Space Complexity Analysis: Master the Art of Algorithm Space Optimization

Question 1

Auxiliary space complexity refers to:

Accepted Answer

Additional space required beyond the input size

Answer

Total space occupied by the algorithm

Answer

Space required to store the input data

Answer

Space required to store the output data

Question 2

In a recursive algorithm, the auxiliary space complexity is typically:

Accepted Answer

O(log n)

Answer

O(1)

Answer

O(n)

Answer

O(n^2)

Question 3

The space complexity of a hash table is typically:

Accepted Answer

O(n)

Answer

O(1)

Answer

O(log n)

Answer

O(n^2)

Question 4

An algorithm has a time complexity of O(n!). What is its space complexity?

Accepted Answer

O(n!)

Answer

O(n)

Answer

O(1)

Answer

O(log n)

Question 5

An algorithm has an auxiliary space complexity of O(1) and a total space complexity of O(n^2). This indicates that the algorithm:

Accepted Answer

Uses a constant amount of additional memory.

Answer

Uses a quadratic amount of additional memory.

Answer

Uses a linear amount of additional memory.

Answer

Uses a logarithmic amount of additional memory.

Question 6

An algorithm with a total space complexity of O(n^2) implies that:

Accepted Answer

The algorithm utilizes a total memory of O(n^2) units

Answer

The algorithm requires an additional O(n^2) memory

Answer

The algorithm requires an additional O(n) memory

Answer

The algorithm utilizes a total memory of O(n) units

Question 7

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

Accepted Answer

The specific architecture of the machine executing the algorithm

Answer

The size of the input

Answer

The use of recursion

Answer

The size of the output

Question 8

An algorithm with a space complexity of O(log n) is considered:

Accepted Answer

Space-efficient

Answer

Space-inefficient

Answer

Neither space-efficient nor space-inefficient

Answer

The efficiency depends on the size of the input

Question 9

Define auxiliary space complexity.

Accepted Answer

The additional space required beyond the input size

Answer

The total memory occupied during execution

Answer

The minimum space needed to store algorithm data

Answer

The average space usage across different inputs

Question 10

Calculate the total space complexity of an algorithm that creates an array of size n, inserts n elements, and performs a linear search on the array.

Accepted Answer

O(n)

Answer

O(n^2)

Answer

O(1)

Answer

O(log n)

Question 11

How does dynamic programming typically impact an algorithm's space complexity?

Accepted Answer

Varies based on the problem and input

Answer

Always reduces it to O(n)

Answer

Increases it to O(n^2) or higher

Answer

Is less than the recursive approach

Question 12

In a scenario where a hash table is used for intermediate storage of a large dataset, which space complexity is most relevant?

Accepted Answer

Total space complexity

Answer

Auxiliary space complexity

Answer

Worst-case space complexity

Answer

Amortized space complexity

Question 13

Which of the following factors does NOT influence an algorithm's space complexity?

Accepted Answer

Processor speed

Answer

Input size

Answer

Data structures utilized

Answer

Recursion

Question 14

An algorithm with O(1) auxiliary space complexity indicates that it:

Accepted Answer

Requires a fixed amount of additional space regardless of input size

Answer

May require varying amounts of space based on input size

Answer

Requires more space as input size increases

Answer

Requires an amount of space proportional to the square of the input size

Question 15

When considering total space complexity, which of the following should be included?

Accepted Answer

Both auxiliary and input data space

Answer

Auxiliary space only

Answer

Input data space only

Answer

Output data space only

Question 16

Which of these is NOT a way to measure an algorithm's space usage?

Accepted Answer

Time complexity

Answer

Constant space

Answer

Total space

Answer

Auxiliary space

Question 17

An algorithm with O(n) space complexity means that its space usage:

Accepted Answer

Increases directly with the size of the input.

Answer

Increases at a rate proportional to the square of the input size.

Answer

Stays the same no matter how big the input is.

Question 18

Why does a binary search on a sorted array have O(log n) space complexity?

Accepted Answer

It uses recursion, and the depth of the recursion is related to the log of the array size.

Answer

It creates a whole new array to hold the sorted elements.

Answer

It needs extra memory for temporary variables.

Question 19

A hash table using chaining to handle collisions has O(n) space complexity because:

Accepted Answer

It might store multiple key-value pairs in the same linked list.

Answer

It uses a different approach to handle collisions (open addressing).

Answer

The hash table has a fixed size.

Question 20

Which technique can help reduce an algorithm's memory usage?

