![DIJKSTRA'S ALGORITHM - PSEUDOCODE
dist[s] ←0 (distance to source vertex is zero)
for all v ∈ V–{s}
do dist[v] ←∞ (set all other distances to infinity)
S←∅ (S, the set of visited vertices is initially empty)
Q←V (Q, the queue initially contains all vertices)
while Q ≠∅ (while the queue is not empty)
do u ← mindistance(Q,dist) (select the element of Q with the min. distance)
S←S∪{u} (add u to list of visited vertices)
for all v ∈ neighbors[u]
do if dist[v] > dist[u] + w(u, v) (if new shortest path found)
then d[v] ←d[u] + w(u, v) (set new value of shortest path)
(if desired, add traceback code)
return dist](https://image.slidesharecdn.com/dijkstrasalgorithm-240628183053-35621125/85/Dijkstra-s-algorithm-for-computer-science-5-320.jpg)
Dijkstra's algorithm for computer science
- 1. DIJKSTRA'S ALGORITHM By Laksman Veeravagu and Luis Barrera
- 2. THE AUTHOR: EDSGER WYBE DIJKSTRA "Computer Science is no more about computers than astronomy is about telescopes." http://www.cs.utexas.edu/~EWD/
- 3. SINGLE-SOURCE SHORTEST PATH PROBLEM Single-Source Shortest Path Problem - The problem of finding shortest paths from a source vertex v to all other vertices in the graph.
- 4. DIJKSTRA'S ALGORITHM Dijkstra's algorithm - is a solution to the single-source shortest path problem in graph theory. Works on both directed and undirected graphs. However, all edges must have nonnegative weights. Approach: Greedy Input: Weighted graph G={E,V} and source vertex v∈V, such that all edge weights are nonnegative Output: Lengths of shortest paths (or the shortest paths themselves) from a given source vertex v∈V to all other vertices
- 5. DIJKSTRA'S ALGORITHM - PSEUDOCODE dist[s] ←0 (distance to source vertex is zero) for all v ∈ V–{s} do dist[v] ←∞ (set all other distances to infinity) S←∅ (S, the set of visited vertices is initially empty) Q←V (Q, the queue initially contains all vertices) while Q ≠∅ (while the queue is not empty) do u ← mindistance(Q,dist) (select the element of Q with the min. distance) S←S∪{u} (add u to list of visited vertices) for all v ∈ neighbors[u] do if dist[v] > dist[u] + w(u, v) (if new shortest path found) then d[v] ←d[u] + w(u, v) (set new value of shortest path) (if desired, add traceback code) return dist
- 16. IMPLEMENTATIONS AND RUNNING TIMES The simplest implementation is to store vertices in an array or linked list. This will produce a running time of O(|V|^2 + |E|) For sparse graphs, or graphs with very few edges and many nodes, it can be implemented more efficiently storing the graph in an adjacency list using a binary heap or priority queue. This will produce a running time of O((|E|+|V|) log |V|)