How does the Dijkstra Algorithm handle graphs with duplicate edges?

The Dijkstra Algorithm is a popular algorithm used to find the shortest path between two nodes in a graph. When it comes to graphs with duplicate edges, the algorithm handles them in a specific way.

In the Dijkstra Algorithm, each edge in the graph is assigned a weight or cost. This weight represents the distance or cost associated with traversing that edge. When there are duplicate edges between two nodes, it means that there are multiple paths connecting those nodes with different weights.

To handle graphs with duplicate edges, the Dijkstra Algorithm considers the edge with the minimum weight at each step. It maintains a priority queue or a min-heap to keep track of the nodes and their tentative distances from the source node. The algorithm starts by initializing the distance of the source node as 0 and the distance of all other nodes as infinity.

As the algorithm progresses, it selects the node with the minimum tentative distance from the priority queue and explores its neighboring nodes. For each neighboring node, the algorithm calculates the tentative distance by adding the weight of the edge connecting the current node to the neighboring node. If this tentative distance is smaller than the previously recorded distance for that node, the distance is updated.

When there are duplicate edges between two nodes, the algorithm will encounter them during the exploration process. It will compare the weights of these duplicate edges and select the one with the minimum weight. This ensures that the algorithm always considers the shortest path possible.

In case there are multiple shortest paths with the same weight, the Dijkstra Algorithm will explore all of them. It will continue to update the distances of the nodes and explore their neighbors until all nodes have been visited or until the destination node is reached.

Overall, the Dijkstra Algorithm handles graphs with duplicate edges by considering the edge with the minimum weight at each step. This ensures that the algorithm finds the shortest path between two nodes, even in the presence of duplicate edges.