Dijkstra’s Algorithm – Shortest Path Algorithms

Dijkstra’s algorithm is a popular algorithm used to find the shortest path between two nodes in a weighted graph. It was invented by Dutch computer scientist Edsger Dijkstra in 1956.

The algorithm works by starting at the source node and iteratively exploring the neighboring nodes with the smallest distance from the source. It then updates the distances of the unexplored neighboring nodes by adding the weight of the edge connecting them to the source node. The process is repeated until all nodes in the graph have been explored or until the destination node has been reached.

Here is a step-by-step explanation of the algorithm:

1. Assign a tentative distance value to every node in the graph, with the source node having a distance of 0 and all other nodes having a distance of infinity.
2. Mark all nodes as unvisited and create an empty set of visited nodes.
3. Set the current node to the source node.
4. For the current node, calculate the tentative distance to each of its unvisited neighbors by adding the weight of the edge connecting them to the source node.
5. If the calculated tentative distance is smaller than the current distance of the neighboring node, update the tentative distance.
6. Mark the current node as visited and remove it from the unvisited set.
7. Select the unvisited node with the smallest tentative distance and set it as the current node.
8. Repeat steps 4-7 until the destination node has been visited or all nodes have been explored.
9. If the destination node has been visited, the shortest path from the source to the destination can be found by tracing back the path with the smallest cumulative distance.

Dijkstra’s algorithm is widely used in network routing protocols, map navigation, and other applications that involve finding the shortest path between two points in a weighted graph.