Online problems: queries arrive one at a time; you must answer before seeing the next. Standard Union-Find works. Offline problems: all queries given upfront; you can process in any order. For offline problems with deletions, reverse time:
Start with final state (all deletions applied)
Process queries in reverse, turning deletions into unions
Answer queries in reverse order Example: "Process edge additions and deletions, answer connectivity after each." - Hard online (need special deletion support)
- Easy offline (reverse order, deletions become additions)
When you see deletion queries, think "can I solve this offline?"