Time and Space Complexity Analysis: Master Algorithm Efficiency

Question 1

Find the time complexity of a linear search algorithm when searching an array of size 'n'.

Accepted Answer

O(n)

Answer

O(1)

Answer

O(log n)

Answer

O(n^2)

Question 2

Which notation is used to represent the upper bound of the worst-case time complexity of an algorithm?

Accepted Answer

Big-O notation

Answer

Big-Theta notation

Answer

Little-o notation

Answer

Big-Omega notation

Question 3

Determine the space complexity of a recursive algorithm that calls itself 'n' times.

Accepted Answer

O(2^n)

Answer

O(n)

Answer

O(log n)

Answer

O(n^2)

Question 4

Find the asymptotic time complexity of a binary search algorithm operating on a sorted array of size 'n'.

Accepted Answer

O(log n)

Answer

O(1)

Answer

O(n)

Answer

O(n^2)

Question 5

Which factor does NOT influence the time complexity of an algorithm?

Accepted Answer

Operating system

Answer

Algorithm design

Answer

Input size

Answer

Hardware specifications

Question 6

Calculate the time complexity of the following nested loop: "for (i = 0; i < n; i++) { for (j = 0; j < n; j++) { print(i, j); } }

Accepted Answer

O(n^2)

Answer

O(n)

Answer

O(n log n)

Answer

O(log n)

Question 7

What is the best practice when analyzing the efficiency of algorithms?

Accepted Answer

Analyze all potential inputs.

Answer

Concentrate on average-case complexity.

Answer

Ignore constants in complexity expressions.

Answer

Assume the best-case scenario.

Question 8

Explain the distinction between time complexity and space complexity.

Accepted Answer

Time complexity measures execution time, while space complexity measures memory usage.

Answer

Space complexity measures execution time, while time complexity measures memory usage.

Answer

They represent the same concept.

Answer

Time complexity applies only to recursive algorithms.

Question 9

Which of the following is NOT an advantage of Big-O notation?

Accepted Answer

Provides exact execution time

Answer

Simplifies complexity analysis

Answer

Allows comparison between algorithms

Answer

Facilitates algorithm optimization

Question 10

Which of the following is NOT a measure of time complexity specific to an algorithmic analysis?

Accepted Answer

Space complexity

Answer

Big-O notation

Answer

Asymptotic analysis

Answer

Worst-case time

Question 11

An algorithm with a time complexity of O(n^2) indicates that the running time grows:

Accepted Answer

Quadratically with the input size

Answer

Linearly with the input size

Answer

Logarithmically with the input size

Answer

Exponentially with the input size

Question 12

Which of the following data structures has a constant space complexity?

Accepted Answer

Array

Answer

Linked list

Answer

Stack

Answer

Trie

Question 13

An algorithm with a higher time complexity is:

Accepted Answer

Always less efficient

Answer

Always more efficient

Answer

Not necessarily less or more efficient

Answer

Neither more nor less efficient

Question 14

An algorithm with a time complexity of O(n^2) will take _____ time to complete as the input size (n) increases.

Accepted Answer

Quadratic time

Answer

Constant time

Answer

Linear time

Answer

Exponential time

Question 15

The space complexity of an algorithm refers to the:

Accepted Answer

Amount of memory required by the algorithm

Answer

Number of steps the algorithm takes

Answer

Type of data structure used

Answer

Size of the input

Question 16

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

Accepted Answer

Constant amount of memory, regardless of the input size

Answer

Memory proportional to the input size

Answer

Memory proportional to the square of the input size

Answer

Memory exponential to the input size

Question 17

The time complexity of a linear search algorithm is:

Accepted Answer

O(n)

Answer

O(1)

Answer

O(log n)

Answer

O(n^2)

Question 18

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

Accepted Answer

Binary search

Answer

Linear search

Answer

Bubble sort

Answer

Selection sort

Question 19

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

Accepted Answer

O(1)

Answer

O(n)

Answer

O(log n)

Answer

O(n log n)

Question 20

Which of the following notations represents the tightest bound on the growth rate of a function?

Accepted Answer

Θ(n)

Answer

O(n)

Answer

Ω(n)

Answer

O(n log n)

Question 21

An algorithm has a time complexity of O(n^2). If the size of the input is doubled, what will be the new time complexity?

Accepted Answer

O(4n^2)

Answer

O(2n^2)

Answer

O(n^2)

Answer

O(1)

Question 22

What is the space complexity of an algorithm that uses a stack data structure to store n elements?

Accepted Answer

O(n)

Answer

O(1)

Answer

O(log n)

Answer

O(n^2)

Question 23

An algorithm has a time complexity of Θ(n). What does this notation imply?

Accepted Answer

The algorithm's running time is both bounded above and below by a linear function.

Answer

The algorithm runs in constant time.

Answer

The algorithm runs in linear time.

Answer

The algorithm's running time is faster than a linear function.

Question 24

An algorithm's time complexity is O(n^2). If the input size is doubled, how much slower will the algorithm run?

Accepted Answer

Four times slower

Answer

Two times slower

Answer

Eight times slower

Question 25

Which of the following is NOT a valid time complexity notation?

Accepted Answer

Σ(n)

Answer

O(n)

Answer

Ω(n)

Answer

Θ(n)

Question 26

What is the space complexity of a linked list?

