> For the complete documentation index, see [llms.txt](https://algorithm.prettylog.com/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://algorithm.prettylog.com/algorithm-problems/algoexpert/medium/cycle-in-graph.md).

# Cycle in Graph -

![](/files/jO6KNI8OH3xRixC316Rq)

* just checking there is a cycle

```jsx
/*
0: white => not yet
1: grey => in traversing a graph
2: black => completed
*/

function cycleInGraph(edges) {
  const hasCycle = dfsAll(edges);
  
  return hasCycle;
}

function dfsAll(adjacencyList) {
  const visited = new Array(adjacencyList.length).fill(0);
  
  for (let i = 0; i < adjacencyList.length; i++) {
    const vertex = i;
    if (visited[vertex] !== 0) continue;
    if (visited[vertex] === 2) continue; 
		// either is fine
    
    const hasCycle = dfs(adjacencyList, vertex, visited);
    console.log({
      visited
    })
    if (hasCycle === true) return true;
  }
  
  return false;
}

function dfs(adjacencyList, here, visited) {
  visited[here] = 1;

  const edges = adjacencyList[here];
  for (let i = 0; i < edges.length; i++) {
    const there = edges[i];
    
    if (visited[there] === 1) return true;
    if (visited[there] === 2) continue;
    const hasCycle = dfs(adjacencyList, there, visited);
    if (hasCycle === true) return true;
  }

  visited[here] = 2;
  return false;
}

// Do not edit the line below.
exports.cycleInGraph = cycleInGraph;
```

```jsx
// traverse short
function dfs(adjacencyList, here, visited) {
  visited[here] = 1;

  const edges = adjacencyList[here];
  for (let i = 0; i < edges.length; i++) {
    const there = edges[i];
    
    if (visited[there] === 1) return true;
    if (visited[there] === 2) continue;
    const hasCycle = dfs(adjacencyList, there, visited);
    if (hasCycle === true) return true;
  }

  visited[here] = 2;
  return false;
}
// traverse more than above
function dfs(adjacencyList, here, visited) {
  visited[here] = 1;

	let hasCycle = false;
  const edges = adjacencyList[here];
  for (let i = 0; i < edges.length; i++) {
    const there = edges[i];
    
    if (visited[there] === 1) return true;
    if (visited[there] === 2) continue;
    hasCycle = dfs(adjacencyList, there, visited);
  }

  visited[here] = 2;
  return hasCycle;
}
```

* v + e, v
* with everything

```jsx
/*
0: white => not yet
1: grey => in traversing a graph
2: black => completed
*/

let hasCycle = false;
function cycleInGraph(edges) {
  hasCycle = false;
  dfsAll(edges);
  
  return hasCycle;
}

function dfsAll(adjacencyList) {
  const totalVisited = new Array(adjacencyList.length).fill(0);
  
  let howManyComponents = 0;
  for (let i = 0; i < adjacencyList.length; i++) {
    const vertex = i;
    
    if (totalVisited[vertex] !== 0) continue; // if it is 1, then error
    howManyComponents += 1;
    
    const visited = new Array(adjacencyList.length).fill(0);
    dfs(adjacencyList, vertex, totalVisited, visited);
  }

  console.log({
    howManyComponents,
    totalVisited,
    hasCycle
  })
}

function dfs(adjacencyList, here, totalVisited, visited) {

  totalVisited[here] = 1;
  visited[here] = 1;

  const edges = adjacencyList[here];
  for (let i = 0; i < edges.length; i++) {
    const there = edges[i];
    if (visited[there] === 1) {
      hasCycle = true;
      // return;
      break;
    }

    if (visited[there] === 2) continue;

    dfs(adjacencyList, there, totalVisited, visited);
  }

  totalVisited[here] = 2;
  visited[here] = 2;
}

// Do not edit the line below.
exports.cycleInGraph = cycleInGraph;
```


---

# Agent Instructions
This documentation is published with GitBook. GitBook is the documentation platform designed so that both humans and AI agents can read, navigate, and reason over technical content effectively. Learn more at gitbook.com.

## Querying This Documentation
If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question.

Perform an HTTP GET request on the current page URL with the `ask` query parameter, and the optional `goal` query parameter:

```
GET https://algorithm.prettylog.com/algorithm-problems/algoexpert/medium/cycle-in-graph.md?ask=<question>&goal=<endgoal>
```

`ask` is the immediate question: it should be specific, self-contained, and written in natural language.
`goal` is optional and describes the broader end goal you are ultimately trying to accomplish on behalf of the user. GitBook uses it to tailor the answer towards what is most useful for that goal.

The response will contain a direct answer to the question and relevant excerpts and sources from the documentation.

Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.