Time Complexity and Big O

Time Complexity and Big O

Time Complexity and Big O. Understanding how algorithm efficiency is measured and optimized. In this article, we’re going to explore the concept of efficiency within computer science and learn some ways to measure and describe this efficiency.

Introduction

Time should always be on a programmer’s mind. Namely, saving users and customers more of it. The less time users spend waiting, the more time they spend doing useful things with your product or service.

Just as with all aspects of life, there are many ways to solve a programming challenge. And — just as with real life — the method you choose could directly affect how long it takes to solve your problem. In this article, we’re going to explore the concept of efficiency within computer science and learn some ways to measure and describe this efficiency. By understanding how efficient our algorithms are, we can get a sense of where we may want to refactor our processes in order to get faster runtimes.

The Concepts

If you’re already familiar with the concepts of time complexity and Big O and just need a quick refresher on how to calculate them, skip ahead to the “Finding Complexity” section.

Okay, so we need a way to easily compare two algorithms in terms of their efficiency. We could try comparing the actual runtimes of our functions but this method has problems. We can’t directly and consistently answer the question “how much time does it take for my code to run?” because it depends on too many variables. How fast your computer is, whether you’re running other applications at the same time, what programming language you’re using, are all factors in determining the actual runtime of your code. So instead of asking this question directly, we ask a similar question: “how does the runtime of my function grow as the size of my input grows?”. This turns out to be a much more important question to answer when thinking about how our algorithm will perform at scale, as opposed to comparing a single runtime of one algorithm to a single runtime of another which really isn’t giving us all the information we need. For example, we could have an algorithm that has a very fast runtime for small inputs, but that time could increase exponentially as the size of our input increases.

Time Complexity

The term we use to describe how our algorithm performs under varying input sizes is its time complexity. Time complexity is a way of labeling — in plain English — how the runtime of a function increases as the size of our input increases. Some examples of time complexity labels are constant time, logarithmic time, linear time, and quadratic time (just to name a few). These labels describe the relationship between the size of our input and our runtime, and you might notice that they also describe the shape of various types of lines on a two-dimensional plot. This gives us a great, easy way to visualize how our runtime changes in regards to the input size. More on this in a bit.

Big O

Big O notation is a way of describing this relationship mathematically, and it looks like this: O(1), O(log n), O(n), O(n²), etc., all representing a different time complexity relationship (constant time, logarithmic time, etc.).

We can use Big O notation to describe time complexity under best, average, and worst-case scenarios, but we’re almost always only concerned with the worst case. Like we’ve said, an algorithm can have very fast runtimes for small inputs (best case), but drastically worse runtimes for larger ones (worst case) so it’s always important to know how your code is going to perform under the most trying circumstances.

Quick note: It’s extremely common to be asked to analyze the complexity of your algorithm in technical/coding interviews. They are typically expecting an answer in Big O notation.

programming computer-science data-science big-o-notation

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