Algorithm Analysis: Master the Efficiency of Algorithms

Question 1

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

Accepted Answer

Binary search

Answer

Linear search

Answer

Bubble sort

Answer

Selection sort

Question 2

What is the worst-case time complexity of a nested loop with one loop having a time complexity of O(n) and the other having a time complexity of O(m)?

Accepted Answer

O(n * m)

Answer

O(n)

Answer

O(m)

Answer

O(n + m)

Question 3

Which data structure offers the most efficient search operation?

Accepted Answer

Hash Table

Answer

Array

Answer

Linked List

Answer

Binary Tree

Question 4

What is the purpose of analyzing an algorithm's space complexity?

Accepted Answer

To determine the memory requirements of an algorithm

Answer

To predict the execution speed of an algorithm

Answer

To estimate the number of steps an algorithm will require

Answer

To compare the efficiency of algorithms

Question 5

What is the big-O notation of an algorithm that takes a constant amount of time regardless of the input size?

Accepted Answer

O(1)

Answer

O(n)

Answer

O(log n)

Answer

O(n^2)

Question 6

Which of the following is NOT a valid technique for optimizing code efficiency?

Accepted Answer

Ignoring insignificant constant factors in time complexity calculations

Answer

Choosing appropriate data structures

Answer

Reducing the number of loop iterations

Answer

Profiling the code to identify bottlenecks

Question 7

What is the difference between a 'strong' and a 'weak' asymptotic bound?

Accepted Answer

Strong bounds provide both a lower bound and an upper bound, while weak bounds only provide an upper bound

Answer

Weak bounds are less pessimistic than strong bounds

Answer

Strong bounds are only used for algorithms with polynomial time complexity

Answer

There is no distinction between strong and weak asymptotic bounds

Question 8

What is the time complexity of performing a binary search on an array of size n?

Accepted Answer

O(log n)

Answer

O(n)

Answer

O(n^2)

Answer

O(1)

Question 9

What is the time complexity of the bubble sort algorithm?

Accepted Answer

O(n^2)

Answer

O(n)

Answer

O(log n)

Answer

O(1)

Question 10

Which of the following is an incorrect asymptotic notation used for algorithm analysis?

Accepted Answer

ω(log n)

Answer

O(n)

Answer

Ω(n)

Answer

O(n^2)

Question 11

An algorithm with a time complexity of O(n) indicates that:

Accepted Answer

Its execution time increases linearly with the input size.

Answer

Its execution time is constant and independent of input size.

Answer

Its execution time increases exponentially with the input size.

Answer

Its execution time is always less than the input size.

Question 12

Which sorting algorithm typically exhibits the best time complexity?

Accepted Answer

Merge Sort

Answer

Bubble Sort

Answer

Insertion Sort

Answer

Selection Sort

Question 13

The recurrence relation T(n) = 2T(n/2) + c represents the time complexity of:

Accepted Answer

Merge sort

Answer

Linear search

Answer

Binary search

Answer

Quick sort

Question 14

Which factor does NOT influence an algorithm's space complexity?

Accepted Answer

Processor speed

Answer

Input data size

Answer

Algorithm's data structures

Answer

Output data size

Question 15

To enhance an algorithm's efficiency, it's most effective to:

Accepted Answer

Consider the specific characteristics of the input data.

Answer

Always choose the algorithm with the lowest time complexity.

Answer

Implement the algorithm in a different programming language.

Answer

Select the algorithm with the most user-friendly interface.

Question 16

Which technique is suitable for reducing the time complexity of a nested loop with O(n^2) complexity?

Accepted Answer

Employing a hash table to minimize redundant computations

Answer

Enlarging the array size to reduce iterations

Answer

Converting the nested loop into a single loop

Answer

Optimizing the inner loop for faster execution

Question 17

The Big-Oh notation is primarily used to express:

Accepted Answer

An algorithm's worst-case time complexity

Answer

An algorithm's average-case space complexity

Answer

An algorithm's best-case time complexity

Answer

An algorithm's lower bound on space complexity

Question 18

What is the time complexity of a linear search algorithm that operates on an array with n elements?

Accepted Answer

O(n)

Answer

O(1)

Answer

O(n^2)

Answer

O(log n)

Question 19

Which of the following is not a valid measure of space complexity?

