Master Space Complexity Analysis in Advanced Data Structures

Question 1

Which operation on a stack has a worst-case space complexity of O(n)?

Accepted Answer

Push

Answer

Pop

Answer

Peek

Question 2

Which of the following techniques is used to optimize the space complexity of a backtracking algorithm for solving the N-Queens problem?

Accepted Answer

Constraint propagation

Answer

Branch and bound

Answer

Memoization

Question 3

Consider a stack that uses an array as its underlying data structure. What is its worst-case space complexity for a series of push and pop operations?

Accepted Answer

O(n)

Answer

O(1)

Answer

O(n^2)

Question 4

Which of the following is **not** a valid approach for optimizing space complexity?

Accepted Answer

Applying recursion techniques

Answer

Using data structures with a smaller memory footprint

Answer

Reducing the number of temporary variables used

Answer

Employing memoization techniques

Question 5

Consider an algorithm that processes an array of size 'n'. Its space complexity can be represented as:

Accepted Answer

O(n)

Answer

O(1)

Answer

O(log n)

Answer

O(n^2)

Question 6

Consider an algorithm that performs a depth-first search on a binary tree. Its space complexity is:

Accepted Answer

O(log n)

Answer

O(1)

Answer

O(n)

Answer

O(n^2)

Question 7

Consider an algorithm that calculates the sum of all elements in a given array. Its auxiliary space requirement is:

Accepted Answer

O(1)

Answer

O(log n)

Answer

O(n)

Answer

O(n^2)

Question 8

Consider an algorithm that performs a breadth-first search on a graph. Its space complexity is:

Accepted Answer

O(n)

Answer

O(1)

Answer

O(log n)

Answer

O(n^2)

Question 9

Which of the following data structures has the highest space complexity?

Accepted Answer

Trie

Answer

Array

Answer

Linked list

Answer

Hash table

Question 10

Consider an algorithm that performs a binary search on a sorted array. Its auxiliary space requirement is:

Accepted Answer

O(1)

Answer

O(log n)

Answer

O(n)

Answer

O(n^2)

Question 11

In an algorithm with nested loops, which of the following variables typically contributes to the auxiliary space complexity?

Accepted Answer

Temporary variables within the inner loop

Answer

Loop control variables

Answer

Input data

Answer

Output data

Question 12

An algorithm uses a stack to store temporary values. If the stack can hold a maximum of k values, what is the worst-case space complexity of the algorithm?

Accepted Answer

O(k)

Answer

O(1)

Answer

O(log k)

Answer

O(k^2)

Question 13

An algorithm uses a hash table with a fixed number of slots. If the input size is large relative to the number of slots, what is the likely space complexity of the algorithm?

Accepted Answer

O(n^2)

Answer

O(1)

Answer

O(log n)

Answer

O(n)

Question 14

Which of the following factors does NOT affect the space complexity of an algorithm?

Accepted Answer

Operating system and hardware

Answer

Input size

Answer

Chosen data structures

Answer

Algorithm design

Question 15

What is the space complexity of an insertion sort algorithm that sorts a linked list of n elements?

Accepted Answer

O(n)

Answer

O(1)

Answer

O(n^2)

Answer

O(log n)

Question 16

What is the space complexity of Dijkstra's algorithm for finding the shortest path between two nodes in a weighted graph?

Accepted Answer

O(m log n)

Answer

O(n)

Answer

O(m)

Answer

O(n log n)

Question 17

Which of the following factors does NOT affect the space complexity of an algorithm?

