How it works?

Union-find keeps a parent array. Each vertex starts as its own root. Two operations drive everything:

• find(x): follow parent links until you reach a root (a vertex that is its own parent). Two vertices are connected when they share a root.
• union(a, b): point one root at the other, merging the two sets.

Kruskal's Algorithm:

1. Process edges from smallest weight to largest.
2. For each edge, find the roots of its endpoints. If they differ, the edge joins two separate pieces: union them and add its weight to the total.
3. If the roots are the same, the edge would form a cycle, so skip it.

After processing every edge, the chosen edges form the MST (for a connected graph, exactly n - 1 of them).