# What is Big O notation?

by Stephen M. Walker II, Co-Founder / CEO

## What is Big O notation?

Big O notation is a mathematical notation that describes the performance or complexity of an algorithm. It provides an upper bound on the number of operations required for an algorithm to complete, as a function of its input size. This helps in understanding how an algorithm will behave as the input size grows, and in comparing the efficiency of different algorithms. The notation is widely used in computer science and software engineering, particularly in the analysis of sorting algorithms, searching algorithms, and other common data structures.

## How is Big O notation used in algorithm analysis?

Big O notation is used in algorithm analysis to describe the performance or complexity of an algorithm as a function of its input size. It provides an upper bound on the number of operations required for an algorithm to complete, which helps in understanding how the algorithm will behave as the input size grows. This is important because it allows us to compare the efficiency of different algorithms and choose the most suitable one for a given problem or application.

For example, if we have two sorting algorithms with different Big O notations, we can determine which one will perform better for large inputs by comparing their upper bounds on operations.

## What are some examples of Big O notation for different algorithms?

Some common examples of Big O notation for different algorithms include:

**Linear search**— O(n), where n is the size of the input array. This means that the number of operations required grows linearly with the size of the input.**Binary search**— O(log n), where n is the size of the input array. This means that the number of operations required grows logarithmically with the size of the input, making it much more efficient than linear search for large inputs.**Bubble sort**— O(n^2), where n is the size of the input array. This means that the number of operations required grows quadratically with the size of the input, making it a very inefficient sorting algorithm for large inputs.**Merge sort**— O(n log n), where n is the size of the input array. This means that the number of operations required grows linearly with the size of the input, but with an additional factor of logarithm, making it more efficient than bubble sort for large inputs.

## How does Big O notation compare the efficiency of different algorithms?

Big O notation is used to compare the efficiency of different algorithms by analyzing their upper bounds on operations as a function of input size. This allows us to determine which algorithm will perform better for large inputs, since we can see how their performance scales with the size of the input. For example, if we have two sorting algorithms with Big O notation of O(n^2) and O(n log n), respectively, we can conclude that the first algorithm will be much less efficient than the second one for large inputs, since its number of operations grows quadratically with the size of the input.

## Why is it important to understand Big O notation in computer science and software engineering?

Understanding Big O notation is important in computer science and software engineering because it provides a standard way of comparing the efficiency of different algorithms, allowing us to choose the most suitable algorithm for a given problem or application. Additionally, knowing how to analyze an algorithm's complexity can help in identifying potential bottlenecks and optimizing code for better performance.