Common complexity classes (O(1), O(n), O(log n), O(n²)) in Data Structures Theory - Practice Problems & Coding Challenges

Challenge - 5 Problems

🧠 Conceptual

intermediate

Understanding constant time complexity O(1)

Which of the following operations typically runs in constant time, O(1)?

A Accessing an element by index in an array

B Searching for an element in an unsorted list

C Sorting a list of numbers

D Traversing all elements in a linked list

💡 Hint

Think about operations that take the same amount of time regardless of input size.

Accessing an element by index in an array takes the same time no matter how big the array is, so it is O(1). Searching or traversing depends on the number of elements, so they are not constant time.

📋 Factual

intermediate

Identifying linear time complexity O(n)

Which scenario best represents an algorithm with linear time complexity O(n)?

A Accessing the last element of a fixed-size array

B Checking if a number is even or odd

C Calculating the sum of the first 100 numbers

D Finding a specific value by scanning each element in a list

💡 Hint

Consider how the time grows as the input size increases.

Scanning each element to find a value means the time grows directly with the number of elements, which is linear O(n). Checking even/odd or accessing fixed positions are constant time.

🔍 Analysis

advanced

Comparing logarithmic time complexity O(log n)

Which of the following algorithms typically runs in logarithmic time O(log n)?

A Binary search on a sorted array

B Linear search on an unsorted array

C Calculating the factorial of a number

D Bubble sort on a list

💡 Hint

Think about algorithms that repeatedly divide the problem size in half.

Binary search divides the search space in half each step, so it runs in O(log n). Linear search and bubble sort take longer as input grows, factorial calculation is not logarithmic.

🚀 Application

advanced

Recognizing quadratic time complexity O(n²)

Which example best illustrates an algorithm with quadratic time complexity O(n²)?

A A single loop that runs n times

B A recursive function that halves the input each call

C Nested loops where each loop runs n times

D Accessing elements in a hash table

💡 Hint

Consider how many times the inner operations run as input size grows.

Nested loops each running n times result in n × n = n² operations, which is quadratic time. Single loops are linear, recursive halving is logarithmic, and hash table access is constant time.

❓ Reasoning

expert

Determining time complexity from code snippet

What is the time complexity of the following code snippet?

def example_function(arr):
    for i in range(len(arr)):
        j = len(arr)
        while j > 0:
            j //= 2
            print(arr[i])

A O(log n)

B O(n log n)

C O(n)

D O(n²)

💡 Hint

Analyze how many times the inner while loop runs for each iteration of the outer for loop.

The outer loop runs n times. The inner while loop divides j by 2 each time, running about log n times. Multiplying gives O(n log n).