Time and Space Complexity Analysis: Master Algorithm Efficiency

Question 1

An algorithm iterates through an array of 'n' elements, performing a constant number of operations on each element. Which complexity class best describes this algorithm's time complexity?

Accepted Answer

O(n)

Answer

O(log n)

Answer

O(n^2)

Answer

O(1)

Question 2

What is the primary objective of time complexity analysis?

Accepted Answer

Determining the worst-case running time of an algorithm.

Answer

Examining all possible inputs to an algorithm.

Answer

Providing a precise running time for an algorithm.

Answer

Analyzing only recursive algorithms.

Question 3

What is the Big O time complexity of an algorithm that iterates through an array, comparing each element to every other element in the array?

Accepted Answer

O(n^2)

Answer

O(n)

Answer

O(n log n)

Question 4

Which time complexity class is impractical for most algorithms and often not a viable option?

Accepted Answer

O(n!)

Answer

O(1)

Answer

O(log n)

Answer

O(n^2)

Question 5

Determine the time complexity of the following code snippet:

```
for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
        // Some operation
    }
}
```

Accepted Answer

O(n^2)

Answer

O(n)

Answer

O(n log n)

Answer

O(log n)

Question 6

What is the time complexity of finding an element in a binary search tree with 'n' nodes?

Accepted Answer

O(log n)

Answer

O(n)

Answer

O(n^2)

Answer

O(1)

Question 7

An array of 'n' integers is given. What is the time complexity of a linear search algorithm that searches for a given target value 'k' within the array?

Accepted Answer

O(n)

Answer

O(1)

Answer

O(log n)

Answer

O(n^2)

Question 8

Which of the following is an atypical time complexity class in algorithm analysis?

Accepted Answer

O(n!)

Answer

O(1)

Answer

O(log n)

Answer

O(n^2)

Question 9

What is the time complexity of the following algorithm?

```
for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
        // Do something
   }
}
```

Accepted Answer

O(n^2)

Answer

O(n)

Answer

O(log n)

Answer

O(1)

Question 10

Which operation typically has the worst-case time complexity of O(n^2), where n represents the input size?

Accepted Answer

Sorting an array using the bubble sort algorithm

Answer

Inserting an element at the start of a linked list

Answer

Searching for an element in a balanced binary search tree

Answer

Traversing a graph using breadth-first search

Question 11

What is the time complexity of the following code snippet? ```python for i in range(n): for j in range(n): print(i, j) ```

Accepted Answer

O(n^2)

Answer

O(n)

Answer

O(log n)

Answer

O(1)

Question 12

An algorithm has a worst-case time complexity of O(n^2). What does this indicate about its behavior?

Accepted Answer

Its runtime increases quadratically with the input size.

Answer

It runs in a constant amount of time.

Answer

Its runtime increases linearly with the input size.

Question 13

Which technique is commonly used to analyze the time complexity of algorithms?

Accepted Answer

Identifying the dominant operation and analyzing its complexity using Big-O notation

Answer

Counting the number of times each line of code is executed

Answer

Using a profiler to measure the actual running time of the algorithm

Answer

Comparing the algorithm's performance to others using a benchmark

Question 14

Which of the following time complexity classes is NOT fundamental in algorithm analysis?

Accepted Answer

O(2^n)

Answer

O(1)

Answer

O(log n)

Answer

O(n^2)

Question 15

Which function has the highest time complexity?

Accepted Answer

O(2^n)

Answer

O(n^2)

Answer

O(n*log(n))

Answer

O(log(n))

Question 16

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

Accepted Answer

O(n!)

Answer

O(1)

Answer

O(n)

Answer

O(log n)

Question 17

Calculate the time complexity of the following piece of code:
```
for (int i = 0; i < n; i++) {
  for (int j = 0; j < n; j++) {
  }
}
```

Accepted Answer

O(n^2)

Answer

O(n)

Answer

O(log n)

Answer

O(1)

Question 18

Using Big-O notation, what is the time complexity of a sequential search algorithm on an input list of size 'n'?

Accepted Answer

O(n)

Answer

O(log n)

Answer

O(n^2)

Answer

O(1)

Question 19

What is the time complexity of an algorithm that iterates through n input elements, performs two arithmetic operations on each element, and adds each element to a linked list?

Accepted Answer

O(n)

Answer

O(log n)

Answer

O(n^2)

Question 20

Determine the time complexity of the following code snippet:

```
for(int i = 0; i < n; i++) {
	for(int j = 0; j < n; j++) {
		System.out.println(i + " " + j);}
}
```

Accepted Answer

O(n^2)

Answer

O(1)

Answer

O(n)

Answer

O(n^3)

Question 21

Determine the time complexity of the bubble sort algorithm.

