perf(prim): index the edges by endpoint instead of rescanning them - #804
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Every time a node joins the tree, the loop walks the whole edge list to find the edges that touch it, so growing an MST costs one pass over the edges per node: O(V*E) before the queue does any work at all. Almost all of that scanning looks at edges that touch neither endpoint. Index the edges by endpoint once, up front, and offer only the edges leaving the node just added. The same candidates reach the queue in the same order, so the tree and the order of its edges are unchanged, including the tie-breaking the existing tests pin down. `visited` also moves to the crate's hasher. Checked against `kruskal` over 200 random connected graphs. About 86% off a 1500-node, 9500-edge graph. The saving grows with the edge count, since the work per node added no longer depends on it.
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Closes #802.
Indexes the edges by endpoint once, up front, and offers only the edges leaving the node just added, instead of walking the whole edge list every time a node joins the tree.
The same candidates reach the queue in the same order, so the tree and the order of its edges are unchanged, including the tie-breaking the existing tests pin down.
visitedalso moves to the crate's hasher.Checking
Verified against
kruskalover 200 random connected graphs. The three existing tests assert exact output and are unaffected.About 86% off a 1500-node, 9500-edge graph, measured against this branch's parent. The saving grows with the edge count, since the work per node added no longer depends on it.
Built on #797, which is included here as the first commit because the indexing change touches the same seeding code. Review that one first; once it lands I will rebase this so only the second commit remains.
All timings measured on Windows 11, Intel Core Ultra 7 265K, 64 GB RAM.