## Dijkstra's algorithm in a weighted and oriented graph in more than 128 words

For a source peak given in the graph, the algorithm looks for the shortest path between that node and all the others.

Here one uses a weighted graph, which is a graph in which each arc (case of a oriented graph) receives a weight. A weighted graph is therefore a special type of labeled graph in which the labels are numbers.

The weight of a chain or path is the sum of the weights of the arcs that make up the chain.

The algorithm enters a weighted graph and a summit from which it calculates distances, the steps are:

Initialization phase:

• On all the tops, a label equal to infinity (or at the maximum possible length – 1) is positioned on all the tops.
• The label is started on A to 0

Treatment phase:

• We treat a summit (here we start with A)
• We mark the summit as visited
• We release the outbound arches from the summit, i.e. we try to update the value of the top-of-the-finish label by distance.
• If the value of the road to the top of the finish is lower than the calculated, the top tag is updated with this total distance.
• The next top to be treated is the one with the lowest weight.

Example: