Graph Theory Questions Medium
Dijkstra's algorithm is a popular algorithm used to find the shortest path between two nodes in a graph. It is named after its inventor, Edsger Dijkstra.
The algorithm works by maintaining a set of unvisited nodes and assigning a tentative distance value to each node. Initially, the distance value of the starting node is set to 0, and all other nodes are set to infinity.
The algorithm then iteratively selects the node with the smallest tentative distance from the set of unvisited nodes. This node is considered as the current node.
For each neighbor of the current node, the algorithm calculates the sum of the tentative distance of the current node and the weight of the edge connecting the current node to its neighbor. If this sum is smaller than the neighbor's current tentative distance, the neighbor's tentative distance is updated with the new value.
After updating the tentative distances of all neighbors, the current node is marked as visited and removed from the set of unvisited nodes. This process continues until all nodes have been visited or the destination node has been reached.
Finally, the algorithm returns the shortest path from the starting node to the destination node by following the path with the smallest cumulative weight.
Dijkstra's algorithm guarantees finding the shortest path in a graph with non-negative edge weights. However, it may not work correctly if the graph contains negative edge weights or cycles. In such cases, alternative algorithms like Bellman-Ford or Floyd-Warshall should be used.