I worked on improving the strongly_connected_components function in this graph. 

This PR eliminates several of the arrays that were used for auxiliary data using various tricks inspired by https://homepages.ecs.vuw.ac.nz/~djp/files/IPL15-preprint.pdf , which reduces memory usage & allocations and improves cache efficiency. This seems to lead to a speedup in every category of random graphs in benchmarking. I would also subjectively claim that this version of the algorithm is more easily readable than Tarjan's original version.

Also put up a gist of a few alternatives I tried out:
https://gist.github.com/saolof/7b5d26a41e6a34ff2b3e76d3fc5541da

spelled function name correctly

Counting downwards instead of upwards has the advantage that rindex becomes a lookup table for components, if we ever decide to return both. Also makes the algorithm invariant crystal clear.

Fixed O(|E|^2) performance bug that used to be an issue for star graphs. 

Minimal change in performance for large random graphs, but significant speedup for graphs that have both lots of SCCs and high node orders.

Co-authored-by: Simon Schoelly <[email protected]>

Previous commit removed the if in front of iszero somehow

Slightly simplified logic and removed the need for zero_t.

Trying to figure out what broke. Can elements of outneighbours be equal to nothing?

testing

Set correct name on method

Added comments.

Added a dispatch to infer the types.

Changed everything to be T-valued. Partly to save space for small graphs represented using smaller types, and partly for correctness on machines where Int = Int32 and where the graph is large enough to require Int64s