Dijkstra's algorithm is a method for determining the shortest pathways between nodes in a graph, which might be used to depict road networks. Edsger W. Dijkstra, a computer scientist, conceived it in 1956 and published it three years later. There are NUMEROUS variations of the algorithm. The original Dijkstra algorithm discovered the shortest path between two nodes, but a more frequent form fixes a single node as the "source" node and finds the shortest pathways from the source to all other nodes in the network, resulting in a shortest-path tree. Let us take a look at Dijkstra's Algorithm to find the shortest path between a given node in a graph to any other node in the graph:

Let us call the node where we are starting the process as the initial node. Let the distance from the initial node to Y be the distance of node Y. Dijkstra's algorithm will begin with unlimited distances and attempt to improve them incrementally.

• Step 1: Mark all nodes that have not been visited yet. The unvisited set is a collection of all the nodes that have not been visited yet.
• Step 2: Assign a tentative distance value to each node: set it to zero for our first node and infinity for all others. The length of the shortest path discovered so far between the node v and the initial node is the tentative distance of a node v. Because no other vertex other than the source (which is a path of length zero) is known at the start, all other tentative distances are set to infinity. Set the CURRENT node to the beginning node.
• Step 3: Consider all of the current node's unvisited neighbours and determine their approximate distances through the current node. Compare the newly calculated tentative distance to the current assigned value and choose the one that is less. If the present node A has a distance of 5 and the edge linking it to a neighbour B has a length of 3, the distance to B through A will be 5 +3 = 8. Change B to 8 if it was previously marked with a distance greater than 8. If this is not the case, the current value will be retained.
• Step 4: Mark the current node as visited and remove it from the unvisited set once we have considered all of the current node's unvisited neighbours. A node that has been visited will never be checked again.
• Stop if the destination node has been marked visited (when planning a route between two specific nodes) or if the smallest tentative distance between the nodes in the unvisited set is infinity (when planning a complete traversal; occurs when there is no connection between the initial node and the remaining unvisited nodes). The algorithm is now complete.
• Step 5: Otherwise, RETURN to step 3 and select the unvisited node indicated with the shortest tentative distance as the new current node.

It is not required to wait until the target node is "visited" as described above while constructing a route: the algorithm can end once the destination node has the least tentative distance AMONG all "unvisited" nodes (and thus could be selected as the next "current"). For arbitrary directed GRAPHS with unbounded non-negative weights, Dijkstra's algorithm is asymptotically the fastest known single-source shortest path algorithm with time complexity of O(|E| + |V|log(|V|)), where  |V| is the number of nodes and|E| is the number of edges in the graph.