Difference between Prim's and Dijkstra's algorithms?

Question

What is the exact difference between Dijkstra\'s and Prim\'s algorithms? I know Prim\'s will give a MST but the tree generated by Dijkstra will also be a MST. Then what is

Answer 1

The key difference between the basic algorithms lies in their different edge-selection criteria. Generally, they both use a priority queue for selecting next nodes, but have different criteria to select the adjacent nodes of current processing nodes: Prim's Algorithm requires the next adjacent nodes must be also kept in the queue, while Dijkstra's Algorithm does not:

def dijkstra(g, s):
    q <- make_priority_queue(VERTEX.distance)
    for each vertex v in g.vertex:
        v.distance <- infinite
        v.predecessor ~> nil
        q.add(v)
    s.distance <- 0
    while not q.is_empty:
        u <- q.extract_min()
        for each adjacent vertex v of u:
            ...

def prim(g, s):
    q <- make_priority_queue(VERTEX.distance)
    for each vertex v in g.vertex:
        v.distance <- infinite
        v.predecessor ~> nil
        q.add(v)
    s.distance <- 0
    while not q.is_empty:
        u <- q.extract_min()
        for each adjacent vertex v of u:
            if v in q and weight(u, v) < v.distance:// <-------selection--------
            ...

The calculations of vertex.distance are the second different point.