Dijkstra Algorithm Questions Medium
The weight function in the Dijkstra Algorithm is used to assign a numerical value, known as weight or cost, to each edge in a graph. This weight represents the distance or cost associated with traversing that edge. The role of the weight function is to guide the algorithm in finding the shortest path from a source vertex to all other vertices in the graph.
By considering the weights of the edges, the Dijkstra Algorithm determines the most efficient path by continuously updating the tentative distances from the source vertex to all other vertices. It selects the vertex with the smallest tentative distance as the current vertex and explores its neighboring vertices, updating their tentative distances if a shorter path is found.
The weight function plays a crucial role in the algorithm's decision-making process, as it influences the selection of the next vertex to explore and the determination of the shortest path. Without the weight function, the algorithm would not be able to differentiate between different paths and would not be able to find the shortest path accurately.
In summary, the weight function assigns weights to edges, representing the cost or distance, and guides the Dijkstra Algorithm in finding the shortest path by considering these weights during the exploration and updating of tentative distances.