"""Utilities for computing Tait colorings from vertex colorings of the dual graph."""
from typing import Any, cast
from sage.all import Graph
from lib.edge_for_dual_edge import get_edge_for_dual_edge

def get_tait_coloring(planar_dual: Graph, coloring: dict[Any, int]) -> dict[Any, int]:
    """Return a Tait (edge 3-coloring) from a vertex 4-coloring of the dual graph."""
    tait_coloring: dict[Any, int] = {}
    for dual_edge in cast(list[Any], planar_dual.edges()):  # type: ignore
        edge = get_edge_for_dual_edge(dual_edge)
        colors = {coloring[edge[0]], coloring[edge[1]]}
        if colors in ({0, 1}, {2, 3}):
            tait_coloring[dual_edge] = 0
        elif colors in ({1, 2}, {0, 3}):
            tait_coloring[dual_edge] = 1
        else:
            tait_coloring[dual_edge] = 2
    return tait_coloring