

def 					_UpperCAmelCase       (  _SCREAMING_SNAKE_CASE					:		dict       ):





    """simple docstring"""


    SCREAMING_SNAKE_CASE_									=						set()
    # edges = list of graph's edges
    SCREAMING_SNAKE_CASE_									=						get_edges(_SCREAMING_SNAKE_CASE       )

    # While there are still elements in edges list, take an arbitrary edge
    # (from_node, to_node) and add his extremity to chosen_vertices and then
    # remove all arcs adjacent to the from_node and to_node
    while edges:
        SCREAMING_SNAKE_CASE_							,			SCREAMING_SNAKE_CASE_									=						edges.pop()
        chosen_vertices.add(_SCREAMING_SNAKE_CASE       )
        chosen_vertices.add(_SCREAMING_SNAKE_CASE       )
        for edge in edges.copy():
            if from_node in edge or to_node in edge:
                edges.discard(_SCREAMING_SNAKE_CASE       )
    return chosen_vertices


def 					_UpperCAmelCase       (  _SCREAMING_SNAKE_CASE					:		dict       ):





    """simple docstring"""


    SCREAMING_SNAKE_CASE_									=						set()
    for from_node, to_nodes in graph.items():
        for to_node in to_nodes:
            edges.add((from_node, to_node)       )
    return edges


if __name__ == "__main__":
       import doctest

       doctest.testmod()

       # graph = {0: [1, 3], 1: [0, 3], 2: [0, 3, 4], 3: [0, 1, 2], 4: [2, 3]}
       # print(f"Matching vertex cover:\n{matching_min_vertex_cover(graph)}")





from typing import List

import numpy as np


def 					_UpperCAmelCase       (  _SCREAMING_SNAKE_CASE					:		dict       ):





    """simple docstring"""


    SCREAMING_SNAKE_CASE_									=						{key: len(_SCREAMING_SNAKE_CASE       ) for key, value in gen_kwargs.items() if isinstance(_SCREAMING_SNAKE_CASE ,   _SCREAMING_SNAKE_CASE       )}
    if len(set(lists_lengths.values()       )       ) > 1:
        raise RuntimeError(
            (
                'Sharding is ambiguous for this dataset: '
                + 'we found several data sources lists of different lengths, and we don\'t know over which list we should parallelize:\n'
                + '\n'.join(f"""\t- key {key} has length {length}""" for key, length in lists_lengths.items()       )
                + '\nTo fix this, check the \'gen_kwargs\' and make sure to use lists only for data sources, '
                + 'and use tuples otherwise. In the end there should only be one single list, or several lists with the same length.'
            )       )
    SCREAMING_SNAKE_CASE_									=						max(lists_lengths.values() ,   default=0       )
    return max(1 ,   _SCREAMING_SNAKE_CASE       )


def 					_UpperCAmelCase       (  _SCREAMING_SNAKE_CASE					:		int ,   _SCREAMING_SNAKE_CASE					:		int       ):





    """simple docstring"""


    SCREAMING_SNAKE_CASE_									=						[]
    for group_idx in range(_SCREAMING_SNAKE_CASE       ):
        SCREAMING_SNAKE_CASE_									=						num_shards // max_num_jobs + (group_idx < (num_shards % max_num_jobs))
        if num_shards_to_add == 0:
            break
        SCREAMING_SNAKE_CASE_									=						shards_indices_per_group[-1].stop if shards_indices_per_group else 0
        SCREAMING_SNAKE_CASE_									=						range(_SCREAMING_SNAKE_CASE ,   start + num_shards_to_add       )
        shards_indices_per_group.append(_SCREAMING_SNAKE_CASE       )
    return shards_indices_per_group


def 					_UpperCAmelCase       (  _SCREAMING_SNAKE_CASE					:		dict ,   _SCREAMING_SNAKE_CASE					:		int       ):





    """simple docstring"""


    SCREAMING_SNAKE_CASE_									=						_number_of_shards_in_gen_kwargs(_SCREAMING_SNAKE_CASE       )
    if num_shards == 1:
        return [dict(_SCREAMING_SNAKE_CASE       )]
    else:
        SCREAMING_SNAKE_CASE_									=						_distribute_shards(num_shards=_SCREAMING_SNAKE_CASE ,   max_num_jobs=_SCREAMING_SNAKE_CASE       )
        return [
            {
                key: [value[shard_idx] for shard_idx in shard_indices_per_group[group_idx]]
                if isinstance(_SCREAMING_SNAKE_CASE ,   _SCREAMING_SNAKE_CASE       )
                else value
                for key, value in gen_kwargs.items()
            }
            for group_idx in range(len(_SCREAMING_SNAKE_CASE       )       )
        ]


def 					_UpperCAmelCase       (  _SCREAMING_SNAKE_CASE					:		List[dict]       ):





    """simple docstring"""


    return {
        key: [value for gen_kwargs in gen_kwargs_list for value in gen_kwargs[key]]
        if isinstance(gen_kwargs_list[0][key] ,   _SCREAMING_SNAKE_CASE       )
        else gen_kwargs_list[0][key]
        for key in gen_kwargs_list[0]
    }





def 					_UpperCAmelCase       (  _SCREAMING_SNAKE_CASE					:		np.random.Generator ,   _SCREAMING_SNAKE_CASE					:		dict       ):





    """simple docstring"""


    SCREAMING_SNAKE_CASE_									=						{len(_SCREAMING_SNAKE_CASE       ) for value in gen_kwargs.values() if isinstance(_SCREAMING_SNAKE_CASE ,   _SCREAMING_SNAKE_CASE       )}
    SCREAMING_SNAKE_CASE_									=						{}
    for size in list_sizes:
        SCREAMING_SNAKE_CASE_									=						list(range(_SCREAMING_SNAKE_CASE       )       )
        rng.shuffle(indices_per_size[size]       )
    # Now let's copy the gen_kwargs and shuffle the lists based on their sizes
    SCREAMING_SNAKE_CASE_									=						dict(_SCREAMING_SNAKE_CASE       )
    for key, value in shuffled_kwargs.items():
        if isinstance(_SCREAMING_SNAKE_CASE ,   _SCREAMING_SNAKE_CASE       ):
            SCREAMING_SNAKE_CASE_									=						[value[i] for i in indices_per_size[len(_SCREAMING_SNAKE_CASE       )]]
    return shuffled_kwargs


