Various forms of Kruskal's min cost spanning tree algorithm.

Kruskal 1:

empty minimum spanning tree T
foreach edge e in (sorted edges by cost) {
   if (adding edge e to T does not create a cycle) {
       add edge e to T
   }
}

Kruskal 2:

empty minimum spanning tree T
foreach edge e in (sorted edges by cost) {
   if (edge e = [ u, v ] has u and v in disjoint components of T) {
       add edge e to T
   }
}

Kruskal 3:

empty minimum spanning tree T
put each vertex v into their own partition
foreach edge e in (sorted edges by cost) {
   consider edge e = [ u, v ]
   if u and v are in different partitions, add edge and merge the partitions
   if (Find(u) != Find(v)) {
       add edge e to T
       Union( u, v )
   }
}