Time complexity (Big O notation) in Data Structures Theory - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to represent the time complexity of a loop that runs n times.

Data Structures Theory

for i in range([1]):
    print(i)

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

A1

Blog n

Cn**2

Dn

Attempts:

3 left

💡 Hint

Common Mistakes

Choosing 1, which means constant time, but the loop depends on n.

Choosing n**2, which is for nested loops, not a single loop.

The loop runs exactly n times, so its time complexity is O(n).

2fill in blank

medium

Complete the code to represent the time complexity of a nested loop where both loops run n times.

Data Structures Theory

for i in range(n):
    for j in range([1]):
        print(i, j)

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

A1

Blog n

Cn

Dn**2

Attempts:

3 left

💡 Hint

Common Mistakes

Choosing 1, which ignores the inner loop.

Choosing log n, which is unrelated to nested loops.

The inner loop runs n times for each of the n iterations of the outer loop, so the total is n * n = n².

3fill in blank

hard

Fix the error in the time complexity expression for a binary search algorithm.

Data Structures Theory

The time complexity of binary search is O([1])

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Alog n

Bn log n

Cn**2

Dn

Attempts:

3 left

💡 Hint

Common Mistakes

Choosing n, which is linear time and too slow for binary search.

Choosing n log n, which is typical for sorting algorithms, not binary search.

Binary search divides the search space in half each time, so it runs in logarithmic time, O(log n).

4fill in blank

hard

Fill the blank to complete the time complexity expression for a function with a loop running n times and a nested loop running log n times.

Data Structures Theory

The time complexity is O(n [1] log n)

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A+

B*

C-

D/

Attempts:

3 left

💡 Hint

Common Mistakes

Using plus instead of multiplication, which changes the meaning.

Using division or subtraction, which are not standard in Big O notation.

The total time complexity is the product of n and log n, so O(n * log n).

5fill in blank

hard

Fill all three blanks to complete the time complexity expression for a function with a constant time operation, a linear loop, and a quadratic nested loop.

Data Structures Theory

Total time complexity: O([1] + [2] + [3])

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A1

B+

Cn

Dn**2

Attempts:

3 left

💡 Hint

Common Mistakes

Omitting the constant term or using multiplication instead of addition.

Confusing n and n squared terms.

The total time complexity adds constant time (1), linear time (n), and quadratic time (n²). The dominant term is n², but the full expression is O(1 + n + n²).