DEV Community

Hanzla Baig
Hanzla Baig

Posted on • Originally published at dev.to on

4 2 2 2 2

Big O Notation: Understanding Time Complexity using Flowcharts

I highly recommend Edison's post on Big-O complexity in JavaScript. It's the friendliest article I've seen on the topic.

Article No Longer Available

I'll be taking points from Edison here as I visualize Big-O time complexity with flowcharts.

O log(n)

Logarithmic Time

log time

The way I visually understand time complexity is by looking at the iterator, i*2 for example , and looking at how many loops the function has.

O(n)

Linear Time

linear time

Linear time and logarithmic time look similar but the output is different because of the conditions of the loop. exampleLogarithmic(100) will return 1, 2, 4, 8, 16, 32, 64, whereas exampleLinear(100) simply loops through all positive integers under 100.

O(n^2)

Quadratic Time

quadratic time

The number of loops coincides with the exponent which n is raised to. You can literally see the function grow bigger as time complexity increases.

O(n^3)

Cubic Time

cubic time

This isn't the only way to understand time complexity, but it is really helpful to literally see the function grow longer as time complexity increases. Sometimes code written in black and white <pre> blocks doesn't get the point across to visual learners.

Now let's have a quiz. What is the time complexity of this function?

Make your guess...

Alt Text

It's linear! I can tell because there's one loop and the iterator doesn't cause the loop to skip over any integers.

What is the time complexity of this function?

Alt Text

Don't doubt yourself. Although this is a bit different from the first examples, it has linear time complexity.

What is the time complexity of this function?

linear

You may see a pattern here. It's linear!

Now, if you've been following my train of logic, this may be a trick question:

Alt Text

I said that the number of loops denoted the exponent n is raised to. So why is does this have linear time complexity and not quadratic?

This would have quadratic time complexity if it showed a for loop inside of another for loop. However, one for loop that runs after another for loop does not have quadratic but rather linear time complexity.

Okay, so what is the time complexity of this function?

linear

There's nothing tricky here. This has quadratic time complexity.

Now, for your last question - a question that questions all the other questions - what is this function's time complexity?

Alt Text

I hope you're looking at the conditions of the for loop as well as the sheer number of loops. This has quadratic time complexity because of the loop condition i<n*n.

I generated the images in this post with my app, whose development process I described in another post:

ender_minyard[

How to get 100 on Lighthouse

ender minyard ・ Aug 30 '20 ・ 2 min read

webperf#speed#javascript#webdev

](/ender_minyard/how-i-got-100-on-lighthouse-2icd)

Sentry blog image

How I fixed 20 seconds of lag for every user in just 20 minutes.

Our AI agent was running 10-20 seconds slower than it should, impacting both our own developers and our early adopters. See how I used Sentry Profiling to fix it in record time.

Read more

Top comments (0)

A Workflow Copilot. Tailored to You.

Pieces.app image

Our desktop app, with its intelligent copilot, streamlines coding by generating snippets, extracting code from screenshots, and accelerating problem-solving.

Read the docs

👋 Kindness is contagious

Dive into an ocean of knowledge with this thought-provoking post, revered deeply within the supportive DEV Community. Developers of all levels are welcome to join and enhance our collective intelligence.

Saying a simple "thank you" can brighten someone's day. Share your gratitude in the comments below!

On DEV, sharing ideas eases our path and fortifies our community connections. Found this helpful? Sending a quick thanks to the author can be profoundly valued.

Okay