The Union‑Find Fellowship: Finding Your Tribe in Code

Short summary

A beginner-friendly tutorial on the Union-Find (Disjoint Set Union) data structure, explained through a gaming metaphor. The author covers the two key optimizations — union by rank and path compression — that bring amortized time per operation to near-constant O(α(n)). Includes a Python implementation and compares the approach against naive BFS/DFS for connectivity queries.

• •Union-Find answers connectivity queries in near-constant amortized time using path compression and union by rank
• •Naive BFS/DFS per query costs O(V+E), ballooning to O(n²) for dense graphs with many queries
• •Includes a compact Python implementation with both optimizations

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