"Black" means we've visited all vertices in subtree and left the vertex. Steps involved in detecting cycle in a directed graph using BFS. The idea is to simply use Kahn’s algorithm for Topological Sorting. Detect cycle in a directed graph using topological sort. Detect cycle in Directed Graph using Topological Sort , In Topological Sort, the idea is to visit the parent node followed by the child node. If there is a cycle in a directed graph, then you can detect this by running a depth-first search over the graph. (Don’t use depth first search, we want just a modification of the basic topological sort.) "White color" means that the vertex hasn't been visited yet. An acyclic graph always has a topological sort. I was trying to write code for detecting a cycle in a directed graph and if there is no cycle then return a topological order of the same. While I was searching for it I came across different techniques like DFS and topological sorting to detect cycle in a directed graph. Please corect me if this is not true. The answer is that both approaches will work. My union find code only get 38/47 test cases passed. And the answer is: If no vertex has indegree 0, we can find a cycle by tracing backwards through vertices with positive indegree; since every vertex on the trace back has a positive indegree, we eventually reach a vertex twice, and the cycle has been found. Your function should return true if the given graph contains at least one cycle, else return false. So, initially all vertices are white. And if the graph contains cycle then it does not form a topological sort, because no node of the cycle can appear before the other nodes of the cycle in the ordering. Topological Sort: TS can be only used to directed graph. "Gray" means that we've visited the vertex but haven't visited all vertices in its subtree. Minimum time taken by each job to be completed given by a Directed Acyclic Graph Hard Given a Directed Acyclic Graph having V vertices and E edges, where each edge {U, V} represents the Jobs U … Topological Sort / Cycle Detection. Detect Cycle in a Directed Graph Given a directed graph, check whether the graph contains a cycle or not. Before going into them, whenever you are dealing with representing graphs in files, you have to decide how you are going to format them. It seems like your question is the following: can you use depth-first search to detect cycles in an undirected graph, or should you use topological sort instead? If there is a cycle, I assume the topological order is useless. What about undirected graphs? Here's a little code for topological sort and cycle detection. The topological sort may not be unique i.e. Use the following approach: consider we have three colors, and each vertex should be painted with one of these colors. 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