# -*- coding: utf-8 -*-
"""
Ramsey numbers.
"""
#   Copyright (C) 2011 by
#   Nicholas Mancuso <nick.mancuso@gmail.com>
#   All rights reserved.
#   BSD license.
import networkx as nx
from ...utils import arbitrary_element

__all__ = ["ramsey_R2"]
__author__ = """Nicholas Mancuso (nick.mancuso@gmail.com)"""

def ramsey_R2(G):
    r"""Approximately computes the Ramsey number `R(2;s,t)` for graph.

    Parameters
    ----------
    G : NetworkX graph
        Undirected graph

    Returns
    -------
    max_pair : (set, set) tuple
        Maximum clique, Maximum independent set.
    """
    if not G:
        return set(), set()

    node = arbitrary_element(G)
    nbrs = nx.all_neighbors(G, node)
    nnbrs = nx.non_neighbors(G, node)
    c_1, i_1 = ramsey_R2(G.subgraph(nbrs).copy())
    c_2, i_2 = ramsey_R2(G.subgraph(nnbrs).copy())

    c_1.add(node)
    i_2.add(node)
    # Choose the larger of the two cliques and the larger of the two
    # independent sets, according to cardinality.
    return max(c_1, c_2, key=len), max(i_1, i_2, key=len)
