7/30/2023 0 Comments Stack vs queue topo sort![]() Since a DAG has only finite paths, there will always exist a longest path P.So, P is the longest path only if the indegree of source vertex u = 0 and outdegree of destination vertex v = 0. For P to meet the definition of the longest path that is finite or acyclic, the source vertex u can’t have any incoming edge, and destination vertex v can’t have any outgoing edge.Let us say it starts from source vertex u and ends at destination vertex v. P is directed and acyclic, so it has a beginning and an end.Let us now consider a path P that represents the longest path in G. In other words, all paths in G are of finite length. Since there is no cycle, there’s no endless loop that exists as a path in the graph. Let's try and prove this assertion and see if it’s accurate:įor any directed acyclic graph G, we can say that it does not contain a cycle. The basis of Kahn’s Algorithm is the following assertion:Ī directed acyclic graph (DAG) G has at least one vertex with the indegree zero and one vertex with the out-degree zero. This article focuses on one of these algorithms: Kahn’s algorithm (Kahn algorithm or Kahn topological sort), which can help people working as software developers/coding engineers solve some complicated-looking questions with more ease. To learn about this in more detail, check out our article on topological sort.Īs you may know, topological sorting can be done using algorithms like Kahn’s algorithm, depth-first search, and some parallel algorithms. This means there may be multiple valid topological orderings possible for the same DAG. Topological order is the result of a linear ordering of a DAG’s vertices such that for every directed edge (U, V) present in it, U comes before V in the topological ordering. One of these sorting algorithms is topological sort, or top sort, which is defined only for directed acyclic graphs (DAGs). If you are a software engineer looking to land your dream job, sorting algorithms are an indispensable part of your technical interview prep.
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