Topological Sorting
TOPOLOGICAL SORTING
A way of #sorting Directed Acyclic Graphs (DAGs) such that for a #directed #edge (u, v), vertex #u comes before vertex #v in the ordering. It aligns the edges in a way that reflects #dependencies among them.
Core Idea
The core idea of topological sort is to |#iteratively select vertices with an indegree of 0 and #remove them along with their #outgoing #edges. These vertices are naturally free of dependencies and can be safely included in the #ordering.
Implementation
To implement this process, you maintain a #queue and start by #enqueuing all vertices with an indegree of 0. Then, you #dequeue a vertex, #add it to the #sorted result, and reduce the indegree of its neighbors. If any neighbor's indegree becomes 0, it's #enqueued for processing.
The process continues until the queue is #empty. If there are still vertices left but none have an indegree of 0, it means the graph has #cycles, making a topological ordering #impossible. This is an important characteristic: topological sort is only #feasible on #DAGs.
Use Cases
This order can be used in various scenarios such as #scheduling #tasks, #compiling #code with #dependencies, and more. Topological sort also finds its #applications in many fields, including project management, build systems, job scheduling in #OS, #resolving dependencies in #software #packages, and more.
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