Algorithms Space & Time Complexity Analysis

Question 1

What is the time complexity of binary search on a sorted array of n elements?

Accepted Answer

O(log n)

Answer

O(n)

Answer

O(n log n)

Answer

O(1)

Question 2

Which Big-O notation describes the worst-case time complexity of bubble sort?

Accepted Answer

O(n²)

Answer

O(n log n)

Answer

O(n)

Answer

O(log n)

Question 3

An algorithm with O(1) space complexity means:

Accepted Answer

It uses a constant amount of extra memory regardless of input size

Answer

It uses memory proportional to input size

Answer

It requires no memory at all

Answer

It uses logarithmic extra memory

Question 4

What is the time complexity of accessing an element by index in a dynamic array (e.g., Python list)?

Accepted Answer

O(1)

Answer

O(log n)

Answer

O(n)

Answer

O(n²)

Question 5

The recurrence T(n) = 2T(n/2) + O(n) describes which well-known algorithm's complexity?

Accepted Answer

Merge sort

Answer

Insertion sort

Answer

Selection sort

Answer

Linear search

Question 6

Which of the following time complexities grows the fastest as n increases?

Accepted Answer

O(2ⁿ)

Answer

O(n log n)

Answer

O(n²)

Answer

O(n³)

Question 7

What does the Master Theorem primarily help determine?

Accepted Answer

The time complexity of divide-and-conquer recurrences

Answer

The correctness of a recursive algorithm

Answer

The optimal base case for recursion

Answer

The space used by a recursive call stack