Scan before you solve

For each problem, extract three things in the first read: the largest n and q, the OPERATION MIX (updates vs queries, ordered vs arbitrary), and what quantity is asked (value? count? existence?). That triple usually pins the algorithm family before you understand the story.

Range question + updates on segments = lazy tree family. Reachability questions = SCC/DSU/union family. "Best swap after building X" = exchange argument on top of the standard construction. Say the family out loud, then verify with the constraints: n = 2e5 with per-op O(n) is dead; O(n log n) or O(n alpha) is alive.