Big O Notation: A Guide for Non-Computer Scientists

If you've ever wondered how computer programs work and why some are faster than others, you may have heard of Big O notation. In this guide, we'll explain what Big O notation is, how it works, and why it's important, all without assuming any prior knowledge of computer science.

## What is Big O notation?

Big O notation is a way of describing the performance of computer programs. Specifically, it describes how the time or space required by a program grows as the size of the input grows. The input can be anything from a list of numbers to a document to be searched.

Big O notation uses mathematical symbols to represent the growth rate of the program's time or space requirements. The "O" stands for "order of magnitude", which is a fancy way of saying "how quickly the requirements grow".

## Types of Big O notation

There are several common types of Big O notation. Here are some of the most important ones:

- O(1): This means that the program's time or space requirements do not depend on the size of the input. It's the fastest possible growth rate.

- O(log n): This means that the program's time or space requirements grow logarithmically with the size of the input. This is faster than linear growth (which we'll explain next), but slower than constant time.

- O(n): This means that the program's time or space requirements grow linearly with the size of the input. This is the most common growth rate for programs that process lists or other collections of data.

- O(n log n): This means that the program's time or space requirements grow "quasi-linearly" with the size of the input. It's faster than quadratic growth (which we'll explain next), but slower than linear growth.

- O(n^2): This means that the program's time or space requirements grow quadratically with the size of the input. This is a common growth rate for programs that involve nested loops or other operations that iterate over data multiple times.

- O(2^n): This means that the program's time or space requirements grow exponentially with the size of the input. This is the slowest possible growth rate and is usually considered impractical for large inputs.

## How to understand Big O notation

To understand Big O notation, it's helpful to think of the input size as a "problem size". For example, if you're searching for a word in a document, the problem size is the length of the document. If you're sorting a list of numbers, the problem size is the number of items in the list.

When we say that a program has a certain Big O notation, we're saying how its time or space requirements grow as the problem size grows. For example, if a program has a Big O notation of O(n), we mean that its time or space requirements grow linearly with the problem size.

## Why is Big O notation important?

Big O notation is important because it allows us to compare the performance of different programs. For example, if we have two programs that both solve the same problem, we can use Big O notation to see which one is more efficient.

Big O notation is also useful for understanding the limitations of programs. For example, if we know that a program has a Big O notation of O(n^2), we know that it will be slow for large inputs and may not be practical to use.

## Conclusion

Big O notation is a powerful tool for understanding the performance of computer programs. By describing the growth rate of a program's time or space requirements, we can compare different programs and understand their limitations.