Dijkstra's Algorithm

Dijkstra's Algorithm
Runtime	O(VE) or O(V^2) depending on data structure
Class	Graph Algorithm, Greedy Algorithm

Dijkstra's algorithm is a solution to the shortest path problem for graphs with positively-weighted edges.

Approach: Greedy

Dijkstra's algorithm centers around this property: of all the edges leaving the source, the shortest edge must be in the shortest path.

To reach the shortest path, Dijkstra always picks the shortest edge leaving the known nodes. In each iteration, it finalizes the distance to a node by picking the shortest one.

Implementation

Dijkstra(G, w, s) {
    // initialize
    for all v in V:
        d[v] = infty
        pi[v] = null
    d[s] = 0
    Q = V   // priority queue of nodes
    while Q is not empty:
        u = Q.extractMin()
        for all v in adj[u]:
            if d[v] > d[u] + w(u,v):
                d[v] = d[u] + w(u,v)
                pi[v] = u