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 … What about undirected graphs? "White color" means that the vertex hasn't been visited yet. Is "topological sort of an undirected graph… Union Find: For this question, since a child can have multiple parents, things get tricky. Am I correct so far? Please corect me if this is not true. "Gray" means that we've visited the vertex but haven't visited all vertices in its subtree. The answer is that both approaches will work. If there is a cycle, I assume the topological order is useless. Here's a little code for topological sort and cycle detection. We have discussed a DFS based solution to detect cycle in a directed graph.In this post, BFS based solution is discussed. Detect cycle in a directed graph using topological sort. Detect Cycle in a Directed Graph Given a directed graph, check whether the graph contains a cycle or not. 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. 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. Thus, the above file defines a directed graph. The idea is to simply use Kahn’s algorithm for Topological Sorting. If there is a cycle in a directed graph, then you can detect this by running a depth-first search over the graph. Before going into them, whenever you are dealing with representing graphs in files, you have to decide how you are going to format them. 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. "Black" means we've visited all vertices in subtree and left the vertex. (Don’t use depth first search, we want just a modification of the basic topological sort.) So, initially all vertices are white. An acyclic graph always has a topological sort. Topological Sort: TS can be only used to directed graph. Your function should return true if the given graph contains at least one cycle, else return false. 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? Topological Sort / Cycle Detection. While I was searching for it I came across different techniques like DFS and topological sorting to detect cycle in a directed graph. My union find code only get 38/47 test cases passed. graph can contain many topological sorts. 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