Enzyme is traditional, but super duper optimized, autodiff, that is, it returns the partial derivatives for one path taken through the program, ignoring other branches. DiscoGrad captures the effects of alternative branches. What's special about enzyme is that the gradient computations benefit from LLVM's optimization passes and language support.
You could model the problem as a graph (each integer represents a vertex and two consecutive integers an edge, e.g. (1, 2, 3) is a graph with nodes 1,2,3 and edges between 1 and 2 and 2 and 3). Then your problem is just to find all connected components of the graph (https://en.wikipedia.org/wiki/Connected_component_(graph_the....
Yeah but realising that two "nodes" of the graph are connected requires doing a set intersection, which I concluded was quite expensive to do between all possible sets. i.e. building the "graph" was an expensive operation... unless I've misunderstood you.
You build from the different tuples in your list just one graph. Then it's just a simple DFS/BFS with one random start node. Which gives you your first component. Then you can get the second if you start at a node which is not in the previous component until you visited all nodes. This should all be in O(n).
[(1, 2, 3), (2, 4, 5)] would result in a graph like this:
1 - 2 - 3
\
4 - 5
Building the (undirected) graph would take linear time, and once it is built, you can do a simple Depth First Search to mark all the connected components.
