Algorithm Analysis: Master the Art of Algorithm Efficiency

Question 1

Which of the following accurately describes the time complexity of a bubble sort algorithm?

Accepted Answer

O(n^2)

Answer

O(n)

Answer

O(n log n)

Answer

O(2^n)

Question 2

Which of the provided options represents a valid Big-O notation for the time complexity of a binary search algorithm?

Accepted Answer

O(log n)

Answer

O(n)

Answer

O(n^2)

Answer

O(2^n)

Question 3

Space complexity of an algorithm pertains to:

Accepted Answer

The memory required by the algorithm's data structures

Answer

The memory required by the algorithm's code

Answer

The time required by the algorithm

Answer

The number of operations performed by the algorithm

Question 4

Among the provided algorithms, which one exhibits a worst-case space complexity of O(n)?

Accepted Answer

Bubble Sort

Answer

Merge Sort

Answer

Quick Sort

Answer

Binary Search

Question 5

What is the order of growth represented by the function f(n) = 3n^2 + 2n + 1?

Accepted Answer

O(n^2)

Answer

O(n)

Answer

O(n^3)

Answer

O(2^n)

Question 6

For analyzing the time complexity of recursive algorithms, which technique can be employed?

Accepted Answer

Master Theorem

Answer

Substitution Method

Answer

Iteration Method

Answer

Amortized Analysis

Question 7

In a worst-case scenario, what is the time complexity of inserting a new element into a balanced binary search tree?

Accepted Answer

O(log n)

Answer

O(n)

Answer

O(n^2)

Answer

O(2^n)

Question 8

Which of the following factors does NOT influence the time complexity of an algorithm?

Accepted Answer

Hardware speed

Answer

Input size

Answer

Algorithm design

Answer

Programming language

Question 9

Determine the time complexity of the bubble sort algorithm.

Accepted Answer

O(n^2)

Answer

O(log n)

Answer

O(n)

Answer

O(n log n)

Question 10

Which of the following is a valid asymptotic notation representing a logarithmic growth?

Accepted Answer

f(n) = O(log n)

Answer

f(n) = O(n*2)

Answer

f(n) = O(2^n)

Answer

f(n) = O(n^0)

Question 11

Consider the following code: for (int i = 0; i < n; i++) { for (int j = 0; j < n; j++) { /* Some operation */ } } What is the time complexity of this nested loop code block?

Accepted Answer

O(n^2)

Answer

O(n)

Answer

O(n*log n)

Answer

O(n^3)

Question 12

Which of the following algorithms has a worst-case time complexity of O(n^2)?

Accepted Answer

Bubble Sort

Answer

Merge Sort

Answer

Quick Sort

Answer

Insertion Sort

Question 13

What does the space complexity of an algorithm primarily measure?

Accepted Answer

The amount of memory required by the algorithm during execution

Answer

The number of operations performed by the algorithm

Answer

The time taken by the algorithm to complete

Answer

The accuracy of the algorithm's results

Question 14

Consider the following code: int[] arr = new int[n]; for (int i = 0; i < n; i++) { for (int j = 0; j < n; j++) { arr[i][j] = i + j; } } What is the space complexity of this nested loop?

Accepted Answer

O(n^2)

Answer

O(n)

Answer

O(n^3)

Answer

O(2^n)

Question 15

Which of the following algorithms solves problems by breaking them down into smaller subproblems of the same type?

Accepted Answer

Quick Sort

Answer

Bubble Sort

Answer

Insertion Sort

Answer

Selection Sort

Question 16

Consider the following code: int fib(int n) { if (n <= 1) { return 1; } else { return fib(n - 1) + fib(n - 2); } } What is the time complexity of this recursive code for calculating Fibonacci numbers?

Accepted Answer

O(2^n)

Answer

O(log n)

Answer

O(n)

Answer

O(n^2)

Question 17

Which algorithm has a time complexity of O(n log n)? Explain your reasoning.

Accepted Answer

Merge Sort

Answer

Linear Search

Answer

Bubble Sort

Answer

Dijkstra's Algorithm

Question 18

Which of the following is NOT a commonly encountered time complexity class?

