Topological sorting is a linear ordering of vertices in a directed graph such that for every directed edge u -> v, vertex u comes before vertex v in the ordering. In simpler terms, it arranges the vertices of a directed graph in such a way that all directed edges go from left to right.
Topological sorting is applicable only to Directed Acyclic Graphs (DAGs). This is because cyclic dependencies cannot be topologically sorted. For instance, if vertex v appears before vertex u in the topological ordering and there is a directed edge u -> v, it would create a cycle in the graph.
Topological sorting has several applications, including:
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Task Scheduling: When tasks have dependencies on each other, topological sorting can determine the order in which tasks should be executed.
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Dependency Resolution: In software or package management systems, where packages may depend on other packages, topological sorting can determine the order of installation to resolve dependencies.
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Symbol Resolution: In compilers, topological sorting can determine the order of symbol resolution or code generation.
The algorithm for topological sorting typically involves using depth-first search (DFS) or breadth-first search (BFS) techniques. DFS-based algorithms are more commonly used for topological sorting. The process involves visiting each vertex of the graph, recursively visiting adjacent vertices, and marking vertices as visited. The vertices are then added to the topological ordering in reverse order of their finishing times in the DFS traversal.
