Introduction to Algorithms: Definition, Types, and Analysis

Question 1

Which characteristic is NOT true for an algorithm?

Accepted Answer

Randomness

Answer

Finiteness

Answer

Definiteness

Answer

Unambiguity

Question 2

An algorithm that executes a loop n times has a time complexity of:

Accepted Answer

O(n)

Answer

O(log n)

Answer

O(n^2)

Answer

O(n!)

Question 3

Which type of sorting algorithm operates by repeatedly splitting the input into smaller and smaller sublists?

Accepted Answer

Merge sort

Answer

Bubble sort

Answer

Selection sort

Answer

Insertion sort

Question 4

What is the primary distinction between recursive and iterative algorithms?

Accepted Answer

Iterative algorithms utilize loops, while recursive algorithms utilize recursion.

Answer

Recursive algorithms utilize loops, while iterative algorithms utilize recursion.

Answer

Recursive algorithms are invariably more efficient than iterative algorithms.

Answer

Iterative algorithms are invariably more efficient than recursive algorithms.

Question 5

Which of the following illustrates an application of dynamic programming?

Accepted Answer

Calculating the Fibonacci sequence

Answer

Performing binary search

Answer

Executing breadth-first search

Answer

Implementing Dijkstra's algorithm

Question 6

What is the primary function of a hash function in a hash table?

Accepted Answer

Mapping a key to a unique location within the table

Answer

Sorting keys within the table

Answer

Searching for a key within the table

Answer

Deleting a key from the table

Question 7

Which of the following is a potential limitation of utilizing binary search trees?

Accepted Answer

Poor performance may result from unbalanced trees

Answer

Binary search trees are unsuitable for large datasets

Answer

Binary search trees are complex to implement

Answer

Binary search trees require excessive memory

Question 8

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

Accepted Answer

O(1)

Answer

O(log n)

Answer

O(n)

Answer

O(n^2)

Question 9

Which of the following algorithms is commonly used for sorting a list of numbers?

Accepted Answer

Bubble Sort

Answer

Depth-First Search

Answer

Breadth-First Search

Answer

Dijkstra's Algorithm

Question 10

What is the main purpose of a greedy algorithm?

Accepted Answer

To find a locally optimal solution at each step

Answer

To always find the optimal solution to a problem

Answer

To minimize the time complexity of the algorithm

Answer

To ensure that the algorithm is always correct

Question 11

Which of the following measures the amount of memory utilized by an algorithm?

Accepted Answer

Space Complexity

Answer

Time Complexity

Answer

Efficiency

Answer

Accuracy

Question 12

Describe the fundamental difference between deterministic and non-deterministic algorithms.

Accepted Answer

A deterministic algorithm always produces the same output for a given input; a non-deterministic algorithm may not.

Answer

A non-deterministic algorithm is always faster than a deterministic algorithm.

Answer

A deterministic algorithm uses more memory than a non-deterministic algorithm.

Answer

There is no difference between deterministic and non-deterministic algorithms.

Question 13

What is the best-case time complexity of the selection sort algorithm?

Accepted Answer

O(1)

Answer

O(n)

Answer

O(n^2)

Answer

O(log n)

Question 14

What is a potential advantage of employing a divide-and-conquer algorithm?

Accepted Answer

Enhanced efficiency for large datasets

Answer

Reduced memory requirements

Answer

Guaranteed accuracy

Answer

Simplicity of implementation

Question 15

What is the significance of the base case in a recursive algorithm?

Accepted Answer

To halt the recursive calls and return a result

Answer

To initialize the recursive calls

Answer

To calculate the time complexity of the algorithm

Answer

To ensure that the algorithm is always correct

Question 16

What is the best time complexity of an algorithm that performs a linear search in an unsorted array of size n?

Accepted Answer

O(n)

Answer

O(1)

Answer

O(log n)

Answer

O(n^2)

Question 17

What is the primary purpose of using a divide-and-conquer algorithm?

Accepted Answer

To decompose a problem into smaller, more manageable subproblems

Answer

To reduce the time complexity of an algorithm

Answer

To improve the space complexity of an algorithm

Answer

To simplify the implementation of an algorithm

Question 18

Which of the following is an example of a greedy algorithm?

Accepted Answer

Prim's algorithm

Answer

Depth-first search

Answer

Merge Sort

Answer

Binary search

Question 19

What is the time complexity of binary search in a sorted array of size n?

Accepted Answer

O(log n)

Answer

O(1)

Answer

O(n)

Answer

O(n^2)

Question 20

Which of the following is NOT a type of sorting algorithm?

