Exercise on Dijkstra’s algorithm

Question

I would like to build, applying Dijkstra's algorithm, all paths of least weight starting from s and arriving at every other vertex of the graph:

This is my attempt.

The distance values are shown in the following table for each step of the algorithm:

The resulting shortest path from s is marked in blu in the following graph:

Is it correct?

Answer 1

It is an easy question, you can implement Dijkstra's algorithm in any perferred programming language.

You can use Mathematica to verify the correctness of your answer.

g = Graph[{s -> a, s -> e, s -> f, a -> b, a -> d, a -> e, a -> f, 
   b -> c, d -> b, d -> c, e -> c, e -> d, f -> d, f -> e},
  EdgeWeight -> {3, 10, 5, 11, 8, 6, 6, 3, 2, 6, 13, 3, 5, 5}, 
  VertexLabels -> "Name", EdgeLabels -> "EdgeWeight"]


Table[HighlightGraph[g, PathGraph@FindShortestPath[g, s, All][v]], {v,
   VertexList[g]}]


{GraphDistanceMatrix[g] // MatrixForm, VertexList[g]}

The graph distance matrix is

Your answer is correct.