Dijkstra Algorithm Questions Long
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 multiple shortest paths, the Dijkstra Algorithm handles them in a specific way.
Firstly, let's understand what is meant by multiple shortest paths. In a graph, multiple shortest paths refer to different paths between two nodes that have the same minimum distance or weight. These paths may have different sequences of nodes but result in the same shortest distance.
When the Dijkstra Algorithm encounters a graph with multiple shortest paths, it follows a specific approach to handle them. Here are the steps involved:
1. Initialization: Start by initializing the algorithm as usual. Set the distance of the source node to 0 and all other nodes to infinity. Mark all nodes as unvisited.
2. Priority Queue: Instead of using a regular queue, the Dijkstra Algorithm utilizes a priority queue to store the nodes. The priority queue is ordered based on the distance from the source node. The node with the smallest distance is always selected first.
3. Exploration: Begin exploring the graph by selecting the node with the smallest distance from the priority queue. Visit all its neighboring nodes and update their distances if a shorter path is found. If multiple paths have the same distance, all of them are considered.
4. Path Tracking: Along with updating the distances, the algorithm also keeps track of the previous node that leads to the current node. This information is stored in a separate data structure called the "predecessor" or "parent" array. It helps in reconstructing the shortest paths later.
5. Shortest Path Selection: After exploring all the nodes and updating their distances, the algorithm identifies the shortest path(s) from the source node to the destination node. This can be done by backtracking from the destination node using the predecessor array.
6. Multiple Shortest Paths: In the case of multiple shortest paths, the algorithm may generate a tree-like structure rather than a single path. This tree represents all the possible shortest paths from the source node to each reachable node in the graph.
7. Output: Finally, the algorithm provides the shortest path(s) from the source node to the destination node, including all the possible paths in the case of multiple shortest paths.
In summary, the Dijkstra Algorithm handles graphs with multiple shortest paths by considering all the paths with the same minimum distance. It generates a tree-like structure representing all the possible shortest paths and provides them as the output.