ALGORITHM Prim(G)
//Input: A weighted connected graph G = (V, E)
//Output: ET, the set of edges composing a minimum spanning tree of G
VT <- {v0} // initialize with any vertex
ET <- empty set
for i <- 1 to |V| - 1 do
    find a minimum-weight edge e* = (v*, u*) among all edges (v, u)
    such that v is in VT and u is in V - VT
    VT <- VT U {u*}
    ET <- ET U {e*}
return ET

ALGORITHM Kruskal(G)
//Input: A weighted connected graph G = (V, E)
//Output: ET, the set of edges composing an MST
sort E in nondecreasing order of the edge weights
ET <- empty set; ecounter <- 0
k <- 0
while ecounter < |V| - 1 do
    k <- k + 1
    if ET U {e_k} is acyclic
        ET <- ET U {e_k}; ecounter <- ecounter + 1
return ET

ALGORITHM Dijkstra(G, s)
//Input: Weighted connected graph G with nonnegative weights and source s
Initialize(Q) // priority queue
for every vertex v in V:
    dv <- infinity; pv <- null
    Insert(Q, v, dv)
ds <- 0; Decrease(Q, s, ds)
VT <- empty set
for i <- 0 to |V| - 1 do
    u* <- DeleteMin(Q)
    VT <- VT U {u*}
    for every vertex u in V - VT adjacent to u* do
        if du* + w(u*, u) < du
            du <- du* + w(u*, u); pu <- u*
            Decrease(Q, u, du)