Algorithm Analysis: Master Algorithm Efficiency for Software Engineers

Question 1

Which of the following is NOT a metric for time complexity?

Accepted Answer

Space complexity

Answer

Big O notation

Answer

Small o notation

Answer

Number of operations

Question 2

An algorithm with a time complexity of O(n^2) means that:

Accepted Answer

The algorithm will run in quadratic time.

Answer

The algorithm will run in constant time.

Answer

The algorithm will run in linear time.

Answer

The algorithm will run in exponential time.

Question 3

Which of the following is an example of an algorithm with a space complexity of O(1)?

Accepted Answer

Creating a new object

Answer

Sorting an array

Answer

Searching for an element in a linked list

Answer

Computing the factorial of a number

Question 4

An algorithm with a time complexity of O(log n) is considered to be:

Accepted Answer

Very efficient

Answer

Inefficient

Answer

Moderately efficient

Answer

Too complex to analyze

Question 5

Which of the following algorithms has the greatest time complexity?

Accepted Answer

Bubble sort

Answer

Merge sort

Answer

Quick sort

Answer

Insertion sort

Question 6

What is the time complexity of an algorithm that performs a binary search on a sorted array of size n?

Accepted Answer

O(log n)

Answer

O(n)

Answer

O(n^2)

Answer

O(1)

Question 7

Which of these is NOT a standard method for analyzing algorithm efficiency?

Accepted Answer

Environmental Impact Assessment

Answer

Time Complexity Analysis

Answer

Space Complexity Analysis

Question 8

Which of the following is **NOT** a commonly used time complexity notation?

Accepted Answer

Big-Alpha

Answer

Big-O

Answer

Big-Omega

Answer

Big-Theta

Question 9

What is the time complexity of the following function? ```function myFunction(n) { for (let i = 0; i < n; i++) { for (let j = 0; j < n; j++) { console.log(i, j); } } }```

Accepted Answer

O(n^2)

Answer

O(1)

Answer

O(n)

Answer

O(n log n)

Question 10

Which data structure is best suited when you need to insert and delete elements efficiently from both the front and the back of the data structure?

Accepted Answer

Queue

Answer

Array

Answer

Linked list

Answer

Stack

Question 11

Which of the following is a key distinction between time complexity and space complexity?

Accepted Answer

Time complexity measures how long it takes to execute an algorithm, while space complexity measures how much memory it requires.

Answer

Time complexity is not affected by the input size, while space complexity is.

Answer

Time complexity is always a constant value, while space complexity can vary depending on the algorithm.

Answer

Space complexity is more important than time complexity for most algorithms.

Question 12

What is the space complexity of the following function? ```function myFunction(n) { let arr = new Array(n); for (let i = 0; i < n; i++) { arr[i] = i; } return arr; }```

Accepted Answer

O(n)

Answer

O(1)

Answer

O(n^2)

Answer

O(log n)

Question 13

What is the asymptotic time complexity of the following function? ```function myFunction(n) { for (let i = 1; i <= n; i++) { for (let j = i + 1; j <= n; j++) { console.log(i, j); } } }```

Accepted Answer

O(n^2)

Answer

O(n log n)

Answer

O(n)

Answer

O(log n)

Question 14

Which of the following is NOT a type of algorithm analysis technique?

Accepted Answer

Error analysis

Answer

Time complexity analysis

Answer

Space complexity analysis

Answer

Efficiency analysis

Question 15

What is the time complexity of the following algorithm: for i in range(n):
for j in range(n):
print(i, j)?

Accepted Answer

O(n^2)

Answer

O(n)

Answer

O(n^3)

Answer

O(log n)

Question 16

Which of the following is an example of a divide-and-conquer algorithm?

Accepted Answer

Merge sort

Answer

Bubble sort

Answer

Factorial calculation

Answer

Linear search

Question 17

What is the space complexity of the following data structure: a singly linked list with n elements?

Accepted Answer

O(n)

Answer

O(n^2)

Answer

O(log n)

Answer

O(1)

Question 18

What is the difference between time complexity and space complexity?

Accepted Answer

Time complexity measures the amount of time an algorithm takes to run, while space complexity measures the amount of memory it uses.

Answer

Time complexity measures the number of operations performed by an algorithm, while space complexity measures the amount of data it manipulates.

Answer

Time complexity is affected by the input size, while space complexity is not.

Answer

Space complexity is affected by the input size, while time complexity is not.

Question 19

What is the time complexity of the following algorithm: for i in range(n):
if i % 2 == 0:
print(i)?

Accepted Answer

O(n)

Answer

O(n^2)

Answer

O(log n)

Answer

O(1)

Question 20

What is the space complexity of the following data structure: a binary search tree with n elements?

Accepted Answer

O(log n)

Answer

O(n)

Answer

O(n^2)

Answer

O(1)

Question 21

When the input to a search algorithm is already sorted in ascending order, how does its time complexity change compared to unsorted input?

Accepted Answer

Improved time complexity

Answer

No change in time complexity

Answer

Increased time complexity

Question 22

How does algorithm complexity affect software development in practice?

Accepted Answer

Impacts software performance and resource usage

Answer

Only relevant for theoretical analysis, not practical applications

Answer

Has no bearing on user satisfaction or software quality

Question 23

In the limit comparison test, how do you determine the order of growth of a time complexity function f(n)?

Accepted Answer

Calculate the limit of f(n)/g(n) as n approaches infinity. If the limit is a non-zero constant, f(n) and g(n) have the same order of growth.

Answer

Find the derivative of f(n) and g(n) and compare their values.

Answer

Substitute n with a simpler variable to simplify the comparison.