Accepted Answer

O(n^2)

Answer

O(n log n)

Answer

O(n)

Answer

O(log n)

Question 22

What is an accurate definition of time complexity?

Accepted Answer

The time taken by an algorithm relative to the size of its input

Answer

The amount of memory used by an algorithm

Answer

The number of iterations in an algorithm

Answer

A fixed value for all algorithms

Question 23

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

Accepted Answer

Stack memory

Answer

Big-O notation

Answer

Omega notation

Answer

Theta notation

Question 24

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

Accepted Answer

Merge sort

Answer

Bubble sort

Answer

Selection sort

Answer

Quick sort

Question 25

What is the time complexity of finding the maximum element in an unsorted array of length n using linear search?

Accepted Answer

O(n)

Answer

O(log n)

Answer

O(n^2)

Answer

O(1)

Question 26

Consider the following code to compute the sum of elements in an array of length n: for i = 1 to n; sum += arr[i];. What is the time complexity of this code?

Accepted Answer

O(n)

Answer

O(log n)

Answer

O(n^2)

Answer

O(1)

Question 27

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

Accepted Answer

Merge Sort

Answer

Bubble Sort

Answer

Selection Sort

Answer

Quick Sort

Question 28

Consider the function: f(n) = n^2 + 2n + 1. What is the Big-O notation of this function?

Accepted Answer

O(n^2)

Answer

O(n)

Answer

O(n^3)

Answer

O(1)

Question 29

Which operation has a constant space complexity?

Accepted Answer

Pushing an element onto a stack

Answer

Searching for an element in a hash table

Answer

Traversing a linked list

Answer

Sorting an array

Question 30

Consider the function: f(n) = 2^n + n^3. What is the dominant term in this function's Big-O notation?

Accepted Answer

2^n

Answer

n

Answer

n^2

Answer

n^3

Question 31

What is the space complexity of a recursive function that calls itself n times with an additional O(1) space per function call?

Accepted Answer

O(n)

Answer

O(1)

Answer

O(n^2)

Answer

O(2^n)

Question 32

Which of the following is a valid Big-O notation for an algorithm that takes O(n^3) time?

Accepted Answer

O(n^3)

Answer

O(n)

Answer

O(n^2)

Answer

O(2^n)

Question 33

An algorithm uses recursion and has a space complexity of O(log n). What can be inferred about the recursion depth of the algorithm?

Accepted Answer

It grows logarithmically with the input size.

Answer

It is constant.

Answer

It grows linearly with the input size.

Answer

It grows exponentially with the input size.

Question 34

An algorithm has a time complexity of O(n^2). Which of the following input sizes would result in the algorithm taking the longest time to run?

Accepted Answer

10000

Answer

10

Answer

100

Answer

1000

Question 35

An algorithm has a time complexity of O(n log n) and a space complexity of O(n). What does this imply about the algorithm's efficiency?

Accepted Answer

It is efficient for large input sizes.

Answer

It is inefficient for large input sizes.

Answer

It is neither efficient nor inefficient for large input sizes.

Answer

Its efficiency depends on the specific input size.

Question 36

An algorithm with a time complexity of O(n^2) will require ______ time to process an input of size n.

Accepted Answer

Quadratic

Answer

Linear

Answer

Logarithmic

Answer

Constant

Question 37

If an algorithm iterates over an input of size n and performs a constant number of operations on each element, what is its time complexity?

Accepted Answer

O(n)

Answer

O(1)

Answer

O(log n)

Answer

O(n^2)

Question 38

An algorithm with a time complexity of O(n) will require ______ time to process an input of size n.

Accepted Answer

Linear time

Answer

Logarithmic time

Answer

Constant time

Answer

Exponential time

Question 39

True or False: An algorithm with a time complexity of O(1) is considered efficient.

Accepted Answer

True

Answer

False

Question 40

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

Accepted Answer

Binary search

Answer

Linear search

Answer

Merge sort

Answer

Quick sort

Question 41

Which of the following techniques is used to reduce the time complexity of a dynamic programming algorithm?

Accepted Answer

Memoization

Answer

Divide and conquer

Answer

Greedy algorithm

Answer

Branch and bound

Question 42

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

Accepted Answer

O(n)

Answer

O(1)

Answer

O(n^2)

Answer

O(log n)

Question 43

Which of the following is the best time complexity for an algorithm that performs a depth-first search on a graph?

Accepted Answer

O(V + E)

Answer

O(1)

Answer

O(n)

Answer

O(n^2)

Question 44

Which sorting algorithm has the worst-case space complexity of O(n^2)?

