How do you use Big O notation to evaluate algorithm performance?

1 What is Big O notation?

Big O notation is a way of expressing the upper bound or worst-case scenario of an algorithm's complexity. It ignores constant factors and lower-order terms that are insignificant for large inputs. For example, if an algorithm takes 3n + 5 steps to complete, its Big O notation is O(n), because the linear term n dominates the constant term 5. Big O notation helps you focus on the most important factor that affects the algorithm's performance.

3 How to compare Big O notation?

To compare the Big O notation of different algorithms, you need to consider how they behave as the input size increases. For example, if you have two algorithms with Big O notation O(n) and O(n^2), the first one is more efficient and scalable than the second one, because it grows slower than the second one. The common Big O notation from fastest to slowest are O(1), O(log n), O(n), O(n log n), O(n^2), O(2^n), and O(n!). The lower the Big O notation, the better the algorithm's performance.

4 How to use Big O notation in coding?

Big O notation is useful for coding because it helps you choose the best algorithm for a given problem and optimize your code. For example, if you need to search for an element in a sorted array, you can use a binary search algorithm with Big O notation O(log n) instead of a linear search algorithm with Big O notation O(n), because the former is faster and more efficient. You can also use Big O notation to analyze the trade-offs between time and space complexity, and decide whether to use more memory or more computation.

5 How to write Big O notation in documentation?

Big O notation is also helpful for documentation because it helps you communicate the performance and expectations of your code to other developers and users. For example, if you write a function that sorts an array, you can use Big O notation to indicate how fast or slow your function is and what kind of inputs it can handle. You can write the Big O notation in comments, docstrings, or annotations, depending on the programming language and style guide you use. For example, in Python, you can write:

def bubble_sort(array):
  """Sorts an array using bubble sort algorithm.
  Args:
    array: A list of numbers.
  Returns:
    A sorted list of numbers.
  Complexity:
    O(n^2) time and O(1) space.
  """
  # Your code here        

6 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?