![]() Step 3 : Remove the pair from the dictionary and relax the edge going towards every adjacent node(s) from the current source ( 2 ). Currentsource nodeĭistance to the adjacent nodefrom the original source ( 0 )ĭistance > distance_between + distance i.e Since ∞ > 5 + 0 Update distance, i.e distance = 5 i.e update pair_to in the dictionary.ĭistance > distance_between + distance i.e Since ∞ > 1 + 0 Update distance, i.e distance = 1 i.e update pair_to in the dictionary.ĭistance > distance_between + distance i.e Since ∞ > 4 + 0 Update distance, i.e distance = 4 i.e update pair_to in the dictionary. The idea is to get the node with the shortest distance from the original source node. Step 2 : Remove the pair from the dictionary and relax the edge going towards every adjacent node(s) from the original source node ( 0 ). ![]() I.e Insert in the dictionary as the distance from the original source (0) to itself is 0. Step 1 : Initialize the distance of the source node to itself as 0 and to all other nodes as ∞. This example of Dijkstra’s algorithm finds the shortest distance of all the nodes in the graph from the single / original source node 0. Update the DICTIONARY with the new pair īelow data structures are used for storing the graph before running Dijkstra’s algorithm Adjacency List : List of pairs of adjacent nodes and their corresponding weights in the graph. distance = length_of_path_to_adjacent_node_from_current_source + distance Ĩ. If ( distance > length_of_path_to_adjacent_node_from_current_source + distance )ħ. For every adjacent_node to the current_source_node doĦ. get_key (node)_with_smallest_value (dist) Remove the key (current_source_node) from the DICTIONARY.ĥ. Insert the pair of for source i.e in a DICTIONARY Ĥ. ![]() Initialize the distance from the source node S to all other nodes as infinite (999999999999) and to itself as 0.Ģ. Since Dijkstra’s algorithm cannot handle negative edge weights, Bellman-Ford algorithm is used for finding the shortest path in a graph containing negative edge weights.Īlgorithm : Dijkstra’s Shortest Path ġ.It uses a priority-based dictionary or a queue to select a node / vertex nearest to the source that has not been edge relaxed.Įdge Relaxation If ( distance > length-of-path-to-adjacent-node-from-current-source + distance ) thenĭistance = length-of-path-to-adjacent-node-from-current-source + distance Note :a) The distance array stores the shortest distance of every node from the source-node.ī) Dijkstra’s algorithm begins by initializing distance = 0 i.e the distance from the first (original) source node to itself is 0.Dijkstra’s algorithm finds the shortest path in a weighted graph containing only positive edge weights from a single source.The key points of Dijkstra’s single source shortest path algorithm is as below :
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