## Find the Big-O notation explained for not-so-technical people from Codility’s very own Head of Engineering, Marcin Kubica, Ph.D.

### Setting the scene

### Painting a pyramid

Imagine that a painter picks up a paint bucket and roller, climbs the pyramid, paints some of it, and returns to the base. How much paint can they carry? I don’t know exactly, but it’s *O*(1) — which is “some,” but a *limited* amount. How much surface can they paint at once? Again, I don’t know exactly how much, but it’s proportional to the amount of paint that is *O*(1). And how about climbing up and down the pyramid? It’s a different story. If the painted area is at height *H*, climbing up and down takes* O*(*H*) time.

Now imagine the part of the pyramid that is beneath the painted area. Its volume is also *O*(*H*), which is proportional to *H. *Since each part of the pyramid is beneath the top surface, **the total time it takes the painters to climb up and down the pyramid is proportional to the pyramid’s volume.**

In other words, climbing up and down the pyramid takes *O*(*N*^3) time, while painting alone takes only *O*(*N*^2) time. For large pyramids, painters would spend more time going up and down the ladder than they would actually painting the surface.