Dijkstra Algorithm Questions Long
In the Dijkstra Algorithm, the destination vertex plays a crucial role in determining the shortest path from the source vertex to all other vertices in a weighted graph. The algorithm aims to find the shortest path from the source vertex to the destination vertex by considering the weights of the edges connecting the vertices.
The significance of the destination vertex lies in its role as the ultimate goal or target vertex. The algorithm starts by initializing the source vertex with a distance of 0 and all other vertices with a distance of infinity. It then iteratively explores the neighboring vertices of the source vertex, updating their distances based on the weights of the edges.
During each iteration, the algorithm selects the vertex with the minimum distance from the source vertex as the current vertex. By doing so, it ensures that the algorithm always considers the most promising path towards the destination vertex. The algorithm continues this process until it reaches the destination vertex or until all vertices have been visited.
The destination vertex serves as the termination condition for the algorithm. Once the algorithm reaches the destination vertex, it can stop the iterations and return the shortest path from the source vertex to the destination vertex. This path is determined by tracing back the predecessors of each vertex from the destination vertex to the source vertex.
In summary, the significance of the destination vertex in the Dijkstra Algorithm is that it acts as the target vertex, guiding the algorithm towards finding the shortest path from the source vertex. It serves as the termination condition and allows the algorithm to determine the shortest path by tracing back the predecessors from the destination vertex to the source vertex.