This guide explains Cycle Detection from first principles. The goal is to understand the problem it solves, why the algorithm works, how to implement it, and where it appears in real software systems.
What problem does it solve?
Cycle Detection belongs to the graph-algorithm toolbox. Before coding, define what the vertices represent, what an edge means, and what result the system actually needs.
The core idea in simple terms
در گراف جهتدار معمولاً سه حالت unvisited، visiting و visited نگه میداریم.
Step-by-step process
- برای هر رأس state نگه میداریم.
- هنگام ورود آن را visiting میکنیم.
- رسیدن به visiting یعنی cycle.
- پس از پایان بررسی، state را visited میکنیم.
JavaScript example
function hasCycle(graph) {
const state = new Map();
function dfs(u) {
if (state.get(u) === 1) return true;
if (state.get(u) === 2) return false;
state.set(u, 1);
for (const v of graph[u] ?? []) if (dfs(v)) return true;
state.set(u, 2); return false;
}
return Object.keys(graph).some(dfs);
}Real-world and workplace examples
- Circular Dependency
- Workflow بینهایت
- Dependency بین Packageها
- اعتبارسنجی DAG
Time and space complexity
O(V + E) time و O(V) space
When should you use it?
Use it when the problem matches this condition: تشخیص dependency و loop ناسالم.
When is it not a good fit?
It is usually not the best choice when: برای reachability ساده، BFS/DFS معمولی کافی است..
Summary
Do not choose an algorithm by name alone. First identify whether the graph is directed or undirected, weighted or unweighted, and whether the goal is traversal, reachability, shortest path, connectivity, spanning structure, or combinatorial optimization.