Algorithms Space & Time Complexity Analysis 3

Question 1

What is the time complexity of finding the minimum element in an unsorted array of n elements?

Accepted Answer

O(n)

Answer

O(log n)

Answer

O(1)

Answer

O(n log n)

Question 2

Which of the following best describes the space complexity of an iterative (non-recursive) merge sort?

Accepted Answer

O(n)

Answer

O(1)

Answer

O(log n)

Answer

O(n²)

Question 3

The time complexity of building a binary heap from an unsorted array using the heapify-down approach is:

Accepted Answer

O(n)

Answer

O(n log n)

Answer

O(n²)

Answer

O(log n)

Question 4

An algorithm is described as O(n!) in time complexity. What category does this fall into?

Accepted Answer

Factorial

Answer

Polynomial

Answer

Logarithmic

Answer

Exponential

Question 5

When analyzing an algorithm with multiple independent phases that run sequentially, what is the overall time complexity if the phases are O(n²), O(n log n), and O(n)?

Accepted Answer

O(n²)

Answer

O(n² + n log n + n)

Answer

O(n² · n log n · n)

Answer

O(3n²)

Question 6

What is the time complexity of a single operation on a balanced binary search tree (e.g., AVL or Red-Black tree) for search, insert, or delete?

Accepted Answer

O(log n)

Answer

O(1)

Answer

O(n)

Answer

O(n log n)

Question 7

Which of the following sorting algorithms achieves O(n) time complexity under specific conditions (e.g., limited integer range)?

Accepted Answer

Counting sort

Answer

Heapsort

Answer

Merge sort

Answer

Quicksort