Shortest path in a directed graph by Dijkstra’s algorithm
Given a directed graph and a source vertex in the graph, the task is to find the shortest distance and path from source to target vertex in the given graph where edges are weighted (non-negative) and directed from parent vertex to source vertices.
- Mark all vertices unvisited. Create a set of all unvisited vertices.
- Assign zero distance value to source vertex and infinity distance value to all other vertices.
- Set the source vertex as current vertex
- For current vertex, consider all of its unvisited children and calculate their tentative distances through the current. (distance of current + weight of the corresponding edge) Compare the newly calculated distance to the current assigned value (can be infinity for some vertices) and assign the smaller one.
- After considering all the unvisited children of the current vertex, mark the current as visited and remove it from the unvisited set.
- Similarly, continue for all the vertex until all the nodes are visited.
Below is the implementation of the above approach:
Distance of 0th vertex from source vertex 0 is: 0
Distance of 1th vertex from source vertex 0 is: 1
Distance of 2th vertex from source vertex 0 is: 3
Distance of 3th vertex from source vertex 0 is: 6
Auxiliary Space: O(V + E)
Related articles: We have already discussed the shortest path in directed graph using Topological Sorting, in this article: Shortest path in Directed Acyclic graph