Minimum number of Branch Vertices spanning tree

Compilation

g++ -std=c++14 backtrack-unionfind.cpp -o backtrack

./backtrack < your-text-file-input.txt

The program reads a stream fom standard input and expects the data to be on the following format:

On the first line three value n m d, where n is the number of vertices, m is the number of edges and d is a dummy value that is a requirement for compatiblity reasons (with the input I'm using);
On the following m lines three values on each u v d, where u and v are the vertices connected by the edge and d is another dummy value.

backtrack.cpp: Works. Worst implementation, uses a structure for disjoint sets that results in inefficiently deep trees and doesn't try to do any bounding or pruning by inviability;
backtrack-unionfind.cpp: Works. Better than previous implementation, uses a efficient unionfind structure with rank optimization.
branch-and-bound.cpp: Works. Does bounding with a modified kruskal for every branch that prohibits a vertex, giving us pruning by inviability and bound. Improves the performance over previous implementations but has to recalculate and re-sort all edge weights every time the bound is calculated
branch-and-bound-no-reorder.cpp: Works. Faster than previous implementation, also runs a kruskal for every branch that prohibits a vertex, but calculates edge weights and sorts them only once
branch-and-bound-no-reorder-heuristic.cpp: Doesn't work yet. Implementing GRASP-like heuristic for MBV problem to be used as starting pont for branch-and-bound-no-reorder.