Accepted Answer

Depth-first search

Answer

Bubble Sort

Answer

Selection Sort

Answer

Quicksort

Question 21

What is the main purpose of using a stack data structure?

Accepted Answer

To store data in a Last-In, First-Out (LIFO) order

Answer

To store data in a First-In, First-Out (FIFO) order

Answer

To store data in a random order

Answer

To store data in a sorted order

Question 22

Which of the following is a benefit of using a queue data structure?

Accepted Answer

FIFO data access

Answer

LIFO data access

Answer

Random data access

Answer

Sorted data access

Question 23

What is a key difference between a linked list and an array?

Accepted Answer

Linked lists are dynamic in size, while arrays are fixed in size.

Answer

Arrays are dynamic in size, while linked lists are fixed in size.

Answer

Linked lists provide direct access to any element, while arrays do not.

Answer

Arrays provide direct access to any element, while linked lists do not.

Question 24

You have an array of numbers. Which algorithm type is best to use to find out if there are any numbers that appear more than once in the array?

Accepted Answer

Iterative

Answer

Recursive

Answer

Divide-and-Conquer

Question 25

What is time complexity, and how is it represented using Big O notation? Provide an example.

Accepted Answer

Time complexity measures the number of steps an algorithm takes, expressed using Big O notation.

Answer

Time complexity refers to the memory an algorithm needs.

Answer

Big O notation is only for recursive algorithms.

Answer

Time complexity is always a fixed value.

Question 26

Which of the following is NOT a characteristic of an algorithm?

Accepted Answer

Output-dependent

Answer

Finite

Answer

Input-driven

Answer

Well-defined

Question 27

What is the time complexity of the following algorithm: for i in range(1, n+1): print(i)?

Accepted Answer

O(n)

Answer

O(1)

Answer

O(log n)

Answer

O(n^2)

Question 28

What is the purpose of a greedy algorithm?

Accepted Answer

To find an approximate solution by making locally optimal choices

Answer

To minimize the number of steps

Answer

To maximize the efficiency of the algorithm

Answer

To guarantee a correct solution

Question 29

Which of the following is a benefit of using dynamic programming?

Accepted Answer

Optimal solutions can be found by breaking down problems into smaller, overlapping subproblems

Answer

It can only be used for small problem sizes

Answer

It is faster than divide-and-conquer algorithms

Answer

It is easy to implement

Question 30

What is the key idea behind the backtracking algorithm?

Accepted Answer

Iteratively explore all possible solutions and backtrack to find a feasible solution

Answer

Recursively divide the problem into smaller subproblems without considering overlaps

Answer

Find an approximation to the optimal solution and iteratively improve it

Answer

Use a greedy approach to construct a solution by making local choices

Question 31

What is the difference between a stack and a queue?

Accepted Answer

Stacks follow LIFO (Last In First Out) while queues follow FIFO (First In First Out)

Answer

Stacks are used for storing data while queues are used for processing data

Answer

Queues are faster than stacks

Answer

Stacks are more efficient than queues

Question 32

What is the worst-case time complexity of a hash table lookup?

Accepted Answer

O(1)

Answer

O(log n)

Answer

O(n)

Answer

O(n^2)

Question 33

Define an algorithm in your own words.

Accepted Answer

A step-by-step process for solving a problem.

Answer

A way to organize and store data.

Answer

A type of computer code.

Answer

A tool for software developers.

Question 34

An algorithm is best described as:

Accepted Answer

A set of precise instructions that solves a problem.

Answer

A computer program that executes a task.

Answer

A mathematical equation that represents a solution.

Answer

A programming language used to create software.

Question 35

Time complexity analysis in algorithms is used to determine:

Accepted Answer

The efficiency of an algorithm in relation to its input size.

Answer

The amount of time it takes an algorithm to run.

Answer

The amount of memory an algorithm requires.

Answer

The correctness of an algorithm's output.

Question 36

For searching a sorted array, which algorithm is commonly used?

Accepted Answer

Binary search

Answer

Linear search

Answer

Depth-first search

Answer

Breadth-first search

Question 37

Greedy algorithms differ from dynamic programming algorithms in that:

Accepted Answer

Greedy algorithms prioritize local optimizations, while dynamic programming aims for global optimization.

Answer

Dynamic programming requires more memory than greedy algorithms.

Answer

Greedy algorithms are always more efficient than dynamic programming algorithms.

