Water Monoids

Solving that water-puddles problem, using as many monoids as possible.

In the toy problem described by I Failed a Twitter Interview, we are given a list of integers

3, 2, 1, 4, 2

representing the heights of walls

3 2 1 4 2

and we imagine pouring water onto this structure such that puddles accumulate in the gaps.

We are then asked: How much water is held by the structure? (In the above example, the answer is 3).

Monoids

I find mys…