Dijkstra algorithm
0 likes290 views
Dijkstra's algorithm is used to find the shortest path between nodes in a weighted graph. It works by assigning initial distances to all nodes from the starting node and updating them as shorter paths are found, extracting the node with the lowest distance, and updating distances for neighboring unvisited nodes. The algorithm returns the shortest distance and path between the starting node and all other nodes in the graph.
![Example 02:
Solution
Visited
Vertex
A B C D E F
A 0 ∞ ∞ ∞ ∞ ∞
B 2 5 ∞ ∞ 11
C 5 7 15 11
D 7 15 11
F 15 11
E 15
if(d(u) + c(u,v) < d(v))
then d(v) = d(u) + c(u,v)
Shortest path from A to E: A, B, E
Distance = 2 + 13 = 15
Dijkstra’s Algorithm Pseudocode
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
A
F D
B
C
E
11
17
1
12
5
2
8 13
5](https://image.slidesharecdn.com/dijkstraalgorithm-210706144230/85/Dijkstra-algorithm-2-320.jpg)
![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/dijkstraalgorithm-210706144230/85/Dijkstra-algorithm-3-320.jpg)
Dijkstra algorithm
- 1. Dijkstra’s Algorithm An algorithm that is used for finding the shortest distance, or path, from starting node to target node in a weighted graph is known as Dijkstra’s Algorithm. Example 01: Solution Visited Vertex A B C D E F A 0 ∞ ∞ ∞ ∞ ∞ F 14 9 ∞ ∞ 7 C 14 9 ∞ 22 B 11 ∞ 20 D 19 20 E 20 if(d(u) + c(u,v) < d(v)) then d(v) = d(u) + c(u,v) Shortest path from A to E: A, C, E Distance = 9 + 11 = 20 A B D C F E 14 8 6 15 7 9 10 11 2
- 2. Example 02: Solution Visited Vertex A B C D E F A 0 ∞ ∞ ∞ ∞ ∞ B 2 5 ∞ ∞ 11 C 5 7 15 11 D 7 15 11 F 15 11 E 15 if(d(u) + c(u,v) < d(v)) then d(v) = d(u) + c(u,v) Shortest path from A to E: A, B, E Distance = 2 + 13 = 15 Dijkstra’s Algorithm Pseudocode 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 A F D B C E 11 17 1 12 5 2 8 13 5
- 3. 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[]