Dijkstra's Algorithm Dijkstra's algorithm is a graph search algorithm that finds the shortest path from a single source vertex to all other vertices in the...
Dijkstra's Algorithm
Dijkstra's algorithm is a graph search algorithm that finds the shortest path from a single source vertex to all other vertices in the graph. It is a greedy algorithm that starts by choosing the source vertex and then greedily selects the vertex with the shortest path to the source vertex among all the unvisited vertices.
Algorithm:
Create a list of all the vertices in the graph, along with a distance of infinity for each vertex.
Set the distance of the source vertex to 0.
For each unvisited neighbor of the current vertex:
Calculate the distance from the source vertex to the neighbor.
If the neighbor has a shorter path from the source to the destination vertex, update the neighbor's distance to the source to the minimum of the original distance and the neighbor's distance.
Example:
Suppose we have the following graph:
A---B---C---D---E
The algorithm would work as follows:
Start with the source vertex A.
Choose B as the nearest neighbor with a distance of 2.
Update the distance of neighbor B to the source to 1 (since the shortest path from A to B is 2).
Repeat steps 2 and 3 for neighbor C, updating the distance to the source to 3.
Continue this process until all neighbors have been visited and the algorithm terminates.
Benefits of Dijkstra's Algorithm:
It finds the shortest path from a single source vertex to all other vertices in the graph.
It is a greedy algorithm, which makes it easy to implement.
It is efficient for large graphs, as it can be implemented in linear time