Dijkstra Algorithm Questions Medium
The relaxation condition in the Dijkstra Algorithm is a crucial step that helps determine the shortest path from a source vertex to all other vertices in a weighted graph. It is responsible for updating the distance values of the vertices as the algorithm progresses.
The relaxation condition compares the current distance value of a vertex with the sum of the distance value of its neighboring vertex and the weight of the edge connecting them. If the sum is smaller than the current distance value, it means that a shorter path has been found, and the distance value of the vertex is updated accordingly.
By continuously applying the relaxation condition to all vertices in the graph, the Dijkstra Algorithm gradually finds the shortest path from the source vertex to all other vertices. This process ensures that the algorithm explores all possible paths and updates the distance values to reflect the shortest path found so far.
In summary, the relaxation condition plays a vital role in the Dijkstra Algorithm by continuously updating the distance values of vertices, allowing the algorithm to find the shortest path efficiently.