Pseudo Code

Lesson 4 of 9 in Coddy's Kruskal's Algorithm - Graph Algorithms course.

kruskal(n, edges):
   parent[i] = i for all i          # each vertex its own set
   total = 0
   repeat until all edges considered:
      pick the unused edge (u, v, w) with the smallest w
      ru = find(u); rv = find(v)
      if ru != rv:                   # no cycle
         parent[ru] = rv             # union
         total += w
   return total

find(x):
   while parent[x] != x: x = parent[x]
   return x

Picking the smallest unused edge each round (min-selection) avoids needing a separate sort.
find walks up to the root; union is a single assignment of one root to the other.

Try it yourself

This lesson doesn't include a code challenge.