![]() ![]() In the context of the previous example, these starting vertices represent algorithms and data structures that don't have any prerequisites you don't need to learn anything else first, hence the sort starts with them. These vertices are the starting points for the topological sort. Vertices with no incoming edges have an in-degree of 0. The in-degree of a vertex is the number of edges pointing at that vertex. Step 1: Find all vertices that have in-degree of 0 This is exactly what topological sort is used for - it will sort things out so that you know what to do first. To learn something you might have to know something else first. If we consider each algorithm to be a vertex in the graph you can clearly see the dependencies between them. If we were to represent these objectives in the form of a graph it would look as follows: In turn, graphs and trees use the idea of linking objects together, so you may need to read up on that first. But before you can learn about the depth-first search algorithm, you need to know what a graph is, and it helps to know what a tree is. What else do you need to learn first before you can fully understand topological sort? Well, topological sort uses depth-first search as well as a stack. Since you're learning about topological sort, let's take this topic as an example. ![]() This might seem daunting at first but we can use topological sort to get things organized. ![]() Let's consider that you want to learn all the algorithms and data structures from the Swift Algorithm Club. The following is not a valid topological sort for this graph, since X and T cannot happen before V: Notice how the arrows all go from left to right. The topological orderings are S, V, W, T, X and S, W, V, T, X. This graph has two possible topological sorts: In other words, a topological sort places the vertices of a directed acyclic graph on a line so that all directed edges go from left to right.Ĭonsider the graph in the following example: Topological sort is an algorithm that orders a directed graph such that for each directed edge u→v, vertex u comes before vertex v. ![]()
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