Thus, the above file defines a directed 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. 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. Is "topological sort of an undirected graph… So, initially all vertices are white. Am I correct so far? 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. Detect cycle in a directed graph using topological sort. While I was searching for it I came across different techniques like DFS and topological sorting to detect cycle in a directed graph. Use the following approach: consider we have three colors, and each vertex should be painted with one of these colors. Please corect me if this is not true. (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. The answer is that both approaches will work. What about undirected graphs? My union find code only get 38/47 test cases passed. Detect Cycle in a Directed Graph Given a directed graph, check whether the graph contains a cycle or not. If there are no cycles, I assume the topological order I found is valid. 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 … Here's a little code for topological sort and cycle detection. Union Find: For this question, since a child can have multiple parents, things get tricky. Your function should return true if the given graph contains at least one cycle, else return false. An acyclic graph always has a 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. The idea is to simply use Kahn’s algorithm for Topological Sorting. Steps involved in detecting cycle in a directed graph using BFS. graph can contain many topological sorts. "Black" means we've visited all vertices in subtree and left the vertex. 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. We have discussed a DFS based solution to detect cycle in a directed graph.In this post, BFS based solution is discussed. I can determine the topological sort of a directed graph using DFS algorithm. Topological Sort / Cycle Detection. 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