Kruskal's algorithm
Kruskal's algorithm:
sort the edges of G in increasing order by length
keep a subgraph S of G, initially empty
for each edge e in sorted order
if the endpoints of e are disconnected in S
add e to S
return S
Note that, whenever you add an edge (u,v), it's always the smallest connecting the part of S
reachable from u with the rest of G, so by the lemma it must be part of the MST.
example
void kruskal (vertex-set V; edge-set E; edge-set T)
int ncomp; /* current number of components */
priority-queue edges /* partially ordered tree */
mfset components; /* merge-find set data structure */
vertex u, v; edge e;
int nextcomp; /* name for new component */
int ucomp, vcomp; /* component names */
{
makenull (T); makenull (edges);
nextcomp = 0; ncomp = n;
for (v$ \in$V) /* initialize a component to have one vertex of V*/
{ nextcomp++ ;
initial (nextcomp, v, components);
}
for (e$ \in$E)
insert (e, edges); /* initialize priority queue of edges */
while (ncomp > 1)
{
e = deletemin (edges);
let e = (u, v);
ucomp = find(u, components);
vcomp = find(v, components);
if (ucomp! = vcomp)
