Partitions to er..'nested partitions'

So I don't have a good name for the objects that I create half-way through this process : the code uses 'solution', which is confusing. Anyway, here is the process:


The left hand side is clear enough, I think, and follows on from the image in the previous post. Conceptually, it is similar to 'gathering' the attachment points into half-bonds in all possible ways. So, the 4 attachment points on the bare carbon fragment can become a triple (half) bond, and a single half bond. This is shown, as [3, 1].

Of course, there are other possibilities, and each combination at each atom fragment has to be paired with each other possibility at each other fragment! If this sounds like a backtracking problem, then you might understand why I did exactly this in the code.

What would be nice, would be to prune the solutions - for example, [[3, 1], [2, 1], [1, 1], [1]] is generated, but is clearly impossible. Neither the triple half-bond, nor the double half-bond have partners. Pruning these would be easy enough; but looking more than one position ahead seems tricky.

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