Accepted Answer

O(1000^n)

Answer

O(log n)

Answer

O(n)

Answer

O(n log n)

Question 19

Determine the Big-O notation for an algorithm that takes n^2 time?

Accepted Answer

O(n^2)

Answer

O(n)

Answer

O(log n)

Answer

O(n log n)

Question 20

Which sorting algorithm exhibits a worst-case time complexity of O(n^2)?

Accepted Answer

Bubble Sort

Answer

Merge Sort

Answer

Quick Sort

Answer

Heap Sort

Question 21

Identify the metric that measures space complexity:

Accepted Answer

Amount of memory utilized

Answer

Number of comparisons

Answer

Execution time

Answer

Number of swaps

Question 22

An algorithm with a time complexity of O(1) is categorized as:

Accepted Answer

Constant-time

Answer

Linear-time

Answer

Quadratic-time

Answer

Exponential-time

Question 23

An algorithm with a space complexity of O(n^3) requires:

Accepted Answer

Cubic memory

Answer

Constant memory

Answer

Linear memory

Answer

Quadratic memory

Question 24

Which advantage is NOT associated with Big-O notation?

Accepted Answer

Provides exact measurements of algorithm efficiency

Answer

Simplifies algorithm analysis

Answer

Facilitates comparison of algorithms

Answer

Enhances code readability

Question 25

An algorithm with a worst-case time complexity of O(n log n) falls under which category?

Accepted Answer

Polynomial time

Answer

Linear time

Answer

Sublinear time

Answer

Exponential time

Question 26

When choosing the best algorithm for a task, how does analyzing its efficiency help?

Accepted Answer

It lets us compare the time and memory different algorithms need for the same task.

Answer

It predicts the exact number of steps an algorithm will take.

Answer

It involves studying the algorithm's source code.

Answer

It relies on intuition and past experiences.

Question 27

Define time complexity.

Accepted Answer

The number of instructions executed by an algorithm for a specific input size

Answer

The time needed for an algorithm to complete in seconds

Answer

The memory required by an algorithm for a specific input size

Answer

The number of recursive calls made by an algorithm

Question 28

Determine the big-O notation for an algorithm with a time complexity of O(n^2).

Accepted Answer

O(n^2)

Answer

O(n)

Answer

O(log n)

Answer

O(n^3)

Question 29

Identify the correct worst-case time complexity of a binary search algorithm.

Accepted Answer

O(log n)

Answer

O(1)

Answer

O(n)

Answer

O(n^2)

Question 30

Determine the time complexity of the Selection Sort algorithm.

Accepted Answer

O(n^2)

Answer

O(n)

Answer

O(n log n)

Answer

O(n^3)

Question 31

Identify the most efficient sorting algorithm for a minimal number of elements (e.g., less than 100 elements).

Accepted Answer

Bubble Sort

Answer

Merge Sort

Answer

Quicksort

Answer

Heapsort

Question 32

Determine the space complexity of an algorithm that stores all elements of an input array in a separate list.

Accepted Answer

O(n)

Answer

O(1)

Answer

O(log n)

Answer

O(n^2)

Question 33

Which factor does not influence algorithm complexity?

Accepted Answer

Hardware architecture

Answer

Input size

Answer

Programming language

Answer

Algorithm design

Question 34

When selecting a data structure for a given problem, which of the following factors is most directly related to space complexity considerations?

Accepted Answer

Size of the input data

Answer

Underlying hardware architecture

Answer

Frequency of data access

Answer

Concurrency requirements

Question 35

Which of the following is NOT a measure used to assess algorithm complexity?

Accepted Answer

Output Size

Answer

Time Complexity

Answer

Space Complexity

Answer

Asymptotic Notation

Question 36

In algorithm design, time complexity and space complexity are often interconnected. Explain the potential trade-offs between these two factors, providing specific examples to support your points.

Accepted Answer

Sometimes, reducing time complexity requires an increase in space complexity.

Answer

Time complexity is always more important than space complexity.

Answer

Space complexity can be ignored if time complexity is low.

