Dijkstra’s algorithm step-by-step

Suppose we have a network of cities with distances between them, and we want to find the shortest path from a starting city (source node) to all other cities in the network. Here’s the dataset representing the graph:

Step-by-Step Execution of Dijkstra’s Algorithm

Step 1: Initialization

1. Set initial distances: Set the initial distance of the source node (A) to zero and all other nodes to infinity.
2. Mark all nodes as unvisited.
3. Priority Queue (or Min-Heap): We use a priority queue to always select the unvisited node with the smallest distance.

Conclusion

Dijkstra’s algorithm is effective for finding shortest paths in graphs with non-negative weights. In this example:

• It systematically updated distances by always choosing the node with the smallest known distance.
• It maintained a record of the shortest path to each city from the starting point.

This approach is widely applicable in areas like route optimization in logistics, network data routing, and pathfinding in AI applications. By leveraging a priority queue, Dijkstra’s algorithm efficiently manages complex search spaces, providing optimal paths in terms of both speed and computational resources.

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