You’re on a tight budget for optimizing algorithms. What’s the best tool to use?

2 Why use Big O notation?

Big O notation is a useful tool for optimizing algorithms because it helps you compare different algorithms and choose the best one for your problem. For example, if you have two algorithms that sort a list of numbers, one with a Big O notation of O(n^2) and one with a O(n log n), you can easily see that the second one is more efficient and faster than the first one, because it grows slower as the input size increases. By using Big O notation, you can avoid wasting time and resources on algorithms that are too slow or too complex for your needs.

3 How to use Big O notation?

In order to utilize Big O notation, it is necessary to understand the basic rules and steps. For example, you must identify the input and output of your algorithm. The input is the data that your algorithm takes as an argument, while the output is the result that your algorithm returns. Additionally, you must count the number of operations that your algorithm performs on the input. An operation is any basic action that your algorithm does, such as assigning or accessing a value. Furthermore, you must find the worst-case scenario for your algorithm. This is the input which causes your algorithm to perform the most operations. Lastly, you must simplify the number of operations using Big O notation. This notation uses symbols and rules to express the number of operations. For instance, O(n) means that the number of operations is proportional to the input size, O(n^2) means that the number of operations is proportional to the square of the input size, and O(1) means that the number of operations is constant, regardless of the input size.

4 Examples of Big O notation

To understand Big O notation, let's analyze some common algorithms. Linear search checks each element one by one and its Big O notation is O(n). Binary search divides the list in half and compares the middle element with the value, and its Big O notation is O(log n). Selection sort finds the smallest element and swaps it with the first element, then finds the second smallest element and swaps it with the second element, resulting in a Big O notation of O(n^2). Lastly, Merge sort divides the list into two halves, sorts each half recursively, and merges the two sorted halves with a Big O notation of O(n log n).

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?