log n) and linear search has a time complexity of O(n).

Answer

Binary search has a time complexity of O(n) and linear search has a time complexity of O(log n).

Answer

Both binary search and linear search have a time complexity of O(n).

Answer

Binary search is more efficient than linear search for all input sizes.

Question 18

How does the size of the input data impact the time complexity of an algorithm?

Accepted Answer

A smaller input size generally results in lower time complexity.

Answer

Time complexity is unaffected by the input size.

Answer

A larger input size enhances the algorithm's efficiency.

Answer

Time complexity stays the same regardless of the input size.

Question 19

Why might the actual running time of an algorithm differ from its theoretical time complexity?

Accepted Answer

Hardware and how the algorithm is written can impact execution speed.

Answer

Input size is the only factor affecting running time.

Answer

Time complexity analysis is only useful for very large inputs.

Answer

Time complexity analysis can accurately predict running time for any input.

Question 20

Determine the asymptotic behavior of the following functions: f(n) = 5n^3 + 2n^2 + log(n), g(n) = 3n^2 log(n), and h(n) = 2^n + 5n.

Accepted Answer

f(n) is O(n^3), g(n) is O(n^2 log n), and h(n) is O(2^n)

Answer

f(n) is O(n^2), g(n) is O(log n), and h(n) is O(n)

Answer

f(n) is O(log n), g(n) is O(n^3), and h(n) is O(n^2)

Answer

f(n) is O(2^n), g(n) is O(n), and h(n) is O(log n)

Question 21

Which of the following is NOT a valid Big-O notation?

Accepted Answer

O(n^2 + n)

Answer

O(n log n)

Answer

O(n^2)

Answer

O(1)

Question 22

What is the primary purpose of using Big-O notation in time complexity analysis?

Accepted Answer

To compare the efficiency of different algorithms

Answer

To calculate the exact running time of an algorithm

Answer

To find the algorithm with the lowest time complexity

Answer

To determine the minimum number of steps an algorithm will take

Question 23

Analyze the time complexity of the given algorithm:

```
for i = 1 to n
    for j = i to n
        for k = 1 to n
            { ... }
```

Calculate the time complexity of this algorithm.

Accepted Answer

O(n^3)

Answer

O(n)

Answer

O(n^2)

Answer

O(n^4)

Question 24

Which of the following sorting algorithms has a worst-case time complexity of O(n^2) and performs pairwise comparisons to sort the elements?

Accepted Answer

Bubble Sort

Answer

Quick Sort

Answer

Merge Sort

Answer

Heap Sort

Question 25

Which of the following is NOT a valid asymptotic notation used to describe the time complexity of algorithms?

Accepted Answer

O(2^n + 1)

Answer

O(n)

Answer

O(log n)

Answer

O(n^2)

Question 26

Which of the following represents the tightest upper bound on the time complexity of the following function: f(n) = n^3 - 2n^2 + 5n + 10?

Accepted Answer

O(n^3)

Answer

O(n)

Answer

O(n^2)

Answer

O(log n)

Question 27

Which of the following algorithm types has a time complexity that is independent of the input size?

Accepted Answer

Constant-Time Algorithm

Answer

Quadratic-Time Algorithm

Answer

Logarithmic-Time Algorithm

Answer

Linear-Time Algorithm

Question 28

Which of the following is the time complexity of a linear search algorithm?

Accepted Answer

O(n)

Answer

O(½n)

Answer

O(n²)

Question 29

Which of the following sorting algorithms has the time complexity of O(n²)?

Accepted Answer

Bubble Sort

Answer

Merge Sort

Answer

Quick Sort

Answer

Heap Sort

Question 30

Which type of analysis is commonly used to determine the efficiency of an algorithm?

Accepted Answer

Asymptotic analysis

Answer

Empirical analysis

Answer

Deterministic analysis

Answer

Statistical analysis

Question 31

What is the order of growth of the function f(n) = n³ + 2n² + 3n?

Accepted Answer

O(n³)

Answer

O(1)

Answer

O(n)

Answer

O(n²)

Question 32

Which of the following is an application of time complexity analysis?

Accepted Answer

Selecting the most efficient algorithm for a given problem

Answer

Refactoring code for readability

Answer

Handling errors in code

Answer

Visualizing large datasets

Question 33

What is the significance of the constant in the Big-O notation?

Accepted Answer

It is ignored for asymptotic analysis because it does not affect the growth rate.

Answer

It indicates the growth rate of the algorithm as the input size increases.

Answer

It represents the number of operations performed by the algorithm.

Answer

It determines the exact running time of the algorithm.