Accepted Answer

The programming language used

Answer

The type of data structure used

Answer

The number of elements to be processed

Answer

The number of recursive calls made

Question 18

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

Accepted Answer

Constant auxiliary space regardless of input size

Answer

Auxiliary space proportional to input size

Answer

Auxiliary space exponential to input size

Answer

Auxiliary space logarithmic to input size

Question 19

An algorithm with a space complexity of O(log n) implies that the:

Accepted Answer

Auxiliary space increases logarithmically with input size

Answer

Auxiliary space increases exponentially with input size

Answer

Auxiliary space decreases exponentially with input size

Answer

Auxiliary space decreases linearly with input size

Question 20

When analyzing the space complexity of an algorithm, we consider:

Accepted Answer

All space required by the algorithm, including input, output, and temporary data

Answer

Only the space required for input and output

Answer

Only the space required for local variables and temporary data

Answer

Only the space required for permanent data structures

Question 21

An algorithm that uses recursion can potentially have:

Accepted Answer

Exponential space complexity

Answer

Constant space complexity

Answer

Linear space complexity

Answer

Quadratic space complexity

Question 22

In algorithm analysis, what is the primary distinction between time 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

Both time and space complexity assess overall algorithm efficiency, encompassing both execution time and memory usage.

Answer

Time complexity is independent of input size, while space complexity is heavily influenced by input size.

Question 23

An algorithm makes recursive calls, where each call requires 'k' auxiliary space. If the algorithm has a maximum recursive depth of 'd', what is the total space complexity of the algorithm?

Accepted Answer

k * d

Answer

k

Answer

k^d

Answer

d + k

Question 24

Determine the space complexity of the merge sort algorithm for an input array with 'n' elements, where each element occupies 'm' space units.

Accepted Answer

O(n * m)

Answer

O(n)

Answer

O(log n)

Answer

O(log n * m)

Question 25

Which optimization techniques can effectively minimize the space complexity of an algorithm?

Accepted Answer

Using a data structure with a reduced memory footprint

Accepted Answer

Employing a hashing function for data storage

Answer

Implementing a more efficient sorting algorithm

Answer

Incorporating recursion within the algorithm

Question 26

How does the size of the input typically affect the space complexity of an algorithm?

Accepted Answer

Input size may increase, decrease, or have no impact on space complexity.

Answer

Input size has no impact on space complexity.

Answer

Input size always increases space complexity.

Answer

Input size only affects the time complexity of an algorithm.

Question 27

Determine the space complexity of a breadth-first search (BFS) on an undirected graph with 'V' vertices and 'E' edges. Explain your reasoning.

Accepted Answer

O(V + E)

Answer

O(V * E)

Answer

O(E)

Answer

O(1)

Question 28

Which of the following is NOT a valid technique for optimizing space complexity?

Accepted Answer

Adding unnecessary variables

Answer

Using efficient data structures

Answer

Reusing memory

Answer

Employing tail recursion elimination

Question 29

An algorithm with a space complexity of O(n) indicates that:

Accepted Answer

The memory requirement increases linearly with the input size.

Answer

The memory requirement decreases exponentially with the input size.

Answer

The memory requirement is constant regardless of the input size.

Question 30

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

Accepted Answer

Bubble Sort

Answer

Merge Sort

Answer

Heap Sort

Answer

Quick Sort

Question 31

What is the auxiliary space complexity of an algorithm that employs a stack to manage function calls?

Accepted Answer

O(n)

Answer

O(n^2)

Answer

O(log n)

Answer

O(1)

Question 32

What is the space complexity of a code snippet that reverses a string using a stack?

Accepted Answer

O(n)

Answer

O(log n)

Answer

O(1)

Question 33

What is a potential drawback of using recursion to solve problems?

Accepted Answer

Increased space complexity due to recursive calls

Answer

Improved efficiency

Answer

Improved code readability

Answer

Easier code debugging

Question 34

Which of the following accurately describes the auxiliary space required by a recursive algorithm?

Accepted Answer

The space occupied by function calls and local variables in the call stack.

Answer

The space occupied by the output of the algorithm.

Answer

The space occupied by the input to the algorithm.

Question 35

Consider an algorithm that creates a copy of an input array. What is the space complexity of this algorithm?

Accepted Answer

O(n)

Answer

O(1)

Answer

O(log n)

Answer

O(n^2)

Question 36

Which of the following algorithms has the most favorable space complexity?

Accepted Answer

In-place sorting

Answer

Selection sort

Answer

Merge sort

Answer

Quick sort

Question 37

Consider an algorithm that traverses a binary tree using depth-first search. What is the space complexity of this algorithm?