Answer

Time complexity and space complexity are completely independent, and optimizing one won't affect the other.

Question 37

What is the primary goal of amortized analysis in algorithm analysis?

Accepted Answer

To determine the average cost of an operation across a series of operations.

Answer

To identify the most efficient scenario for an algorithm.

Answer

To pinpoint the least efficient scenario for an algorithm.

Answer

To calculate the average cost of an algorithm across all possible inputs.

Question 38

Classify the following time complexity classes into their respective asymptotic behavior:

1. O(1)
2. O(log n)
3. O(n)
4. O(n^2)

Accepted Answer

1. Constant
2. Logarithmic
3. Linear
4. Quadratic

Answer

1. Constant
2. Quadratic
3. Logarithmic
4. Linear

Answer

1. Logarithmic
2. Constant
3. Linear
4. Quadratic

Question 39

Which notation is commonly used to describe the time complexity of an algorithm?

Accepted Answer

Big-O

Answer

Omega

Answer

Theta

Answer

Little-o

Question 40

What does a time complexity of O(n) indicate?

Accepted Answer

The algorithm's running time grows linearly with the size of the input.

Answer

The algorithm's running time grows exponentially with the size of the input.

Answer

The algorithm's running time is constant for all input sizes.

Question 41

Which statement about big-O notation is not true?

Accepted Answer

It provides precise information about the actual running time of an algorithm.

Answer

It allows for comparison of algorithms with different input sizes.

Answer

It helps simplify the analysis of algorithms.

Question 42

Determine the time complexity of the following algorithm:
for i = 1 to n:
  for j = 1 to n:
    print(i, j)

Accepted Answer

O(n^2)

Answer

O(n log n)

Answer

O(log n)

Answer

O(n)

Question 43

Which sorting algorithm generally has the best average-case time complexity?

Accepted Answer

Merge sort

Answer

Bubble sort

Answer

Insertion sort

Answer

Selection sort

Question 44

What does the space complexity of an algorithm measure?

Accepted Answer

The amount of memory space required by the algorithm.

Answer

The speed at which the algorithm executes.

Answer

The number of inputs the algorithm can handle.

Answer

The number of operations performed by the algorithm.

Question 45

The amortized time complexity of a stack data structure is:

Accepted Answer

O(1)

Answer

O(log n)

Answer

O(n^2)

Answer

O(n)

Question 46

What is the main purpose of algorithm analysis?

Accepted Answer

To assess the efficiency and performance of algorithms.

Answer

To develop new and innovative algorithms.

Answer

To understand the theoretical foundations of algorithms.

Question 47

Which of the following is NOT a benefit of using asymptotic analysis?

Accepted Answer

Provides an exact running time for all inputs

Answer

Provides a worst-case scenario estimation

Answer

Allows comparison of algorithms independent of hardware

Answer

Simplifies analysis of large algorithms

Question 48

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

Accepted Answer

O(1)

Answer

O(log n)

Answer

O(n)

Answer

O(n^2)

Question 49

Which of the following is the optimal choice for searching a large sorted array?

Accepted Answer

Binary search

Answer

Selection sort

Answer

Linear search

Answer

Bubble sort

Question 50

Which of the following functions has a time complexity of O(log n)?

Accepted Answer

Binary search

Answer

Bubble sort

Answer

Linear search

Question 51

What is the space complexity of an algorithm that stores all input data in an array?

Accepted Answer

O(n)

Answer

O(log n)

Answer

O(1)

Answer

O(n^2)

Question 52

Which of the following algorithms is most efficient for finding the minimum value in an unsorted array?

Accepted Answer

Linear search

Answer

Merge sort

Answer

Bubble sort

Answer

Binary search

Question 53

What is the purpose of using a worst-case analysis in algorithm analysis?

Accepted Answer

To determine the upper bound on resources required by an algorithm

Answer

To determine the best-case resources required by an algorithm

Answer

To determine the average resources required by an algorithm

Question 54

What is the time complexity of an algorithm that traverses a linked list sequentially?

Accepted Answer

O(n)

Answer

O(1)

Answer

O(log n)

Answer

O(n^2)