Space complexity analysis in Data Structures Theory - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to represent the space complexity of storing an array of size n.

Data Structures Theory

Space complexity = O([1])

Drag options to blanks, or click blank then click option'

An^2

B1

Clog n

Dn

Attempts:

3 left

💡 Hint

Common Mistakes

Confusing time complexity with space complexity.

Choosing constant space when space grows with input size.

The space needed to store an array grows linearly with the number of elements, so it is O(n).

2fill in blank

medium

Complete the code to express the space complexity of a recursive function that calls itself n times without extra storage.

Data Structures Theory

Space complexity = O([1])

Drag options to blanks, or click blank then click option'

An log n

Bn

C1

Dlog n

Attempts:

3 left

💡 Hint

Common Mistakes

Assuming recursion uses constant space.

Confusing the number of calls with the space used.

Each recursive call adds a new layer to the call stack, so the space grows linearly with n, making it O(n).

3fill in blank

hard

Fix the error in the space complexity expression for a function that creates a 2D matrix of size n x n.

Data Structures Theory

Space complexity = O([1])

Drag options to blanks, or click blank then click option'

An^2

Bn

Clog n

D1

Attempts:

3 left

💡 Hint

Common Mistakes

Using O(n) instead of O(n²) for 2D structures.

Confusing time complexity with space complexity.

A 2D matrix with n rows and n columns stores n*n elements, so the space complexity is O(n²).

4fill in blank

hard

Fill both blanks to complete the space complexity of a function that stores a list and a dictionary each with n elements.

Data Structures Theory

Space complexity = O([1] + [2])

Drag options to blanks, or click blank then click option'

An

B1

Dlog n

Attempts:

3 left

💡 Hint

Common Mistakes

Assuming dictionary uses constant space.

Not adding the space of both data structures.

Both the list and dictionary store n elements, so their space complexities add up to O(n + n) which simplifies to O(n).

5fill in blank

hard

Fill all three blanks to complete the space complexity of a function that creates a list of size n, a set of size n, and a constant number of variables.

Data Structures Theory

Space complexity = O([1] + [2] + [3])

Drag options to blanks, or click blank then click option'

An

C1

Dlog n

Attempts:

3 left

💡 Hint

Common Mistakes

Counting constant variables as O(n).

Confusing logarithmic space with linear space.

The list and set each use O(n) space, and the constant variables use O(1). The total is O(n + n + 1), which simplifies to O(n).

Practice

1. What does space complexity measure in an algorithm?

easy

A. The number of steps the algorithm performs

B. The time it takes for the algorithm to run

C. The number of errors the algorithm produces

D. The amount of memory the algorithm uses as input size grows

Solution

1. Step 1: Understand the definition of space complexity

   Space complexity refers to how much memory or storage an algorithm needs while running, especially as the input size increases.

2. Step 2: Differentiate from time complexity

   Time complexity measures how long an algorithm takes, not memory usage. Hence, space complexity is about memory.

3. Final Answer:

   The amount of memory the algorithm uses as input size grows -> Option D

4. Quick Check:

   Space complexity = memory usage [OK]

Hint: Space complexity = memory needed as input grows [OK]

Common Mistakes:

• Confusing space complexity with time complexity
• Thinking it measures steps or errors
• Ignoring memory usage in the definition

2. Which of the following correctly represents constant space complexity in Big O notation?

easy

A. O(n)

B. O(1)

C. O(n^2)

D. O(log n)

Solution

1. Step 1: Recall Big O notation for constant space

   Constant space means the algorithm uses the same amount of memory regardless of input size.

2. Step 2: Identify the notation for constant space

   O(1) means constant space, O(n) means linear, O(n^2) quadratic, and O(log n) logarithmic space.

3. Final Answer:

   O(1) -> Option B

4. Quick Check:

   Constant space = O(1) [OK]

Hint: Constant space always uses O(1) [OK]

Common Mistakes:

• Choosing O(n) for constant space
• Confusing time and space complexity notations
• Misunderstanding logarithmic space

3. Consider the following pseudocode:
function example(arr):
  temp = []
  for i in arr:
    temp.append(i)
  return temp
What is the space complexity of this function?

medium

A. O(n^2)

B. O(1)

C. O(n)

D. O(log n)

Solution

1. Step 1: Analyze memory usage for the temporary list

   The function creates a new list 'temp' and appends each element from input 'arr', so 'temp' grows linearly with input size n.

2. Step 2: Determine space complexity based on 'temp'

   Since 'temp' stores all elements, space used is proportional to n, so space complexity is O(n).

3. Final Answer:

   O(n) -> Option C

4. Quick Check:

   New list size = input size n -> O(n) space [OK]

Hint: Extra list storing all input means O(n) space [OK]

Common Mistakes:

• Assuming constant space because no nested loops
• Confusing time complexity with space complexity
• Ignoring the temporary list's size

4. Identify the error in the following code regarding space complexity:
def process(n):
  result = 0
  for i in range(n):
    temp = [0] * n
    result += sum(temp)
  return result
What is the space complexity and what is the mistake?

medium

A. O(n), mistake: temp list is recreated inside loop causing high memory use

B. O(1), mistake: temp list should be outside loop to save memory

C. O(n^2), mistake: temp list size grows each iteration

D. O(n), mistake: result variable should be a list

Solution

1. Step 1: Analyze space used by 'temp' inside the loop

   Each iteration creates a list 'temp' of size n, but it is discarded after the iteration ends, so peak memory is O(n).

2. Step 2: Identify the mistake in memory usage

   Recreating 'temp' inside the loop wastes memory repeatedly; better to create once outside the loop.

3. Final Answer:

   O(n), mistake: temp list is recreated inside loop causing high memory use -> Option A

4. Quick Check:

   Repeated list creation inside loop = O(n) space [OK]

Hint: Creating large lists inside loops wastes memory [OK]

Common Mistakes:

• Thinking space is O(1) because temp is local
• Assuming temp grows each iteration (it doesn't)
• Confusing time complexity with space complexity

5. You have a nested list of size n, where each element is a list of size n (an n x n matrix). You want to create a new list that contains the sum of each inner list. What is the space complexity of storing the sums?

hard

A. O(n)

B. O(log n)

C. O(1)

D. O(n^2)

Solution

1. Step 1: Understand the input structure

   The input is an n x n matrix (list of n lists, each of size n), so total elements are n^2.

2. Step 2: Analyze the output list size

   The output list stores one sum per inner list, so it has n elements, which means space complexity is O(n).

3. Final Answer:

   O(n) -> Option A

4. Quick Check:

   One sum per inner list -> O(n) space [OK]

Hint: One value per inner list means O(n) space [OK]

Common Mistakes:

• Assuming output space is O(n^2) like input
• Confusing input size with output size
• Ignoring that sums reduce data size