Disjoint Set
Disjoint Set / Union-Find tracks a collection of non-overlapping groups and supports two key operations: find which group an item belongs to, and union two groups.
ابدأ بهذا النموذج الذهني
Disjoint Set / Union-Find tracks a collection of non-overlapping groups and supports two key operations: find which group an item belongs to, and union two groups.
كيف يعمل، بلا مصطلحات زائدة
Each set has a representative root.
Path compression and union by rank/size make repeated operations almost constant amortized time.
اقرأ الخوارزمية كسلسلة من القرارات
Identify the invariant that must always remain true.
Follow the read/update path through the structure.
After a mutation, restore the invariant before returning.
Read a tiny input by hand and write down the state after every important operation. For Disjoint Set, the goal is to make the invariant visible rather than to memorize code.
amortized near O(1)
Do not quote this complexity mechanically. Ask which operation or input dimension it describes, then derive the cost from the loops, recursion depth, data-structure operations and any preprocessing assumptions.
مناسب لـ
- Kruskal MST
- Connectivity queries
- Cycle detection in undirected graphs
ما الذي يسوء عادةً
- Memorizing complexity without understanding representation.
- Ignoring worst-case shape or resizing/rebalancing costs.
صيغة إجابة احترافية
Name both optimizations—path compression and union by rank/size—and explain that the amortized complexity is inverse-Ackermann, effectively constant for practical sizes.
What problem does Disjoint Set solve?
Disjoint Set / Union-Find tracks a collection of non-overlapping groups and supports two key operations: find which group an item belongs to, and union two groups.
ماذا يجب أن أذكر عن التعقيد؟
Its typical cost here is amortized near O(1), but a complete answer should connect that cost to the representation, input constraints and the dominant operations.
ما الخطأ الأكثر شيوعاً؟
Memorizing complexity without understanding representation.