DAA Series Graphs Part 9 :- directed acyclic graph (DAG) | Shortest Path in DAG

DAA Series Graphs Part 9 :- directed acyclic graph (DAG) | Shortest Path in DAG Access The Playlist from here :-    • design and analysis of algorithms(DAA)   Get Best Notes Of DAA From Here:- https://drive.google.com/drive/folder... About Video :- Shortest Path in a Directed Acyclic Graph (DAG): An optimized algorithm to find the shortest path between two vertices in a directed acyclic graph. The Shortest Path in a Directed Acyclic Graph (DAG) algorithm offers an efficient and reliable solution for determining the shortest path between any two vertices in a graph structure. DAGs are directed graphs that do not contain any cycles, making them particularly useful for modeling scenarios where there is a natural ordering or hierarchy among the nodes. By leveraging the acyclic nature of the graph, this optimized algorithm achieves superior performance in terms of time and space complexity. It employs a dynamic programming approach, utilizing a topological ordering of the vertices to systematically compute the shortest path. The algorithm begins by assigning an initial distance value of infinity to all vertices except the source vertex, which is set to zero. It then iteratively updates the distance values for each vertex based on the weights of the edges connecting them. By gradually relaxing the edges in the topological order, the algorithm ensures that all necessary calculations are performed, leading to the determination of the shortest path. As the algorithm progresses, it maintains a data structure called the shortest path tree, which stores the parent-child relationships among the vertices. This tree is continuously updated as the shortest paths are discovered, ensuring that the final result contains the shortest path from the source vertex to the destination vertex. With its optimized design, the Shortest Path in a Directed Acyclic Graph algorithm is capable of handling large-scale graphs efficiently, making it an invaluable tool in various domains such as network routing, project scheduling, and resource allocation. Its ability to identify the shortest path with reduced time complexity and minimal memory requirements makes it a go-to solution for solving complex graph traversal problems. #DAGs #graphtheory #datastructures #algorithm #ComputationalComplexity #dataflow #bigdata #ParallelComputing #machinelearning #datascience directed acyclic graph directed acyclic graphs directed acyclic graph example directed acyclic graph in compiler design directed acyclic graph dag how to draw directed acyclic graph directed acyclic graph for expressions directed acyclic graphs in compiler design how to draw directed acyclic graph in compiler design directed acyclic graph in cd wat is directed acyclic graph what is directed acyclic graph directed acyclic graph werking directed acyclic graph shortest path in directed acyclic graph shortest path in directed acyclic graph gfg shortest paths shortest path directed graph single source shortest path in directed acyclic graph single source shortest path shortest path algorithm directed acyclic graph example shortest path in directed graph directed acyclic graphs shortest path in dag examples of single shortest path in directed acyclic graph