How do Dijkstra's Algorithm Work?

Dijkstra's algorithm is a popular graph traversal algorithm used to find the shortest path between nodes in a weighted graph. It was developed by computer scientist Edsger Dijkstra in 1956.

Here is a step-by-step explanation of how Dijkstra's algorithm works:

1. Initialization: 

Start by selecting a source node and set its distance to 0. Assign infinite distance to all other nodes. Mark all nodes as unvisited.

2. Selection of the minimum distance node:

Choose the node with the minimum distance from the set of unvisited nodes. Initially, this will be the source node.

3. Visit neighbors: 

For the selected node, examine all its neighboring nodes (adjacent nodes) that have not been visited. Calculate the distance from the source node to each neighboring node through the current node. Update the distance of each neighboring node if the newly calculated distance is smaller than the current assigned distance.

4. Mark node as visited: 

Once all the neighboring nodes have been examined, mark the current node as visited.

5. Repeat: 

Repeat steps 2 to 4 until all nodes have been visited or the destination node has been visited (if you are only interested in finding the shortest path to a specific destination).

6. Path reconstruction: 

After visiting all nodes or reaching the destination node, you can reconstruct the shortest path from the source node to the destination node by backtracking from the destination node to the source node using the assigned distances and the graph's edges.


The algorithm works by iteratively selecting the node with the minimum distance from the set of unvisited nodes and updating the distances of its neighboring nodes. This process continues until all nodes have been visited or the destination node has been visited.

Dijkstra's algorithm guarantees that once a node has been marked as visited, the assigned distance to that node is the shortest possible distance from the source node. This property is used to ensure that the algorithm finds the shortest paths correctly.

It's worth noting that Dijkstra's algorithm assumes that the graph does not contain negative weight edges. If negative weights are present, a different algorithm, such as the Bellman-Ford algorithm, should be used. Additionally, Dijkstra's algorithm can be modified to track the actual path or prioritize certain nodes based on additional criteria. 

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