Union Find
In plain terms
The algorithm behind disjoint sets for merging and querying groups.
Going deeper
Union-find supports two operations: union (merge two groups) and find (which group is this in?), made fast with optimizations. It elegantly solves connectivity questions.
Under the hood
Path compression flattens trees and union by rank keeps them shallow, yielding nearly O(1) amortized operations.
Examples
Kruskal's algorithm, percolation, friend circles, dynamic connectivity.
Think of it like...
Like tracing everyone back to their family head to see if two people are related.