Answer

Dynamic programming can solve problems that greedy algorithms cannot.

Question 38

What is an advantage of using divide-and-conquer algorithms?

Accepted Answer

They can solve large problems by breaking them into smaller subproblems.

Answer

They are always more efficient than brute-force algorithms.

Answer

They can solve any type of problem.

Answer

They are easy to implement and understand.

Question 39

The primary purpose of algorithm analysis is to:

Accepted Answer

Evaluate the efficiency of an algorithm.

Answer

Verify the correctness of an algorithm.

Answer

Predict the scalability of an algorithm.

Answer

Assess the security of an algorithm.

Question 40

Which metric is used to measure the space complexity of an algorithm?

Accepted Answer

Number of memory units utilized

Answer

Number of operations performed

Answer

Running time of the algorithm

Answer

Size of the input data

Question 41

Statement: All algorithms produce deterministic outputs.

Accepted Answer

False

Answer

True

Question 42

The worst-case time complexity of a binary search algorithm is:

Accepted Answer

O(log n)

Answer

O(n)

Answer

O(n^2)

Answer

O(1)

Question 43

Time complexity analysis measures the:

Accepted Answer

Number of operations performed by the algorithm relative to input size

Answer

Total memory usage of the algorithm

Answer

Time required for the algorithm to complete

Answer

Efficiency of the algorithm for varying input sizes

Question 44

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

Accepted Answer

Merge Sort

Answer

Linear Search

Answer

Bubble Sort

Answer

Insertion Sort

Question 45

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

Accepted Answer

O(n)

Answer

O(1)

Answer

O(log n)

Answer

O(n^2)

Question 46

A recursive algorithm is one that:

Accepted Answer

Calls itself one or more times

Answer

Manipulates a stack data structure

Answer

Always terminates

Answer

Has a constant time complexity

Question 47

What is the key idea behind dynamic programming?

Accepted Answer

Breaking down a problem into smaller subproblems and storing solutions to avoid redundant calculations

Answer

Using recursion to solve a problem

Answer

Searching for the optimal solution by examining all possible combinations

Answer

Approximating the solution using heuristics

Question 48

Which of the following is NOT a benefit of using an algorithm?

Accepted Answer

Guaranteeing the optimal solution for every problem

Answer

Solving complex problems efficiently

Answer

Automating repetitive tasks

Answer

Improving accuracy and precision

Question 49

Which attribute is NOT characteristic of an algorithm?

Accepted Answer

Ambiguousness

Answer

Finite

Answer

Well-defined

Answer

Effectiveness

Question 50

What is the primary goal of time complexity analysis?

Accepted Answer

Estimating the number of steps required by an algorithm to execute

Answer

Evaluating the memory usage of an algorithm

Answer

Validating the accuracy of an algorithm

Question 51

Which of the following is a commonly used sorting algorithm?

Accepted Answer

Merge Sort

Answer

Linear Search

Answer

Binary Tree

Answer

Hash Map

Question 52

What is the primary purpose of Big O notation?

Accepted Answer

Representing the asymptotic complexity of algorithms

Answer

Depicting the size of data processed by algorithms

Answer

Analyzing the time taken by algorithms in specific scenarios

Question 53

Which of the following algorithms is a greedy algorithm?

Accepted Answer

Dijkstra's Algorithm

Answer

Linear Search

Answer

Binary Search

Answer

Bubble Sort

Question 54

What is the key difference between an algorithm and a heuristic?

Accepted Answer

Algorithms provide guaranteed optimal solutions, while heuristics offer approximate solutions

Answer

Algorithms are less efficient than heuristics

Answer

Heuristics are easier to implement than algorithms

Question 55

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

Accepted Answer

Merge Sort

Answer

Bubble Sort

Answer

Binary Search

Answer

Linear Search

Question 56

What is the objective of space complexity analysis?

Accepted Answer

Determining the amount of memory required by an algorithm

Answer

Evaluating the correctness of an algorithm

Answer

Analyzing the time taken by an algorithm

Question 57

Which algorithm type is non-deterministic?

Accepted Answer

Randomized Algorithm

Answer

Greedy Algorithm

Answer

Dynamic Programming Algorithm

Answer

Divide-and-Conquer Algorithm

Question 58

What is the primary distinction between a polynomial time algorithm and an exponential time algorithm?

Accepted Answer

Polynomial time algorithms have a running time bounded by a polynomial function, while exponential time algorithms have a running time bounded by an exponential function.

Answer

Polynomial time algorithms are always faster than exponential time algorithms.