Topological sorting is the process of arranging the vertices of a Directed Acyclic Graph (DAG) in a linear order such that for every directed edge u -> v, vertex u comes before vertex v in the ordering. This technique is widely used in scenarios where tasks must be performed in a specific order, such as task scheduling, resolving dependencies, or course prerequisites. There are two main algorithms to achieve topological sorting: Depth-First Search (DFS) and Kahn’s algorithm. In the DFS-based approach, you perform a DFS traversal and add vertices to the topological order as they are fully explored (i.e., when all their outgoing edges are visited). This results in a reverse post-order of the DFS traversal. In Kahn’s algorithm, you iteratively remove vertices with no incoming edges, ensuring that all dependencies are resolved before removing a vertex. In TypeScript, you can implement both methods using adjacency lists to represent the graph. Topological sorting is particularly useful in applications like task scheduling systems, where certain jobs depend on others, or in compiler design, where the compilation order of modules must follow the dependency chain.