As a programmer, you’ve probably heard the phrase “Big O notation” a lot. But what is it, and why is it so significant? This beginner’s guide will explain what Big O notation is, how it works, and why it is important in the world of programming.

What is Big O Notation?

At its core, Big O notation is a way of describing the time complexity of an algorithm. In other words, it’s a measure of how long an algorithm takes to run based on the size of its input. The “O” in Big O stands for “order of magnitude,” which essentially means that it’s a way of estimating how an algorithm’s running time scales with respect to the size of its input.

For example, suppose you have an algorithm that sorts a list of numbers in ascending order. The length of time it takes to perform the method is determined by the size of the list. The algorithm will execute quickly if the list is only a few numbers long. However, if the list is really big (for example, millions of numbers), the method will take significantly longer to perform.

Big O notation provides a way of expressing this relationship between an algorithm’s input size and its running time. It does this by providing a “worst-case scenario” estimate of how long the algorithm will take to run. In other words, it tells you how long the algorithm will take to run if you give it the largest possible input size.

How Does Big O Notation Work?

The concept of “asymptotic analysis” underpins Big O notation. This means that it is concerned with how an algorithm operates when the size of its input approaches infinity. In other words, it is not concerned with how long an algorithm takes to run for a certain input size (such as a list of 100 values), but rather with how it performs as the input size increases.

To understand how Big O notation works, let’s look at a few examples:

• O(1): This notation represents algorithms that take a constant amount of time to run, regardless of the input size. An example of this would be accessing a specific element in an array. It doesn’t matter how big the array is; accessing a specific element will always take the same amount of time.
• O(n): This notation represents algorithms that have a linear relationship between input size and running time. An example of this would be iterating through an array and performing a simple operation on each element.
• O(n^2): This notation represents algorithms that have a quadratic relationship between input size and running time. An example of this would be nested loops that iterate through an array and perform an operation on each pair of elements.

There are other additional Big O notations, but these three are the most prevalent. The key point to remember is that Big O notation allows you to categorize algorithms based on how they scale with input size.

Why Does Big O Notation Matter?

So why is Big O notation important? For one thing, it provides a way of comparing different algorithms and determining which one is more efficient. If you have two algorithms that accomplish the same task, but one has a time complexity of O(n) and the other has a time complexity of O(n^2), you know that the first algorithm will be faster for large input sizes.