Shorted paths algorithms

 





Shorted Path Properties






Dijkstra's algorithm (Java code)






edge-weighted Direct Acyclic Graphs (DAGs)

Negative Weights

Shortest paths summary Dijkstra’s algorithm. ・Nearly linear-time when weights are nonnegative. ・Generalization encompasses DFS, BFS, and Prim. 
Acyclic edge-weighted digraphs. ・Arise in applications. ・Faster than Dijkstra’s algorithm. ・Negative weights are no problem. 
Negative weights and negative cycles. ・Arise in applications. ・If no negative cycles, can find shortest paths via Bellman-Ford. ・If negative cycles, can find one via Bellman-Ford. 
Shortest-paths is a broadly useful problem-solving model.

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