Generate a python program that has the following intention:

The program is an implementation of a minimum spanning tree algorithm. A minimum spanning tree is a subgraph of a graph that includes all the vertices and has the minimum total weight of the edges. The weight of an edge is represented by a function weight_by_line that takes an edge as input and returns its weight.

The algorithm works by repeatedly adding the edge with the smallest weight to the set of edges in the minimum spanning tree. The choice of the next edge is based on the divide-and-conquer approach, which divides the vertices into two sets based on the edge that is being considered. The algorithm then checks if one of the sets already contains the other set and if not, it adds the edge to the minimum spanning tree.

The function minimum_spanning_tree takes a dictionary weight_by_line as input and returns a set of edges that form the minimum spanning tree. The algorithm first initializes the set of edges in the minimum spanning tree to an empty set. It then loops through all the edges in the input graph, sorted by their weight. For each edge, the algorithm divides the vertices into two sets based on the edge and checks if one of the sets already contains the other set. If not, the edge is added to the minimum spanning tree.

The function divide_by_point is a dictionary that maps each vertex to a set of vertices that are divided by the edge with that vertex as one of the endpoints. The algorithm uses this dictionary to keep track of which vertices have already been divided and to make sure that the same edge is not added to the minimum spanning tree more than once.

In summary, the program implements a minimum spanning tree algorithm that uses the divide-and-conquer approach to find the set of edges with the minimum total weight that connect all the vertices in the graph. The algorithm is efficient because it only considers the edges with the smallest weight at each step and does not reconsider edges that have already been added to the minimum spanning tree.