So my lecture notes gave a "tabular" Dijkstra's algorithm which first constructs a distance matrix that contains the distances from every node $i$ to node $j$.
Then it proceeds:
List the node names in order (the example uses the alphabet). Take start node and write 0 beneath it, understrike it to signify that it's the final value, also list the distances to all the other nodes from the start node.
Move one row below and consider node B, write to it the shortest path (which coming from $A$ is 1). Then list all the distances to the other nodes as well, taking in account the distance that one came from $A$ to $B$. Again select the smallest path and understrike it for $B$. Continue ...
The final result in this case comes out to look like:
But particularly, since watching the def. for Dijkstra's algo in another site (https://brilliant.org/wiki/dijkstras-short-path-finder/), why doesn't one just take the shortest path directly? Why tabulate and construct distance matrices? Shouldn't it be clear that simply taking the shortest paths is both 1) most efficient and 2) feasible, since one knows all the distances.