Dijkstra Algorithm
Dijkstra’s algorithm, named after its discoverer, Dutch computer scientist Edsger Dijkstra, is a greedy algorithm that solves the single-source shortest path problem for a directed graph G = (V, E) with non-negative edge weights i.e. we assume that w(u, v) ≥ 0 for each edge (u, v) ∈ E.
Dijkstra’s algorithm maintains a set of S of vertices whose final shortest-path weights from the source have already been determined. That is, all vertices v ∈ S, we have d[v] = δ(s, v) the algorithm repeatedly selects the vertex u ∈ V-S with the minimum shortest-path estimate, inserts u into S and relaxes all edges leaving u. We maintain a min-priority queue Q that contains all the vertices in V – s keyed by their d values. Graph G is represented by adjacency lists.
DIJKSTRA (G, w, s)
1. INITIALIZE-SINGLE-SOURCE (G, s)
2. S ← φ
3. Q ← V[G]
4. while Q ≠ φ
5. do u ← EXTRACT-MIN (Q)
6. S ← S ∪ {u}
7. for each vertex v ∈ Adj[u]
8. do RELAX (u, v, w)
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