Topological sorting is applicable when you have a directed graph, and you want to arrange its vertices in a linear order such that for every directed edge u -> v, vertex u comes before vertex v in the ordering. In other words, topological sorting is applicable when:
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You have a directed acyclic graph (DAG): Topological sorting can only be performed on directed acyclic graphs (DAGs). If the graph contains cycles, it's not possible to arrange its vertices in a way that respects the direction of the edges without violating the acyclic property.
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You need to determine the order of operations or dependencies: Topological sorting is commonly used in scenarios where you have tasks, operations, or elements that depend on each other, and you need to determine the order in which they should be executed or processed. For example:
- Task scheduling: Tasks that depend on other tasks must be scheduled after their dependencies.
- Dependency resolution: In software or package management systems, packages may depend on other packages, and topological sorting determines the order of installation to resolve dependencies.
- Symbol resolution: In compilers, topological sorting determines the order of symbol resolution or code generation.
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You want to detect cycles: While topological sorting itself requires a DAG, the process of attempting to perform topological sorting can also be used to detect cycles in a graph. If a cycle is detected during the topological sorting process, it indicates that the graph is not a DAG and cannot be topologically sorted.
Overall, topological sorting is applicable in various scenarios where you need to establish a linear ordering of elements based on directed dependencies, and it provides a way to handle tasks, operations, or dependencies in a systematic and efficient manner.
