The shortest path algorithm

Finding the shortest path, and optimization of routes based on time and distance, has countless implementations in the real world for transportation and map-related applications. The same algorithms also apply to network routing protocols such as Intermediate System to Intermediate System (IS-IS) and OSPF (Open Shortest Path First). There are various algorithms, optimizations, and heuristics available to solve shortest path problems including, but not limited to, A*, Dijkstra, and the Bellman-Ford algorithm.

In graph theory, Dijkstra's shortest-path algorithm is one of the most well-known algorithms. It is a special case of the A* algorithm, which helps in solving the problem of finding the shortest path in a graph, from the source node to the destination. This problem is also known as a single-source shortest path problem because it is possible to discover the shortest path given the single source (vertex).

In various practical applications, each link or edge...