# Waterfall challenge

I just finished preparing slides for my new computational thinking class, and since I don’t want to start on anything new half an hour before I leave the office, I went on twitter and saw this interesting post. It’s a programming challenge described here, with an imperative solution, and with a functional solution described in the first post.

The imperative solution is rather involved and looks like this:

The functional solution is more elegant but also a bit slower. Broken into three functions, as it is in the blog post referenced above, it looks like this:

Well, if you want to write fast code, your first thought should be: can I come up with a simple algorithm. Later, you can worry about implementing it.

Here, we have a problem that involves figuring out if a wall at any given position has higher walls to the left and the right, and if so, what the smallest wall to the left or right are. So, very easily, we can break it down into collecting a list of the tallest wall seen to the left and to the right of each position. This is something we can compute with the accumulate and accumulate_right functions from purrr. After that, we can solve the problem by mapping over these two vectors and the vector of wall heights, and we have a three line solution to the challenge.

Not only is this solution much simpler, it is also a lot faster.

Update: Ok, if I had been smarter half an hour ago I would have seen that the pmap expression was overkill. A vector expression will work just fine and be faster.

## Author: Thomas Mailund

My name is Thomas Mailund and I am a research associate professor at the Bioinformatics Research Center, Uni Aarhus. Before this I did a postdoc at the Dept of Statistics, Uni Oxford, and got my PhD from the Dept of Computer Science, Uni Aarhus.