posts: union-find: add presentation
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@ -24,3 +24,27 @@ operations: `ds.union(lhs, rhs)` and `ds.find(elem)`.
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[series]: {{< ref "/series/lesser-known-algorithms-and-data-structures/">}}
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<!--more-->
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## What does it do?
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The _Union-Find_ data structure allows one to store a collection of sets of
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elements, with operations for adding new sets, merging two sets into one, and
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finding the representative member of a set. Not only does it do all that, but it
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does it in almost constant (amortized) time!
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Here is a small motivating example for using the _Disjoint Set_ data structure:
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```python
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def connected_components(graph: Graph) -> list[set[Node]]:
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# Initialize the disjoint set so that each node is in its own set
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ds: DisjointSet[Node] = DisjointSet(graph.nodes)
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# Each edge is a connection, merge both sides into the same set
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for (start, dest) in graph.edges:
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ds.union(start, dest)
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# Connected components share the same (arbitrary) root
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components: dict[Node, set[Node]] = defaultdict(set)
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for n in graph.nodes:
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components[ds.find(n)].add(n)
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# Return a list of disjoint sets corresponding to each connected component
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return list(components.values())
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```
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