[V. Vyssotsky] Develop an implementation of the algorithm discussed in Section 20.2 that builds the MST by adding edges one at a time and deleting the longest edges on the cycle formed (see Exercise 20.34). Use a parent-link representation of a forest of MST subtrees. Hint: Reverse links when traversing paths in trees.
Exercise 20.34
Prove that repeated application of the cycle property gives an MST.