Topological Sorting
Topological sorting is a linear ordering of the vertices of a directed acyclic graph (DAG) such that for every directed edge from vertex u to vertex v, u comes before v in the ordering. It is a fundamental algorithm in graph theory used to schedule tasks with dependencies, ensuring that prerequisites are completed before dependent tasks. This concept is widely applied in project management, build systems, and course scheduling.
Developers should learn topological sorting when working with dependency resolution problems, such as in build tools (e.g., Make, Gradle) to determine the order of compilation, or in task scheduling systems to manage workflows. It is essential for handling directed acyclic graphs in applications like package managers (e.g., npm, pip) to install dependencies correctly, and in data processing pipelines to ensure data flows without cycles.