Cycle Detection
Cycle Detection is a algorithm in the graphs family. This graph algorithm works over vertices and edges, usually using an adjacency list/matrix plus explicit state such as visited, distance, parent or indegree.
先从这个心智模型开始
Cycle Detection is a algorithm in the graphs family. This graph algorithm works over vertices and edges, usually using an adjacency list/matrix plus explicit state such as visited, distance, parent or indegree.
它如何工作，不堆砌不必要的术语
Cycle Detection should be understood through its invariant and the state it changes at each step.
The practical complexity in this reading is Varies by implementation / input constraints; always connect that cost to the actual loops, recursion, data structure operations or input assumptions.
把算法读成一连串决策
Define directed/undirected and weighted/unweighted assumptions.
Choose the graph representation.
Track algorithm state and handle disconnected/cyclic cases explicitly.
Read a tiny input by hand and write down the state after every important operation. For Cycle Detection, the goal is to make the invariant visible rather than to memorize code.
Varies by implementation / input constraints
Do not quote this complexity mechanically.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.
适用场景
- Use the algorithm only when its graph assumptions match the problem.
通常哪里会出错
- Forgetting disconnected components.
- Mixing weighted and unweighted shortest-path algorithms.
- Not protecting against revisits/cycles.
专业回答结构
A strong interview explanation of Cycle Detection should cover the problem it solves, its invariant, the important data structure/state, its Varies by implementation / input constraints cost, and the constraint that would make you choose a different approach.
What problem does Cycle Detection solve?
Cycle Detection is a algorithm in the graphs family. This graph algorithm works over vertices and edges, usually using an adjacency list/matrix plus explicit state such as visited, distance, parent or indegree.
关于复杂度应该提到什么？
Its typical cost here is Varies by implementation / input constraints, but a complete answer should connect that cost to the representation, input constraints and the dominant operations.
最常见的错误是什么？
Forgetting disconnected components.