"""Utilities for working with planar dual graphs."""
from typing import Any
from sage.all import Graph


def find_vertex_for_dual_face(dual_face: Any) -> Any | None:
    """Return the primal vertex shared by all faces in the dual face, or None."""
    shared_vertices = None
    for dual_edge in dual_face:
        vertices = set(map(lambda e: e[0], dual_edge[0]))
        if shared_vertices:
            shared_vertices.intersection_update(vertices)
        else:
            shared_vertices = vertices
        if len(shared_vertices) == 1:
            return shared_vertices.pop()
    return None


def _dual_edge_has_vertex(dual_edge: Any, vertex: Any) -> bool:
    return any(vertex in edge for dual_vertex in dual_edge for edge in dual_vertex)


def find_dual_face_for_removed_vertex(planar_dual: Graph, vertex: Any) -> Any | None:
    """Return the dual face of length 5 whose every dual edge contains the given vertex."""
    for dual_face in list[Any](planar_dual.faces()):  # type: ignore[call-arg]
        if len(dual_face) == 5 and all(_dual_edge_has_vertex(de, vertex) for de in dual_face):
            return dual_face
    return None