Big O Notation

Big O is used to find how long it will take for an algorithm to run and the amount of space required for the code. In development and programming, programmers must weigh trade offs like system demands, program simplicity, and output desirability. Big O helps with this analysis.

What is Big O Notation?

This mathematical notation incorporates algebraic terms to determine the level of complexity for code. It is used to find how long it will take for an algorithm to run and the amount of space required for the code. Rather than talking about the runtime speed itself, big O notation looks at how fast the runtime grows as the input, denoted with n, grows. In function notation, it looks at how fast a function of n, F(n) grows as n grows.

There are different types of complexity which include constant O(1), linear O(n), polynomial O(n2) or O(n3), logarithmicO(log n), exponential O(nn) or O(2n), and factorial O(nn!). The “O” in the name stands for “order.” the polynomial, n2, has a second order. In computer science, constant and logarithmic complexity are the most desirable. Constant complexity means that no matter what the input size is, the runtime will remain the same. Logarithmic complexity occurs when program runtime increases slowly even with large increases in input sizes.

Steps to Calculate Big O

To calculate big O, follow these steps:

  1. Separate the algorithm into code blocks or individual operations.
  2. Calculate the big O of each code block/operation.
  3. Add the big O of each operation together.
  4. Remove any constants.
  5. Choose the highest order term, or type of complexity. This is the complexity or big O of the algorithm.

Why is Big O Notation Useful?

This type of analysis is also called asymptotic analysis because it searches for the limit behavior of a function as it approaches infinity or a particular value. The runtime of an algorithm is always the ultimate worst-case runtime, or the highest amount of runtime reached. If a program is composed of multiple code blocks with different runtimes, then the runtime considered is always the worst value since it will have the largest effect on the set of code as a whole.

In computer science, big O notation is used:

  • when comparing two algorithms as the number of inputs, n, increases;
  • by programmers to determine an approximate runtime of algorithms based on an input set; and
  • as a form of algorithm analysis.

Algorithm analysis is important because it allows for more efficient codes to be produced and chosen. It also allows programmers to consider using more productive coding practices.

This notation does come with caution. One is that the method ignores constants which are still needed to run in programs and affect the runtime optimization. Additionally, when code is adjusted for better optimization, readability, time to maintain, and time required to code may suffer. The benefits must outweigh any risks that may occur. As you become a more experienced programmer, you will find that these decisions become second nature. If you are interested in computer science and computer programming, this is a useful method to understand for your future coding projects and a great skill to add to your resume.

How to Learn Big O Notation

This mathematics-based skill can be learned from bootcamps designed specifically for learning how to calculate and use this information in the computer programming world. Bootcamps are offered in-person, online, and via hybrid combinations of the two formats. Check them out below!

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