Final step : nested partition thingies to actual molecules

So, the last step:

One thing to note about this is that the algorithm again has to backtrack to get all the molecules for any sub-partition list (another name for the things like [[3, 1], [3], [1, 1], [1]]).

Anyway, on the right hand side is the final (only) molecule made for this nested partition. It has the [4, 3, 2, 1] partition structure, naturally, and the correct constitutional formula.

Now what would be nice, would be to combine the second and third steps, so that only those nested partitions that produce valid molecules were tried. However, as the saying goes : "First, make it work, then make it work fast".

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