How does Union find work?

Union Find: Making Sense of Connections

Ever stumbled upon a problem where you need to figure out if things are connected, or how they group together? That’s where Union Find, also known as Disjoint Set Union (DSU), comes to the rescue. It’s like having a super-efficient tool for managing groups of friends, where you can quickly check if two people are in the same circle or merge two groups together. Think of it as your go-to data structure for untangling connectivity puzzles.

So, what’s the big idea? Union Find is all about keeping track of elements neatly divided into separate, non-overlapping sets. Each set gets a representative – like the president of a club – who acts as the set’s identifier. The magic happens with two main actions:

• Find(x): This is like asking, “Hey, which club does this person ‘x’ belong to?” It tells you the representative of the set ‘x’ is part of, effectively revealing its group membership.
• Union(x, y): Time to merge! This combines the groups of ‘x’ and ‘y’ into one big happy family. Now, ‘x’ and ‘y’ are officially in the same set.

Let’s get our hands dirty with a basic example. Imagine you have an array where each element initially thinks it’s the boss of its own little world.

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