How does the Dijkstra algorithm work to find the shortest path in a graph?

How does the Dijkstra algorithm work to find the shortest path in a graph?

The Dijkstra algorithm is a popular and efficient algorithm used to find the shortest path from a source vertex to all other vertices in a weighted graph. It works by maintaining a set of vertices whose shortest distance from the source vertex is already known, and gradually expanding this set until all vertices have been included.

At the start, the algorithm initializes the source vertex with a distance of 0 and all other vertices with an infinite distance. It then repeatedly selects the vertex with the minimum distance from the set of vertices whose shortest distance is not yet known, updates the distances of its neighbors if a shorter path is found, and marks the selected vertex as visited.

This process continues until all vertices have been visited, or until the target vertex is reached. At this point, the shortest path to all vertices from the source vertex will have been determined. The Dijkstra algorithm is notable for its ability to handle graphs with positive edge weights and produce accurate shortest path results.

In summary, the Dijkstra algorithm efficiently finds the shortest path in a graph by iteratively selecting the next closest vertex and updating the distances of its neighbors until all vertices have been included in the shortest path tree.