What is 'Path Compression' and 'Union by Rank'?

What is 'Path Compression' and 'Union by Rank'?

Approach: Describe the two key optimizations for Union-Find.

Path compression flattens the tree during Find. Union by rank attaches the shorter tree to the root of the taller tree. Together, they make operations almost constant time.

Follow-up: What is the resulting complexity per operation?

Key concepts: flattening, shorter trees, inverse ackermann.