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Union-Find (Disjoint Set Union): connectivity and grouping.

Union-Find answers 'are these in the same group?' near-instantly and powers connected-components, cycle detection, and clustering. The signal is path compression plus union by rank for near-O(1) operations. Here is the answer.

Updated Aug 2026 · Grounded in real Applied AI Engineer interview loops and written to a senior-engineer editorial bar.

Union-Find answers 'are these in the same group?' near-instantly and powers connected-components, cycle detection, and clustering. The signal is path compression plus union by rank for near-O(1) operations. Here is the answer.

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