Dijkstra Algorithm

Dijkstra's algorithm finds the shortest path between any two graph vertices. It differs from the minimum spanning tree in that the shortest distance between two vertices may not include all of the graph's vertices. Djikstra used this property in the opposite direction, i.e. we overestimated the distance of each vertex from the starting vertex. Then we visit each node and its neighbours to find the shortest subpath between them. The algorithm takes a greedy approach in that it seeks the next best solution in the hope that the result is the best solution for the entire problem.

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[]

Solution:

Let's do it in tabular form

Applications of Dijkstra's Algorithm

• To determine the shortest path.

• In social networking software

• In a telecommunications network

• To locate the locations on the map