Dijkstra Searching Algorithms Shortest.pptx
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The Dijkstra algorithm is used to find the shortest path between a source node and all other nodes in a graph. It works by assigning initial distances from the source node of infinity for all other nodes. It then repeatedly selects the unvisited node with the lowest distance, calculates the distance through it to each neighbor, and updates distances if shorter than the previous value. It returns the shortest distances and predecessors for each node. The algorithm works for both directed and undirected graphs that are connected.
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![Dijkstra Algorithm
function dijkstra(G, S)
for each vertex V in G
distance[V] <- infinite
previous[V] <- NULL
If V != S, add V to Priority Queue Q
distance[S] <- 0
while Q IS NOT EMPTY
U <- Extract MIN from Q
for each unvisited neighbour V of U
tempDistance <- distance[U] + edge_weight(U, V)
if tempDistance < distance[V]
distance[V] <- tempDistance
previous[V] <- U
return distance[], previous[]](https://image.slidesharecdn.com/dijkstrasearchingalgorithms-240229163419-46388680/85/Dijkstra-Searching-Algorithms-Shortest-pptx-3-320.jpg)
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Dijkstra Searching Algorithms Shortest.pptx
- 2. Dijkstra Algorithm • It is used for solving the single source shortest path problem. • It computes the shortest path from one particular source node to all other remaining nodes of the graph. • Dijkstra algorithm works only for connected graphs. • It only provides the value or cost of the shortest paths. • Dijkstra algorithm works for directed as well as undirected graphs.
- 3. Dijkstra Algorithm function dijkstra(G, S) for each vertex V in G distance[V] <- infinite previous[V] <- NULL If V != S, add V to Priority Queue Q distance[S] <- 0 while Q IS NOT EMPTY U <- Extract MIN from Q for each unvisited neighbour V of U tempDistance <- distance[U] + edge_weight(U, V) if tempDistance < distance[V] distance[V] <- tempDistance previous[V] <- U return distance[], previous[]