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10 cards from this deck
A minimum spanning tree (MST) of a connected, weighted graph
Subset of edges connecting all vertices with no cycles and minimum total weight
Sort all edges in ascending order by weight
v−1v-1v−1 edges
Disjoint sets (union-find)
O(eloge)O(e \log e)O(eloge) where eee is the number of edges
O(eloge+elogv)O(e \log e + e \log v)O(eloge+elogv)
O(v)O(v)O(v) for union-find structures
Connected graphs (otherwise gives spanning forest)
When edge weights are not distinct
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