Accepted Answer

O(h)

Answer

O(log n)

Answer

O(n^2)

Answer

O(n)

Question 38

Consider an algorithm that calculates the frequency of each element in an array. What is the space complexity of this algorithm?

Accepted Answer

O(n + k)

Answer

O(n^2)

Answer

O(n)

Answer

O(k)

Question 39

What is the definition of space complexity in the context of algorithms?

Accepted Answer

The amount of memory space an algorithm requires to execute, expressed as a function of the input size.

Answer

The efficiency of an algorithm in terms of how it uses resources like memory and CPU.

Answer

The number of steps an algorithm performs to reach a solution, as a function of the input size.

Answer

The time it takes an algorithm to complete, measured as a function of the input size.

Question 40

What is the space complexity of an algorithm that modifies an input array in-place without creating additional data structures?

Accepted Answer

O(1)

Answer

O(n log n)

Answer

O(log n)

Answer

O(n)

Question 41

An algorithm uses a stack to store intermediate results. In the worst-case scenario, the stack holds a number of elements proportional to the input size (n). What is the algorithm's space complexity?

Accepted Answer

O(n)

Answer

O(log n)

Answer

O(n log n)

Answer

O(1)

Question 42

Which of the following algorithms has the highest space complexity, generally requiring the most memory for large input sizes?

Accepted Answer

Generating all possible permutations of a string with length n.

Answer

Performing a binary search on a sorted array of size n.

Answer

Finding the maximum element in a sorted array of size n.

Question 43

How does recursion potentially impact the space complexity of an algorithm?

Accepted Answer

Each recursive call adds a new stack frame to the call stack, which can lead to high space complexity, especially for deeply nested recursion.

Answer

Recursion has no significant impact on space complexity; it primarily affects time complexity.

Answer

Recursion generally leads to lower space complexity compared to iterative solutions.

Question 44

Which of the following is NOT a commonly used technique for optimizing the space complexity of an algorithm?

Accepted Answer

Using a more efficient sorting algorithm (e.g., quicksort instead of bubble sort) primarily improves time complexity, not necessarily space complexity.

Answer

Reusing data structures instead of creating new ones.

Answer

Using in-place algorithms whenever possible.

Question 45

Consider two algorithms, A with space complexity O(n) and B with O(log n). What can be generally concluded about their space requirements as the input size grows significantly?

Accepted Answer

Algorithm B will generally require significantly less space than algorithm A for large inputs.

Answer

Both algorithms will have identical space requirements for large inputs.

Answer

Algorithm A will always require less space than algorithm B.

Question 46

An algorithm uses an array to store all the elements it processes. What is its space complexity?

Accepted Answer

O(n)

Answer

O(1)

Answer

O(log n)

Question 47

Which of the following is a common optimization technique that can help reduce the space complexity of an algorithm?

Accepted Answer

Using a hash table instead of an array can often reduce space complexity, especially for lookup operations.

Answer

Adding a recursive call generally increases space complexity due to the call stack.

Answer

Duplicating data structures almost always increases space complexity.

Answer

Increasing the number of input variables usually leads to higher space complexity.

Question 48

What is the space complexity of an algorithm performing a depth-first search on a tree?

Accepted Answer

O(h), where h is the height of the tree.

Answer

O(n)

Answer

O(n^2)

Answer

O(log n)

Question 49

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

Accepted Answer

Bubble sort

Answer

Quick sort

Answer

Merge sort

Answer

Heap sort

Question 50

An algorithm that processes a linked list using a single pointer has a space complexity of:

Accepted Answer

O(1)

Answer

O(log n)

Answer

O(n)

Answer

O(n^2)

Question 51

An algorithm that uses a binary tree to store data has a space complexity of:

Accepted Answer

O(n)

Answer

O(log n)

Answer

O(1)

Answer

O(n^2)

Question 52

Which of the following is a valid approach to analyze the space complexity of an algorithm?

Accepted Answer

Counting the number of variables used

Answer

Estimating the input size

Answer

Measuring the execution time

Answer

Ignoring auxiliary space requirements