How does the Dijkstra Algorithm handle graphs with weighted edges?

The Dijkstra Algorithm is a popular algorithm used to find the shortest path between two nodes in a graph. It can handle graphs with weighted edges by considering the weights of the edges during the path calculation.

When dealing with weighted edges, the Dijkstra Algorithm assigns a weight value to each edge in the graph. This weight represents the cost or distance associated with traversing that particular edge. The algorithm then uses these weights to determine the shortest path from a starting node to all other nodes in the graph.

Here is a step-by-step explanation of how the Dijkstra Algorithm handles graphs with weighted edges:

1. Initialize the algorithm:
- Set the starting node as the current node.
- Assign a distance value of 0 to the starting node and infinity to all other nodes.
- Create an empty set to keep track of visited nodes.

2. Visit the neighbors of the current node:
- For each neighbor of the current node, calculate the tentative distance from the starting node.
- Compare the tentative distance with the current distance value of the neighbor.
- If the tentative distance is smaller, update the distance value of the neighbor.

3. Mark the current node as visited:
- Add the current node to the set of visited nodes.

4. Select the next node:
- Choose the unvisited node with the smallest distance value as the next current node.
- If there are no unvisited nodes left, the algorithm is complete.

5. Repeat steps 2-4 until all nodes have been visited:
- Continue visiting the neighbors of the current node, updating the distance values if necessary, and marking the current node as visited.
- Keep track of the shortest path to each node by storing the previous node that leads to it.

6. Retrieve the shortest path:
- Once the algorithm has visited all nodes, the shortest path from the starting node to any other node can be retrieved.
- Starting from the destination node, follow the chain of previous nodes until reaching the starting node to obtain the shortest path.

By considering the weights of the edges, the Dijkstra Algorithm ensures that the shortest path it finds is the one with the lowest total weight. This makes it suitable for solving problems where the edges represent distances, costs, or any other form of weight in a graph.