An Overview of Big-O Notation

How the efficiency between same purpose algorithms are judged

When you first started programming, the primary concern was figuring out an algorithm (or function, when put into practice) that would accomplish the task at hand. As your skills progressed, you started working on larger projects and studying concepts that would prepare you for a career in software engineering. One of the first concepts you would inevitably come across is asymptotic notation, or what is colloquially known as Big O Notation.

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In short, Big O Notation describes how long it takes a function to execute (runtime) as the size of an input becomes arbitrarily large. Big O can be represented mathematically as O(n), where “O” is growth rate (or order) of the function, and “n” is the size of the input. Translated into English, the runtime grows on the order of the input, or in the case of say O(n²), the order of the square of the size of the input.

This is a very important concept that will come up not only in your technical interviews, but also during your career when implementing solutions to handle large datasets. In this post I’ll give a brief overview on Big O analysis, simplifications, and calculations.

Big O Analysis

When using Big O to analyze an algorithm (asymptotic analysis), it should be noted that it primarily concerns itself with the worst and average case scenarios. For example, the runtime of an algorithm which sequentially searches a data set for a value that happens to be last, would be the worst case scenario.

Figuring out the worst case scenario is safe and thus never underestimated, though sometimes it may be overly pessimistic. Ultimately whether you analyze for worst or average case will depend on the use of your algorithm. For the typical problem the average case of an algorithm may be suitable, for cryptographic problems it’s usually best to seek out the worst case.

Heuristics for Calculating Big O

When calculating Big O, there are a couple of shortcuts that can help you

expedite the process:

  • Arithmetic, assignment, accessing an element in a array/object (by index/key) are all constant time, O(1)
  • In a loop, the runtime is the loop itself multiplied by whatever is in the loop

Keep these in mind for when you calculate the Big O for an algorithm I’ll provide towards the end.

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An Overview of Big-O Notation
Vern  Greenholt

Vern Greenholt


What Is Big O Notation?

As programmers, we often find ourselves asking the same two questions over and over again:

  1. How much time does this algorithm need to complete?
  2. How much space does this algorithm need for computing?

To put it in other words, in computer programming, there are often multiple ways to solve a problem, so

  1. How do we know which solution is the right one?
  2. How do we compare one algorithm against another?

The big picture is that we are trying to compare how quickly the runtime of algorithms grows with respect to the size of their input. We think of the runtime of an algorithm as a function of the size of the input, where the output is how much work is required to run the algorithm.

To answer those questions, we come up with a concept called Big O notation.

  • Big O describes how the time is taken, or memory is used, by a program scales with the amount of data it has to work on
  • Big O notation gives us an upper bound of the complexity in the worst case, helping us to quantify performance as the input size becomes arbitrarily large
  • In short, Big O notation helps us to measure the scalability of our code

Time and Space Complexity

When talking about Big O Notation it’s important that we understand the concepts of time and space complexity, mainly because_ Big O Notation_ is a way to indicate complexities.

Complexity is an approximate measurement of how efficient (or how fast) an algorithm is and it’s associated with every algorithm we develop. This is something all developers have to be aware of. There are 2 kinds of complexities: time complexity and space complexity. Time and space complexities are approximations of how much time and space an algorithm will take to process certain inputs respectively.

Typically, there are three tiers to solve for (best case scenario, average-case scenario, and worst-case scenario) which are known as asymptotic notations. These notations allow us to answer questions such as: Does the algorithm suddenly become incredibly slow when the input size grows? Does it mostly maintain its fast run time performance as the input size increases?

#performance #development #big o complexity #big o notation #big data

Ryleigh  Hamill

Ryleigh Hamill


Time Complexity & Big O notation | DSA-One Course - All you Need in One place

Hey guys, In this video, we’ll be talking about Time complexity and Big O notation. This is the first video of our DSA-One Course. We’ll also learn how to find the time complexity of Recursive problems.

Practice here:

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Silly mistakes that can cost ‘Big’ in Big Data Analytics

Big Data has played a major role in defining the expansion of businesses of all kinds as it helps the companies to understand their audience and devise their business techniques in accordance with the requirement.

The importance of ‘Data’ has been spoken very highly in the modern-day business. Thus, while using big data analysis, the companies must keep away from these minor mistakes otherwise it could have a major impact on their performances. Big Data analysis can be the silver bullet that can answer your questions and help your business to scale newer heights.

Read More: Silly mistakes that can cost ‘Big’ in Big Data Analytics

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Big Data can be The ‘Big’ boon for The Modern Age Businesses

The rapid growth of technology has led to many people opting for online services, and thus the collection and maintenance of data becomes a significant factor for any company. Big data analytics service providers can help the companies get a massive edge over their competitors as they would manage the data well and allow the businesses to make better business decisions. It will provide you with a combination of increased customer experience, revenue, and reduced cost and thus will create a win-win situation for your business. Big data technologies will be your perfect ally in excelling in the cut-throat business environment and come out with flying colors.

Read More: Big Data can be The ‘Big’ boon for The Modern Age Businesses

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Ian  Robinson

Ian Robinson


A Quick Overview of Metacat API for Discoverable Big Data

Introduction to Metacat API

MetacatAPI is an Application Programming Interface provides an interface and helps connect the two applications and enable them to communicate with each other. Whenever we use an application or send a request, the application connects to the internet and sends the request to the server, and the server then, in response, provides the fetched data.

The data set at any organization is stored in different data warehouses like Amazon S3 (via Hive), Druid, Elasticsearch, Redshift, Snowflake, and MySql.Spark, Presto, Pig, and Hive are used to consume, process, and produce data sets. Due to numerous data sources and to make the data platform interoperate and work as a single data warehouse Metacat was built. Metacat is a metadata exploration API service. Metadata can be termed as the data about the data. Metacat explores Metadata present on Hive, RDS, Teradata, Redshift, S3, and Cassandra.

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