Question 34

An algorithm has a time complexity of O(n^2). How does its running time change as the input size increases?

Accepted Answer

Quadratically

Answer

Logarithmically

Answer

Linearly

Question 35

What is the time complexity of an algorithm that performs a constant number of operations regardless of the size of the input?

Accepted Answer

O(1)

Answer

O(log n)

Answer

O(n)

Answer

O(n^2)

Question 36

Consider the following code: for (int i = 0; i < n; i++) { for (int j = i; j < n; j++) { ... } } What is the time complexity of this algorithm?

Accepted Answer

O(n^2)

Answer

O(n log n)

Answer

O(log n)

Answer

O(n)

Question 37

What is the time complexity of a linear search on an unsorted array?

Accepted Answer

O(n)

Answer

O(n^2)

Answer

O(1)

Answer

O(log n)

Question 38

Which of the following operations on a binary tree has a time complexity of O(n)?

Accepted Answer

Tree Traversal

Answer

Tree Deletion

Answer

Tree Search

Answer

Tree Insertion

Question 39

Consider an algorithm that iteratively calculates the sum of all the numbers from 1 to n. What is the time complexity of this algorithm?

Accepted Answer

O(n)

Answer

O(1)

Answer

O(n^2)

Answer

O(log n)

Question 40

Consider an algorithm that performs a binary search on a sorted array and returns the position of the element if found, or -1 if not found. What is the time complexity of this algorithm?

Accepted Answer

O(log n)

Answer

O(n^2)

Answer

O(1)

Answer

O(n)

Question 41

**Question**:  Which of the following best represents the best-case time complexity for a linear search algorithm operating on a sorted array containing n elements?

Accepted Answer

**Answer**: O(1)

Answer

**Distractor**: O(log n)

Answer

**Distractor**: O(n)

Answer

**Distractor**: O(n^2)

Question 42

**Question**: What is the time complexity of a bubble sort algorithm operating on an array containing n elements?

Accepted Answer

**Answer**: O(n^2)

Answer

**Distractor**: O(n log n)

Answer

**Distractor**: O(n)

Answer

**Distractor**: O(log n)

Question 43

**Question**: Which of the following algorithms has a worst-case time complexity of O(log n)?

Accepted Answer

**Answer**: Binary search

Answer

**Distractor**: Quick sort

Answer

**Distractor**: Merge sort

Answer

**Distractor**: Selection sort

Question 44

**Question**: What is the time complexity of a recursive function that makes n recursive calls to itself and performs constant work in each call?

Accepted Answer

**Answer**: O(n^n)

Answer

**Distractor**: O(n)

Answer

**Distractor**: O(2^n)

Answer

**Distractor**: O(log n)

Question 45

**Question**: Which of the following is an example of an algorithm with a constant time complexity?

Accepted Answer

**Answer**: Accessing an element from an array by its index

Answer

**Distractor**: Traversing a linked list

Answer

**Distractor**: Searching for an element in a sorted array using linear search

Answer

**Distractor**: Sorting an array using bubble sort

Question 46

**Question**: In the context of time complexity analysis, what does Big-O notation represent?

Accepted Answer

**Answer**: Upper bound on the asymptotic growth rate of an algorithm

Answer

**Distractor**: Lower bound on the time required to execute an algorithm

Answer

**Distractor**: Exact number of operations performed by an algorithm

Question 47

**Question**: Which of the following time complexity notations indicates exponential growth?

Accepted Answer

**Answer**: O(2^n)

Answer

**Distractor**: O(n)

Answer

**Distractor**: O(n^2)

Answer

**Distractor**: O(log n)

Question 48

**Question**: What is the time complexity of an algorithm that iterates over an array of size n and performs the same constant number of operations on each element?

Accepted Answer

**Answer**: O(n)

Answer

**Distractor**: O(log n)

Answer

**Distractor**: O(n^2)

Answer

**Distractor**: O(1)

Question 49

**Question**: Which of the following algorithms performs the fewest comparisons in the worst case when searching for a target element in a sorted array?

Accepted Answer

**Answer**: Binary search

Answer

**Distractor**: Bubble sort

Answer

**Distractor**: Selection sort

Answer

**Distractor**: Linear search

Question 50

**Question**: What is the time complexity of an algorithm that recursively divides a problem into smaller subproblems of equal size and solves each subproblem independently, continuing this process until the subproblems are small enough to be solved directly?

Accepted Answer

**Answer**: O(n log n)

Answer

**Distractor**: O(2^n)

Answer

**Distractor**: O(n^2)

Answer

**Distractor**: O(n)