Accepted Answer

Number of steps needed to run the algorithm

Answer

Number of bytes needed to store the algorithm's code

Answer

Number of bits needed to store the input data

Answer

Number of registers utilized by the algorithm

Question 20

Which asymptotic notation represents the lower bound for the performance of an algorithm in the best-case scenario?

Accepted Answer

Ω(n)

Answer

O(n)

Answer

Θ(n)

Answer

O(1)

Question 21

Among the following sorting algorithms, which one exhibits the highest efficiency for sorting an array containing n elements?

Accepted Answer

Quick Sort

Answer

Bubble Sort

Answer

Selection Sort

Answer

Merge Sort

Question 22

What is the time complexity of executing a binary search on a sorted array with n elements?

Accepted Answer

O(log n)

Answer

O(1)

Answer

O(n)

Answer

O(n^2)

Question 23

Which of the following accurately describes a benefit of utilizing recursion in the design of algorithms?

Accepted Answer

Simpler and clearer code structure

Answer

Enhanced readability

Answer

Reduced memory usage

Answer

Accelerated execution speed

Question 24

What is the worst-case time complexity observed with the quicksort algorithm?

Accepted Answer

O(n^2)

Answer

O(n)

Answer

O(n log n)

Answer

O(1)

Question 25

In the context of algorithm analysis, what is the purpose of considering the input size parameter?

Accepted Answer

To represent the number of elements present in the input data set

Answer

To determine the time needed to execute the algorithm

Answer

To evaluate the space complexity of the algorithm

Answer

To identify the type of data being processed

Question 26

Which of the following is a measure of time complexity?

Accepted Answer

Big-O notation

Answer

Code readability

Answer

Efficiency

Answer

Speed

Question 27

Which of the following is a measure of algorithm complexity?

Accepted Answer

Time complexity

Answer

Simplicity

Answer

Understandability

Answer

Code readability

Question 28

To optimize an algorithm that repeatedly concatenates strings, which strategy is most effective?

Accepted Answer

Use a StringBuilder object.

Answer

Use a linked list.

Answer

Use a tree structure.

Answer

Use a hash table.

Question 29

Analyze the time complexity of the function f(n) = n^2 + 2n - 3, assuming the input list has size n.

Accepted Answer

O(n^2)

Answer

O(n)

Answer

O(log n)

Answer

O(n!)

Question 30

Which Θ notation accurately represents the function f(n) = 2n^3 + 3n^2 + 5n + 7?

Accepted Answer

Θ(n^3)

Answer

Θ(n^2)

Answer

Θ(n)

Question 31

Consider the statement: 'An algorithm with a time complexity of O(1) is always faster than an algorithm with a time complexity of O(n)'. Explain why this statement is not always true.

Accepted Answer

For small inputs, O(n) algorithms can execute faster than O(1) algorithms.

Answer

O(1) algorithms always have a lower time complexity than O(n) algorithms.

Answer

This statement is always true because O(1) represents a constant time complexity.

Question 32

What is the time complexity of a binary search algorithm?

Accepted Answer

O(log n)

Answer

O(n^2)

Answer

O(1)

Answer

O(n)

Question 33

Which of the following sorting algorithms is the most efficient for small datasets?

Accepted Answer

Insertion sort

Answer

Bubble sort

Answer

Merge sort

Question 34

What is the purpose of asymptotic notation?

Accepted Answer

To describe the behavior of an algorithm's complexity as the input size grows towards infinity.

Answer

To describe the exact complexity of an algorithm for all input sizes.

Answer

To compare the efficiency of different algorithms for specific input sizes.

Question 35

Which of the following is a limitation of asymptotic analysis?

Accepted Answer

It only provides an approximation of the worst-case running time or space usage of an algorithm, not the exact values.

Answer

It is too theoretically complex to be used in practice.

Answer

It can only be applied to small datasets.

Question 36

Which of the following is the most common approach to determine the time complexity of an algorithm?

Accepted Answer

Analyze the algorithm and count the number of elementary operations it performs and the number of times each operation is executed.

Answer

Run the algorithm on different input sets and measure the running time.

Answer

Use a profiler to measure the time spent in each part of the algorithm.

Question 37

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

Accepted Answer

The running time increases quadratically as the size of the input increases.

Answer

The running time is constant regardless of the size of the input.

Answer

The running time increases linearly as the size of the input increases.

