Boruvka
Every component picks its cheapest outgoing edge simultaneously; components halve each round.
Round 1: 6 components. Each picks its cheapest edge to another component: component 0 picks 0-2 (3); component 1 picks 1-2 (1); component 2 picks 1-2 (1); component 3 picks 1-3 (2); component 4 picks 3-4 (2); component 5 picks 2-5 (5). 5 distinct edges, because two components often pick the same one.
What you will see
All components choose at once; the forest merges in parallel rounds.
Cost
| Best | O(E log V) |
|---|---|
| Average | O(E log V) |
| Worst | O(E log V) |
| Space | O(V) |
How you work with it here
play it through, step one change at a time, scrub to any step, run it on your own input, predict what happens next, try operations in any order.
Screen readers: Edges announce endpoints, weight and state (candidate, accepted, rejected); each step announces the decision and the reason.
Reduced motion: Accepted edges thicken with a crossfade; no travelling highlights.