Accepted Answer

O(n)

Answer

O(1)

Answer

O(n^2)

Answer

O(log n)

Question 27

Which of the following algorithms has the best average-case time complexity?

Accepted Answer

Binary search

Answer

Linear search

Answer

Bubble sort

Answer

Quicksort

Question 28

Which data structure has the worst-case time complexity of O(n log n) for finding a specific element?

Accepted Answer

Tree

Answer

Array

Answer

Linked list

Answer

Hash table

Question 29

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

Accepted Answer

O(2^n)

Answer

O(n)

Answer

O(n log n)

Answer

O(n!)

Question 30

What is the time complexity of traversing a singly linked list with 'n' nodes from start to end?

Accepted Answer

O(n)

Answer

O(1)

Answer

O(log n)

Answer

O(n^2)

Question 31

Which of the following options describes the time complexity of a linear search algorithm?

Accepted Answer

O(n)

Answer

O(1)

Answer

O(log n)

Answer

O(n^2)

Question 32

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

Accepted Answer

O(1)

Answer

O(log n)

Answer

O(n)

Answer

O(n^2)

Question 33

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

Accepted Answer

Considers constant factors in the analysis

Answer

Provides an asymptotic approximation of complexity

Answer

Compares the growth rate of functions

Answer

Describes the worst-case time complexity

Question 34

What does the space complexity of an algorithm measure?

Accepted Answer

The amount of memory required to execute the algorithm

Answer

The number of iterations in the algorithm

Answer

The number of comparisons performed

Answer

The size of the input data

Question 35

Which of the following algorithms has a space complexity of O(n^2)?

Accepted Answer

Bubble sort

Answer

Merge sort

Answer

Quick sort

Answer

Radix sort

Question 36

Which asymptotic notation represents an exponential increase in time complexity with input size?

Accepted Answer

O(2^n)

Answer

O(n^2)

Answer

O(n)

Answer

O(n log n)

Question 37

An algorithm that takes O(n^2) time to complete has a time complexity that is:

Accepted Answer

Quadratic

Answer

Linear

Answer

Logarithmic

Answer

Constant

Question 38

The space complexity of an algorithm is typically measured in terms of:

Accepted Answer

The number of variables used

Answer

The number of lines of code

Answer

The execution time

Answer

The size of the output

Question 39

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

Accepted Answer

Providing a precise estimation of execution time

Answer

Identifying the most efficient algorithm

Answer

Comparing different algorithms

Answer

Characterizing algorithm behavior

Question 40

An algorithm with a time complexity of O(1) is said to run in:

Accepted Answer

Constant time

Answer

Linear time

Answer

Polynomial time

Answer

Exponential time

Question 41

Which of the following data structures typically has a worst-case time complexity of O(n^2) for search operations?

Accepted Answer

Linked list

Answer

Hash table

Answer

Array

Question 42

Space complexity measures the amount of:

Accepted Answer

Memory required by an algorithm

Answer

Complexity of an algorithm

Answer

Efficiency of an algorithm

Answer

Time taken by an algorithm

Question 43

An algorithm with a space complexity of O(log n) requires memory that grows:

Accepted Answer

Logarithmically

Answer

Quadratically

Answer

Exponentially

Answer

Linearly

Question 44

The average-case time complexity of a binary search on a sorted array is:

Accepted Answer

O(log n)

Answer

O(1)

Answer

O(n)

Answer

O(n^2)

Question 45

An algorithm with a time complexity of O(1) implies that:

Accepted Answer

The number of operations performed remains constant, regardless of the input size.

Answer

The number of operations increases linearly with the input size.

Answer

The number of operations increases exponentially with the input size.

Question 46

Which sorting algorithm has a time complexity of O(n log n)?

Accepted Answer

Merge Sort

Answer

Bubble Sort

Answer

Selection Sort

Answer

Insertion Sort

Question 47

The space complexity of an algorithm describes its:

Accepted Answer

Memory usage as the input size changes.

Answer

Running time as the input size changes.

Answer

Efficiency compared to other algorithms.

Question 48

Asymptotic analysis focuses on:

Accepted Answer

The behavior of an algorithm as the input size approaches infinity.

Answer

The exact running time of an algorithm for any input size.

Answer

The influence of hardware and software on algorithm performance.

Question 49

Binary Search, when used to search a sorted array, has a time complexity of:

Accepted Answer

O(log n)

Answer

O(n^2)

Answer

O(1)

Answer

O(n)

Question 50

If an algorithm with a time complexity of O(n^2) has an input size that is doubled, its new running time will be:

Accepted Answer

Four times the original running time.

Answer

Half the original running time.

Answer

Unchanged from the original running time.

Answer

Double the original running time.

Question 51

When analyzing time complexity, we primarily focus on the:

Accepted Answer

Worst-case scenario

Answer

Average-case scenario

Answer

Best-case scenario

Question 52

An algorithm with a space complexity of O(1) means that:

Accepted Answer

Its memory usage remains constant throughout the execution

Answer

Its memory usage grows exponentially with the input size

Answer

Its memory usage grows linearly with the input size

Question 53

The significance of Big-O notation in complexity analysis lies in its ability to:

Accepted Answer

Describe how an algorithm's resource usage grows relative to the input size

Answer

Provide exact running times of algorithms

Answer

Compare the performance of different programming languages