Dijkstra’s algorithm solves the “single source shortest path problem”, which means that it finds the minimum distance from a given “source” node to every other node in the graph (or at least every con...Dijkstra’s algorithm solves the “single source shortest path problem”, which means that it finds the minimum distance from a given “source” node to every other node in the graph (or at least every connected node). The simplified version is similar to the breadth-first search in the previous section except that we replace the set called seen with a dictionary called dist, which maps from each node to its distance from the source:
Move v to X and for each edge (v, u) such that v is in V \ X, update the current distance to u, i.e., do d(s, u) = min(d(s, u), d(s, v) + w(v, u)), where w(v, u) is the length of the edge from v to u....Move v to X and for each edge (v, u) such that v is in V \ X, update the current distance to u, i.e., do d(s, u) = min(d(s, u), d(s, v) + w(v, u)), where w(v, u) is the length of the edge from v to u. In order to see why the algorithm is correct, notice that if u, ..., w, v is the shortest path from u to v, then it can be constructed from the shortest path from u to w by adding the edge between w and v to it.
