fig minimum cost paths and total cost from source vertex minimum cost path between any two vertices in weighted graph this algorithm can beand sometimes isgeneralized to find the minimum cost path between source vertex and all other vertices in graph this algorithm is known as dijkstra' algorithm figure shows the result of running dijkstra' algorithm on the graph first presented in fig the purple edges show the minimum cost paths from source vertex to all other vertices in the graph the orange values are the minimum cost of reaching each vertex from source vertex efficiently finding minimum cost path from one vertex to another is used in all kinds of problems including network routingtrip planningand other planning problems where vertices represent intermediate goals and edges represent the cost of transitioning between intermediate goals these kind of planning problems are very common dijkstra' algorithm proceeds in greedy fashion from the single source vertex each vertexvin the graph is assigned cost which is the sum of the weighted edges on the path from the source to initially the source vertex is assigned cost all other vertices are initially assigned infinite cost anything greater than the sum of all weights in the graph can serve as an infinite value this copy belongs to 'acha