Dijkstra's Algorithm

Dijkstra's Algorithm is a shortest path algorithm used in graph theory, developed in 1956 by Dutch computer scientist Edsger W. Dijkstra. This algorithm is used to find the shortest paths from a specific starting node to all other nodes in a graph. It operates on weighted graphs—where edges have specific weights—and is valid only for graphs that do not contain negative-weight edges.

Working Principle

Dijkstra's Algorithm employs a greedy approach. At each step, it selects the node with the shortest known distance so far and attempts to extend this path to reach other nodes.

1- Initialization:

2- Selection of the Node with Shortest Distance:

3- Updating Neighboring Nodes:

4- Marking as Visited:

5- Repetition:

6- Result:

Dijkstra's Algorithm graph

Time Complexity

The time complexity of Dijkstra's Algorithm depends on the data structure used:

• When using an array: O(V²)
• When using a priority queue (min-heap): O((V+E)log V)

Here, V represents the number of vertices and E represents the number of edges.

Limitations

• Negative-Weight Edges: Dijkstra's Algorithm does not produce correct results for graphs containing negative-weight edges. For such cases, the Bellman-Ford Algorithm can be used.
• Directed Graphs: The algorithm works on both directed and undirected graphs.

Dijkstra's Algorithm is widely used in fields such as route finding, network routing, and geographic information systems.