Accepted Answer

Memoization

Answer

Branch prediction

Answer

Inline function expansion

Answer

Loop unrolling

Question 21

An algorithm with a fixed memory footprint, regardless of input size, has:

Accepted Answer

Constant space complexity

Answer

Linear space complexity

Answer

Logarithmic space complexity

Answer

Quadratic space complexity

Question 22

A depth-first traversal of a binary tree has O(h) space complexity, where 'h' is:

Accepted Answer

The height of the tree

Answer

The number of leaves in the tree

Answer

The number of connections (edges) in the tree

Answer

The total number of nodes in the tree

Question 23

Which of the following is the auxiliary space complexity of an algorithm that sorts a linked list using the merge sort technique?

Accepted Answer

O(n)

Answer

O(n^2)

Answer

O(1)

Question 24

Consider an algorithm that processes an input array of size n. It creates a new array of the same size and performs constant-time operations on each element of both arrays. What is the total space complexity of this algorithm?

Accepted Answer

O(n)

Answer

O(1)

Answer

O(n^2)

Answer

O(log n)

Question 25

Which of the following data structures has the worst space complexity for searching operations?

Accepted Answer

Linked list

Answer

Array

Answer

Binary search tree

Answer

Hash table

Question 26

An algorithm allocates memory to store the input data and an additional constant amount of space for its variables. What is the auxiliary space complexity of this algorithm?

Accepted Answer

O(1)

Answer

O(log n)

Answer

O(n^2)

Answer

O(n)

Question 27

Consider two algorithms with total space complexities of O(n^2) and O(n log n), respectively. Which algorithm would be more efficient in terms of space usage for a very large input?

Accepted Answer

O(n log n)

Answer

Cannot be determined

Answer

Both are equally efficient

Answer

O(n^2)

Question 28

Which of the following strategies can be used to optimize the space complexity of an algorithm?

Accepted Answer

Using in-place operations

Answer

Storing unnecessary data

Answer

Using recursive calls

Answer

Increasing the input size

Question 29

Consider an algorithm that takes an array of n elements as input. It creates a new array of the same size and copies each element from the input array to the new array. What is the total space complexity of this algorithm?

Accepted Answer

O(n)

Answer

O(1)

Answer

O(log n)

Answer

O(n^2)

Question 30

Which of the following data structures has the best space complexity for insertion operations?

Accepted Answer

Array

Answer

Linked list

Answer

Hash table

Question 31

An algorithm requires constant space to store its variables and an additional space proportional to the number of elements processed. What is the auxiliary space complexity of this algorithm?

Accepted Answer

O(n)

Answer

O(log n)

Answer

O(1)

Answer

O(n^2)

Question 32

Consider an algorithm that performs a binary search on a sorted array. What is the space complexity of this algorithm?

Accepted Answer

O(1)

Answer

O(log n)

Answer

O(n^2)

Answer

O(n)

Question 33

Which of the following is NOT a type of space complexity analysis?

Accepted Answer

Temporal analysis

Answer

Auxiliary space analysis

Answer

Amortized analysis

Answer

Total space analysis

Question 34

An algorithm with auxiliary space complexity of O(1) means that it uses:

Accepted Answer

Constant extra space

Answer

Linear extra space

Answer

Quadratic extra space

Answer

Exponential extra space

Question 35

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

Accepted Answer

Bubble sort

Answer

Merge sort

Answer

Quick sort

Answer

Selection sort

Question 36

An algorithm with a space complexity of O(log n) uses:

Accepted Answer

Logarithmic extra space

Answer

Constant extra space

Answer

Linear extra space

Answer

Quadratic extra space

Question 37

Which data structure has a space complexity of O(1) for inserting and deleting elements?

Accepted Answer

Hash table

Answer

Stack

Answer

Array

Answer

Linked list

Question 38

An algorithm with a total space complexity of O(n) has:

Accepted Answer

Linear extra space

Answer

Polynomial extra space

Answer

Logarithmic extra space

Answer

Constant extra space

Question 39

Which of the following is a way to optimize the space complexity of an algorithm?

Accepted Answer

Using dynamic programming

Answer

Adding more parameters

Answer

Increasing the input size

Answer

Decreasing the number of iterations

Question 40

An algorithm with a space complexity of O(n log n) uses:

Accepted Answer

Logarithmic extra space for each element

Answer

Constant extra space

Answer

Quadratic extra space

Answer

Linear extra space

Question 41

Which of the following is an example of an algorithm with a polynomial space complexity?

Accepted Answer

Factorial calculation

Answer

Merge sort

Answer

Binary search

Answer

Bubble sort

Question 42

An algorithm that processes n elements using an array has a total space complexity of:

Accepted Answer

O(n)

Answer

O(1)

Answer

O(n^2)

Answer

O(log n)