Answer

Plot the graphs of f(n) and g(n) and analyze their slopes.

Question 24

Which of the following is NOT a measure of time complexity?

Accepted Answer

Lines of code

Answer

Asymptotic analysis

Answer

Worst-case time complexity

Answer

Big O notation

Question 25

An algorithm with a time complexity of O(n^2) is classified as:

Accepted Answer

Quadratic

Answer

Linear

Answer

Logarithmic

Question 26

Which of the following algorithms typically has the best time complexity?

Accepted Answer

Merge sort

Answer

Bubble sort with an optimized flag to stop early

Answer

Selection sort

Answer

Insertion sort

Question 27

Space complexity refers to:

Accepted Answer

The amount of memory used by the algorithm

Answer

The time taken by the algorithm to complete

Answer

The input size of the algorithm

Answer

The number of instructions executed by the algorithm

Question 28

An algorithm with a space complexity of O(1) is called:

Accepted Answer

Constant space

Answer

Exponential space

Answer

Linear space

Answer

Quadratic space

Question 29

Which technique is commonly used to analyze the time complexity of a recursive algorithm?

Accepted Answer

Master theorem

Answer

Big-O notation

Answer

Empirical analysis

Answer

Amortized analysis

Question 30

Big-Theta notation is used to describe:

Accepted Answer

The exact growth rate of an algorithm

Answer

The lower bound of an algorithm

Answer

The average-case time complexity of an algorithm

Answer

The upper bound of an algorithm

Question 31

The process of improving an algorithm's time complexity is called:

Accepted Answer

Algorithm optimization

Answer

Algorithm implementation

Answer

Algorithm testing

Answer

Algorithm analysis

Question 32

What is a measure of an algorithm's efficiency?

Accepted Answer

Time complexity

Answer

User-friendliness

Answer

Portability

Answer

Clarity

Question 33

What is the best-case time complexity of a binary search algorithm?

Accepted Answer

O(1)

Answer

O(n^2)

Answer

O(log n)

Answer

O(n)

Question 34

What is the average-case time complexity of the quicksort algorithm?

Accepted Answer

O(n log n)

Answer

O(1)

Answer

O(n^2)

Answer

O(n)

Question 35

Which notation is commonly used to measure the performance of an algorithm?

Accepted Answer

Big O notation

Answer

Execution time

Answer

Code length

Answer

Number of statements

Question 36

Which of the following best describes the notion of 'time complexity' for an algorithm?

Accepted Answer

The mathematical function representing the amount of time the algorithm takes to complete, based on input size.

Answer

The total number of instructions the algorithm executes.

Question 37

Identify the algorithm that exhibits O(log n) time complexity.

Accepted Answer

Binary Search

Answer

Selection Sort

Answer

Linear Search

Answer

Bubble Sort

Question 38

Which algorithm exemplifies O(2^n) time complexity?

Accepted Answer

Recursion without a base case

Answer

Selection Sort

Answer

Linear Search

Answer

Binary Search

Question 39

Which factors influence the time complexity of an algorithm?

Accepted Answer

Input size, algorithm design, and hardware platform

Answer

Only input size

Answer

Only algorithm design

Question 40

What is a key advantage of employing asymptotic analysis in describing algorithm time complexity?

Accepted Answer

It allows for algorithm comparison independent of constant factors and specific hardware platforms.

Answer

It is easy to implement.

Answer

It provides a precise measurement of execution time.

Question 41

Which approach is most effective in reducing an algorithm's space complexity?

Accepted Answer

Utilizing more efficient data structures

Answer

Employing recursion

Answer

Increasing hardware resources

Answer

Enlarging input size

Question 42

Which algorithm stands out for its superior space complexity performance?

Accepted Answer

In-place sorting

Answer

Bubble Sort

Answer

Merge Sort

Answer

Selection Sort

Question 43

What is a fundamental limitation of algorithm analysis?

Accepted Answer

It cannot precisely predict an algorithm's execution time on a specific hardware platform.

Answer

It is excessively complex and impractical.

Answer

It is only applicable to algorithms with known time complexity.

Question 44

Determine the time complexity of the Bubble Sort algorithm:

Accepted Answer

O(n^2)

Answer

O(n)

Answer

O(1)

Answer

O(n log n)

Question 45

What is the space complexity of a Binary Search Tree (BST)?

Accepted Answer

O(n)

Answer

O(log n)

Answer

O(1)

Question 46

Which of the following is the best way to analyze the performance of an algorithm?

Accepted Answer

Through empirical testing

Answer

Through theoretical analysis

Answer

Through simulation

Question 47

Which of the following is NOT a time complexity measure?

Accepted Answer

Average complexity

Answer

Ω notation

Answer

O notation

Answer

Θ notation

Question 48

An algorithm with a time complexity of O(n^2) is considered:

Accepted Answer

Quadratic

Answer

Linear

Answer

Logarithmic

Answer

Polynomial

Question 49

Which of the following algorithms has the lowest time complexity?

Accepted Answer

Binary search

Answer

Selection sort

Answer

Bubble sort

Answer

Linear search

Question 50

What is the space complexity of an algorithm that uses a stack to store its input?

Accepted Answer

O(n)

Answer

O(1)

Answer

O(log n)

Answer

O(n^2)

Question 51

Which of the following asymptotic notations represents the best-case time complexity?

Accepted Answer

Ω

Answer

?

Answer

O

Answer

Θ

Question 52

An algorithm with a time complexity of O(log n) is characterized as:

Accepted Answer

Logarithmic

Answer

Exponential

Answer

Polynomial

Answer

Constant