sample_example.py

from src.certifier import strongly_separates  

def unify_edges(edges: list[tuple[int, int]]):
    """
    Ensures that there are no duplicated or reversed duplicated edges in the edge list.

    Given a list of edges, this function removes duplicates by treating an edge (u, v)
    as identical to (v, u). The resulting list contains only one representative of each
    undirected edge.
    """
    edges_set = set()

    for (vertex1, vertex2) in edges:
        if (vertex1, vertex2) in edges_set or (vertex2, vertex1) in edges_set:
            continue

        edges_set.add((vertex1, vertex2))

    return list(map(list, edges_set))


def build_system(edges: list[tuple[int, int]]):
    """
    Builds a separator system where each path is a single edge.

    For each edge in the input list, this function creates a trivial path consisting
    of the two endpoints of that edge. The resulting system uses the set of edges
    itself as the separator system.
    """
    paths = []

    for (a, b) in edges:
        paths.append([a, b])

    return paths

if __name__ == "__main__":
    raw_edges = [(a, b) for a in range(4) for b in range (4) if a != b]
    K_4 = unify_edges(raw_edges)

    separating_path_system = build_system(K_4)

    # “Checks whether the edge set of K_4 itself separates it.”
    is_separated = strongly_separates(K_4, separating_path_system)

print("Correctly separates!\n")
print(f"{'Separating System:':<20}{separating_path_system}")
print(f"{'Graph:':<20}{K_4}")