Dijkstra Algorithm Questions Medium
The Dijkstra Algorithm is a popular algorithm used to find the shortest path between two nodes in a graph. It works by iteratively exploring the nodes in the graph and updating the shortest distance from the source node to each node.
Here is a step-by-step explanation of how the Dijkstra Algorithm works:
1. Initialize the algorithm by setting the distance of the source node to 0 and all other nodes to infinity. Mark all nodes as unvisited.
2. Select the node with the smallest distance as the current node and mark it as visited.
3. For each neighbor of the current node, calculate the distance from the source node through the current node. If this distance is smaller than the previously recorded distance for the neighbor, update the distance.
4. After updating the distances for all neighbors, mark the current node as visited.
5. Repeat steps 2-4 until all nodes have been visited or the destination node has been visited.
6. Once the destination node has been visited, the algorithm terminates. The shortest path from the source node to the destination node can be obtained by backtracking from the destination node to the source node using the recorded distances.
The Dijkstra Algorithm guarantees that the shortest path to each node is found in a greedy manner, meaning that at each step, the algorithm chooses the node with the smallest distance. This ensures that once a node is visited, its distance is finalized and will not be updated again.
It is important to note that the Dijkstra Algorithm only works correctly for graphs with non-negative edge weights. If there are negative edge weights, a different algorithm like the Bellman-Ford Algorithm should be used.