Given a directed graph, check whether the graph contains a cycle or not. Your function should return true if the given graph contains at least one cycle, else return false. For example, the following graph contains two cycles 0->1->2->3->0 and 2->4->2, so your function must return true.
We have discussed a DFS based solution to detect cycle in a directed graph. In this post, BFS based solution is discussed.
The idea is to simply use Kahn’s algorithm for Topological Sorting
Steps involved in detecting cycle in a directed graph using BFS.
Step-1: Compute in-degree (number of incoming edges) for each of the vertex present in the graph and initialize the count of visited nodes as 0.
Step-2: Pick all the vertices with in-degree as 0 and add them into a queue (Enqueue operation)
Step-3: Remove a vertex from the queue (Dequeue operation) and then.
- Increment count of visited nodes by 1.
- Decrease in-degree by 1 for all its neighboring nodes.
- If in-degree of a neighboring nodes is reduced to zero, then add it to the queue.
Step 4: Repeat Step 3 until the queue is empty.
Step 5: If count of visited nodes is not equal to the number of nodes in the graph has cycle, otherwise not.
How to find in-degree of each node?
There are 2 ways to calculate in-degree of every vertex:
Take an in-degree array which will keep track of
1) Traverse the array of edges and simply increase the counter of the destination node by 1.
for each node in Nodes indegree[node] = 0; for each edge(src,dest) in Edges indegree[dest]++
Time Complexity: O(V+E)
2) Traverse the list for every node and then increment the in-degree of all the nodes connected to it by 1.
for each node in Nodes If (list[node].size()!=0) then for each dest in list indegree[dest]++;
Time Complexity: The outer for loop will be executed V number of times and the inner for loop will be executed E number of times, Thus overall time complexity is O(V+E).
The overall time complexity of the algorithm is O(V+E)
Time Complexity : O(V+E)
- Detect Cycle in a Directed Graph
- Detect Cycle in a directed graph using colors
- Detect cycle in the graph using degrees of nodes of graph
- Detect cycle in an undirected graph
- Detect cycle in an undirected graph using BFS
- Detect a negative cycle in a Graph | (Bellman Ford)
- Disjoint Set (Or Union-Find) | Set 1 (Detect Cycle in an Undirected Graph)
- Convert the undirected graph into directed graph such that there is no path of length greater than 1
- Check if a directed graph is connected or not
- Hierholzer's Algorithm for directed graph
- Convert Directed Graph into a Tree
- Euler Circuit in a Directed Graph
- Clone a Directed Acyclic Graph
- Longest Path in a Directed Acyclic Graph | Set 2
- All Topological Sorts of a Directed Acyclic Graph
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