Question 38

Which of the following algorithms has the lowest time complexity for finding the smallest element in an unsorted array?

Accepted Answer

Linear search

Answer

Binary search

Answer

Bubble sort

Answer

Merge sort

Question 39

What is the space complexity of an algorithm that creates a copy of an input array in a new array?

Accepted Answer

O(n)

Answer

O(n^2)

Answer

O(log n)

Answer

O(1)

Question 40

Which of the following is a common optimization technique used to improve algorithm efficiency?

Accepted Answer

Memoization

Answer

Recursion

Answer

Polymorphism

Answer

Iteration

Question 41

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

Accepted Answer

O(log n)

Answer

O(n)

Answer

O(1)

Answer

O(n^2)

Question 42

Which of the following is the closest approximation of the time complexity of an algorithm that performs two nested loops, where both loops iterate from 1 to n?

Accepted Answer

O(n^2)

Answer

O(log n)

Answer

O(n)

Answer

O(1)

Question 43

What is the purpose of using big-O notation in algorithm analysis?

Accepted Answer

To describe the upper bound on the worst-case running time or space usage of an algorithm, ignoring constant factors.

Answer

To compare the efficiency of different algorithms in all cases.

Answer

To describe the exact number of operations an algorithm performs.

Question 44

Which of the following is the time complexity of bubble sort, a sorting algorithm that repeatedly compares adjacent elements and swaps them if they are in the wrong order?

Accepted Answer

O(n^2)

Answer

O(log n)

Answer

O(1)

Answer

O(n)

Question 45

Which of the following is the Big-O notation of the function f(n) = 3n^2 + 2nlogn?

Accepted Answer

O(n^2)

Answer

O(1)

Answer

O(n)

Answer

O(nlogn)

Question 46

Which of the following techniques can be used to improve the efficiency of an algorithm by using a more efficient data structure?

Accepted Answer

Using a better data structure

Answer

Adding more comments

Answer

Using a less efficient programming language

Answer

Increasing the number of loops

Question 47

Which of the following algorithm design paradigms, where a problem is recursively divided into smaller subproblems, is used in Merge Sort?

Accepted Answer

Divide-and-conquer

Answer

Greedy

Answer

Dynamic programming

Answer

Backtracking

Question 48

Which of the following data structures is used to implement a priority queue, a data structure where elements are served in order of their priority?

Accepted Answer

Heap

Answer

Linked List

Answer

Stack

Answer

Array

Question 49

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

Accepted Answer

Reliability

Answer

Space complexity

Answer

Asymptotic analysis

Answer

Time complexity

Question 50

What is the time complexity of a linear search algorithm operating on a list of size n?

Accepted Answer

O(n)

Answer

O(log n)

Answer

O(1)

Answer

O(n^2)

Question 51

Which sorting algorithm offers the most efficient time complexity?

Accepted Answer

Merge Sort

Answer

Insertion Sort

Answer

Selection Sort

Answer

Bubble Sort

Question 52

What is the space complexity of a binary search algorithm?

Accepted Answer

O(log n)

Answer

O(n^2)

Answer

O(n)

Answer

O(1)

Question 53

Which technique is employed to evaluate the growth rate of functions?

Accepted Answer

Asymptotic Analysis

Answer

Binary Search

Answer

Recursion

Answer

Dynamic Programming

Question 54

What is the Big-O notation for an algorithm performing a consistent number of operations irrespective of the input size?

Accepted Answer

O(1)

Answer

O(log n)

Answer

O(n)

Question 55

Which of the following is NOT an advantage of asymptotic analysis?

Accepted Answer

Simplicity

Answer

Eliminates the need for practical testing

Answer

Enables comparison of algorithms

Answer

Provides estimates for worst-case scenarios

Question 56

What is the time complexity of a recursive algorithm that makes n recursive calls?

Accepted Answer

O(n^n)

Answer

O(n)

Answer

O(log n)

Answer

O(n log n)

Question 57

Which algorithm design technique focuses on saving space?

Accepted Answer

Dynamic Programming

Answer

Sorting

Answer

Recursion

Answer

Greedy Algorithms

Question 58

What is the worst-case time complexity of the heapsort algorithm?

Accepted Answer

O(n log n)

Answer

O(1)

Answer

O(n)

Answer

O(n^2)