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Detect cycle in a directed graph using topological sort. Steps involved in detecting cycle in a directed graph using BFS. If there are no cycles, I assume the topological order I found is valid. 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. My union find code only get 38/47 test cases passed. Thus, the above file defines a directed graph. The idea is to simply use Kahn’s algorithm for Topological Sorting. Union Find: For this question, since a child can have multiple parents, things get tricky. If there is a cycle, I assume the topological order is useless. Topological Sort / Cycle Detection. Am I correct so far? The topological sort may not be unique i.e. Your function should return true if the given graph contains at least one cycle, else return false. Use the following approach: consider we have three colors, and each vertex should be painted with one of these colors. 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. "Black" means we've visited all vertices in subtree and left the vertex. 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 the given graph contains a cycle, then there is at least one node which is a parent as well as a child so this will break Topological Order. What about undirected graphs? "White color" means that the vertex hasn't been visited yet. An acyclic graph always has a topological sort. 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 in a directed graph, then you can detect this by running a depth-first search over the graph. 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. Here's a little code for topological sort and cycle detection. Topological Sort: TS can be only used to directed graph. We have discussed a DFS based solution to detect cycle in a directed graph.In this post, BFS based solution is discussed. So, initially all vertices are white. (Don’t use depth first search, we want just a modification of the basic topological sort.) The answer is that both approaches will work. Before going into them, whenever you are dealing with representing graphs in files, you have to decide how you are going to format them. "Gray" means that we've visited the vertex but haven't visited all vertices in its subtree. 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