posts: union-find: add presentation

content/posts/2024-06-24-union-find/index.md

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