Accepted Answer

Bubble sort

Answer

Merge sort

Answer

Quick sort

Answer

Radix sort

Question 45

What is a key benefit of using Big-O notation?

Accepted Answer

Simplifies the analysis of algorithm efficiency

Answer

Provides absolute time complexity

Answer

Eliminates the need for empirical testing

Answer

Guarantees optimal algorithm performance

Question 46

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

Accepted Answer

Binary search

Answer

Linear search

Answer

Selection sort

Answer

Insertion sort

Question 47

What is the time complexity of the bubble sort algorithm?

Accepted Answer

O(n^2)

Answer

O(n)

Answer

O(n log n)

Answer

O(n^3)

Question 48

Consider the following code:
 while (i < n) { 
j = 0; 
 while (j < i) { 
j++; 
 } 
i++; 
}
What is the time complexity of this code?

Accepted Answer

O(n^2)

Answer

O(n)

Answer

O(n^3)

Answer

O(n log n)

Question 49

Which of the following is a valid asymptotic bound for 2n^2 + 3n + 5?

Accepted Answer

O(n^2)

Answer

O(n)

Answer

O(n^3)

Answer

O(2n^2)

Question 50

Consider the following code snippet:

```python
for i in range(n):
    for j in range(i + 1, n):
        # Do something
```

What is the time complexity of this code?

Accepted Answer

O(n^2)

Answer

O(n)

Answer

O(n log n)

Answer

O(n^3)

Question 51

Among the following sorting algorithms, which one has the best average-case time complexity?

Accepted Answer

Merge Sort

Answer

Bubble Sort

Answer

Selection Sort

Answer

Insertion Sort

Question 52

Identify the key distinction between time complexity and space complexity.

Accepted Answer

Time complexity measures the number of operations, while space complexity measures the memory usage.

Answer

Time complexity is more crucial than space complexity for most applications.

Answer

Space complexity is only relevant for algorithms handling large datasets.

Answer

Time complexity and space complexity are always proportional.

Question 53

Determine the time complexity of a nested loop that iterates over an array of size 'n' and a list of size 'm'.

Accepted Answer

O(n * m)

Answer

O(n)

Answer

O(n + m)

Answer

O(n^2)

Question 54

Which algorithm has a time complexity of O(n), where n is the number of elements in the input?

Accepted Answer

Linear search

Answer

Binary search

Answer

Bubble sort

Answer

Merge sort

Question 55

Which of the following is NOT a common time complexity class?

Accepted Answer

O(n!)

Answer

O(1)

Answer

O(log n)

Answer

O(n^2)

Question 56

An algorithm searches an unsorted array for the maximum element by comparing each element with every other element. What is the time complexity of this algorithm?

Accepted Answer

O(n^2)

Answer

O(n)

Answer

O(log n)

Answer

O(1)

Question 57

Which of the following is an uncommon time complexity class?

Accepted Answer

O(n!)

Answer

O(1)

Answer

O(log n)

Answer

O(n^2)

Question 58

What is the time complexity of an algorithm that uses binary search to find an element in a sorted array of 'n' elements?

Accepted Answer

O(log n)

Answer

O(1)

Answer

O(n)

Answer

O(n^2)

Question 59

Analyze the time complexity of the following code snippet:

```  
int[] arr = {1,2,3,4,5};
int sum = 0;
for (int i = 0; i < arr.length; i++){
    sum = sum + arr[i];
}
System.out.print(sum);  
```

Accepted Answer

O(n)

Answer

O(1)

Answer

O(log n)

Answer

O(n^2)

Question 60

What is the best-case space complexity of a stack data structure?

Accepted Answer

O(1)

Answer

O(n)

Answer

O(log n)

Answer

O(n^2)

Question 61

Analyze the time complexity of the provided code snippet:

``` 
int sum = 0; 
for (int i = 0; i < n; i++) { 
    for (int j = 0; j < n; j++) { 
        sum += i * j; 
    } 
} 
```

Accepted Answer

O(n^2)

Answer

O(n)

Answer

O(log n)

Answer

O(n log n)

Question 62

An algorithm runs in constant time if its execution time remains the same regardless of the input size. Which time complexity class represents this behavior?

Accepted Answer

O(1)

Answer

O(log n)

Answer

O(n)

Question 63

Determine the time complexity of a nested loop with n outer iterations and m inner iterations, using Big-O notation.

Accepted Answer

O(n*m)

Answer

O(m)

Answer

O(n)

Question 64

Identify the most appropriate Big-O notation for the asymptotic upper bound time complexity of the function f(n) = n^2 + 3n + 5.

Accepted Answer

O(n^2)

Answer

O(n)

Answer

O(n^3)

Answer

O(1)