What are the steps involved in implementing the Dijkstra Algorithm?

The Dijkstra Algorithm is a popular algorithm used to find the shortest path between two nodes in a graph. The steps involved in implementing the Dijkstra Algorithm are as follows:

1. Initialize the graph: Create a graph representation with nodes and edges. Assign a weight or cost to each edge, representing the distance or cost to traverse from one node to another.

2. Set the starting node: Choose a starting node from which to find the shortest path.

3. Initialize distances: Assign a tentative distance value to every node in the graph. Set the distance of the starting node to 0 and all other nodes to infinity.

4. Create a priority queue: Use a priority queue to keep track of the nodes and their tentative distances. The priority queue should prioritize nodes with the smallest tentative distance.

5. Process nodes: While the priority queue is not empty, select the node with the smallest tentative distance and mark it as visited.

6. Update distances: For each neighboring node of the current node, calculate the tentative distance by adding the cost of the current node to the weight of the edge connecting the current node to the neighboring node. If this tentative distance is smaller than the previously assigned distance, update the distance value.

7. Repeat steps 5 and 6: Continue selecting the node with the smallest tentative distance from the priority queue and updating distances until all nodes have been visited or the destination node has been reached.

8. Track the shortest path: During the process, keep track of the previous node that leads to the current node with the smallest tentative distance. This information will be used to reconstruct the shortest path later.

9. Reconstruct the shortest path: Starting from the destination node, follow the previous node information to trace back the shortest path to the starting node.

10. Output the shortest path: Once the shortest path has been reconstructed, output the path and the total distance/cost associated with it.

These steps ensure that the Dijkstra Algorithm efficiently finds the shortest path between two nodes in a graph by iteratively updating the distances and selecting the node with the smallest tentative distance.