lowerCAmelCase      :				Any     			=[
    ['''ab-e1''', '''ac-e3''', '''ad-e5''', '''bc-e4''', '''bd-e2''', '''be-e6''', '''bh-e12''', '''cd-e2''', '''ce-e4''',
     '''de-e1''', '''df-e8''', '''dg-e5''', '''dh-e10''', '''ef-e3''', '''eg-e2''', '''fg-e6''', '''gh-e6''', '''hi-e3'''],
    ['''ab-e1''', '''ac-e3''', '''ad-e5''', '''bc-e4''', '''bd-e2''', '''be-e6''', '''cd-e2''', '''de-e1''', '''df-e8''',
     '''ef-e3''', '''eg-e2''', '''fg-e6'''],
    ['''ab-e1''', '''ac-e3''', '''bc-e4''', '''bd-e2''', '''de-e1''', '''df-e8''', '''dg-e5''', '''ef-e3''', '''eg-e2''',
     '''eh-e12''', '''fg-e6''', '''fh-e10''', '''gh-e6'''],
    ['''ab-e1''', '''ac-e3''', '''bc-e4''', '''bd-e2''', '''bh-e12''', '''cd-e2''', '''df-e8''', '''dh-e10'''],
    ['''ab-e1''', '''ac-e3''', '''ad-e5''', '''bc-e4''', '''bd-e2''', '''cd-e2''', '''ce-e4''', '''de-e1''', '''df-e8''',
     '''dg-e5''', '''ef-e3''', '''eg-e2''', '''fg-e6''']
]







def     A__	(       __A						):







    '''simple docstring'''
    _lowerCamelCase  :		Union[str, Any]			    =    set()
    for row in edge_array:
        for item in row:
            distinct_edge.add(item[0]						)
    return list(_SCREAMING_SNAKE_CASE						)







def     A__	(       __A ,			__A						):







    '''simple docstring'''
    _lowerCamelCase  :		List[str]			    =    ['0'] * len(_SCREAMING_SNAKE_CASE						)
    for i, row in enumerate(_SCREAMING_SNAKE_CASE						):
        for item in row:
            if distinct_edge in item[0]:
                _lowerCamelCase  :		Tuple			    =    '1'
                break
    return "".join(_SCREAMING_SNAKE_CASE						)







def     A__	(       __A						):







    '''simple docstring'''
    _lowerCamelCase  :		List[str]			    =    get_distinct_edge(_SCREAMING_SNAKE_CASE						)
    _lowerCamelCase  :		Any			    =    {}

    for item in distinct_edge:
        _lowerCamelCase  :		List[str]			    =    get_bitcode(_SCREAMING_SNAKE_CASE ,			_SCREAMING_SNAKE_CASE						)
        # print('bit',bit)
        # bt=''.join(bit)
        _lowerCamelCase  :		Optional[Any]			    =    bit.count("""1"""						)
        _lowerCamelCase  :		List[str]			    =    [s, bit]
    # Store [Distinct edge, WT(Bitcode), Bitcode] in descending order
    _lowerCamelCase  :		int			    =    [
        [k, v[0], v[1]]
        for k, v in sorted(frequency_table.items() ,			key=lambda __A						: v[1][0] ,			reverse=_SCREAMING_SNAKE_CASE						)
    ]
    return sorted_frequency_table







def     A__	(       __A						):







    '''simple docstring'''
    _lowerCamelCase  :		List[Any]			    =    {}
    for _, item in enumerate(_SCREAMING_SNAKE_CASE						):
        nodes.setdefault(item[2] ,			[]						).append(item[0]						)
    return nodes







def     A__	(       __A						):







    '''simple docstring'''
    _lowerCamelCase  :		int			    =    {}
    for key, value in nodes.items():
        _lowerCamelCase  :		List[str]			    =    value
    return cluster







def     A__	(       __A						):







    '''simple docstring'''
    return [i * 100 / len(_SCREAMING_SNAKE_CASE						) for i in cluster]







def     A__	(       ):







    '''simple docstring'''
    print("""\nNodes\n"""						)
    for key, value in nodes.items():
        print(_SCREAMING_SNAKE_CASE ,			_SCREAMING_SNAKE_CASE						)
    print("""\nSupport\n"""						)
    print(_SCREAMING_SNAKE_CASE						)
    print("""\n Cluster \n"""						)
    for key, value in sorted(cluster.items() ,			reverse=_SCREAMING_SNAKE_CASE						):
        print(_SCREAMING_SNAKE_CASE ,			_SCREAMING_SNAKE_CASE						)
    print("""\n Graph\n"""						)
    for key, value in graph.items():
        print(_SCREAMING_SNAKE_CASE ,			_SCREAMING_SNAKE_CASE						)
    print("""\n Edge List of Frequent subgraphs \n"""						)
    for edge_list in freq_subgraph_edge_list:
        print(_SCREAMING_SNAKE_CASE						)







def     A__	(       __A ,			__A ,			__A ,			__A						):







    '''simple docstring'''


    for i in cluster[ca]:
        _lowerCamelCase  :		Tuple			    =    0
        _lowerCamelCase  :		List[str]			    =    ca + 1
        while ca < max(cluster.keys()						):
            for j in cluster[ca]:
                if int(_SCREAMING_SNAKE_CASE ,			2						) & int(_SCREAMING_SNAKE_CASE ,			2						) == int(_SCREAMING_SNAKE_CASE ,			2						):
                    if tuple(nodes[i]						) in graph:
                        graph[tuple(nodes[i]						)].append(nodes[j]						)
                    else:
                        _lowerCamelCase  :		Tuple			    =    [nodes[j]]
                    count += 1
            if count == 0:
                _lowerCamelCase  :		Dict			    =    ca + 1
            else:
                break







def     A__	(       __A ,			__A						):







    '''simple docstring'''
    _lowerCamelCase  :		Dict			    =    cluster[max(cluster.keys()						)]
    _lowerCamelCase  :		int			    =    'Header'
    _lowerCamelCase  :		Dict			    =    {}
    for i in x:
        if (["Header"],) in graph:
            graph[(["Header"],)].append(x[i]						)
        else:
            _lowerCamelCase  :		Union[str, Any]			    =    [x[i]]
    for i in x:
        _lowerCamelCase  :		Dict			    =    [['Header']]
    _lowerCamelCase  :		Optional[int]			    =    1
    while i < max(_SCREAMING_SNAKE_CASE						) - 1:
        create_edge(_SCREAMING_SNAKE_CASE ,			_SCREAMING_SNAKE_CASE ,			_SCREAMING_SNAKE_CASE ,			_SCREAMING_SNAKE_CASE						)
        _lowerCamelCase  :		Union[str, Any]			    =    i + 1
    return graph







def     A__	(       __A ,			__A ,			__A ,			__A=None						):







    '''simple docstring'''
    _lowerCamelCase  :		Union[str, Any]			    =    (path or []) + [start]
    if start == end:
        paths.append(_SCREAMING_SNAKE_CASE						)
    for node in graph[start]:
        if tuple(_SCREAMING_SNAKE_CASE						) not in path:
            my_dfs(_SCREAMING_SNAKE_CASE ,			tuple(_SCREAMING_SNAKE_CASE						) ,			_SCREAMING_SNAKE_CASE ,			_SCREAMING_SNAKE_CASE						)







def     A__	(       __A ,			__A ,			__A						):







    '''simple docstring'''
    _lowerCamelCase  :		Optional[int]			    =    int(s / 100 * (len(_SCREAMING_SNAKE_CASE						) - 1)						)
    for i in cluster[k]:
        my_dfs(_SCREAMING_SNAKE_CASE ,			tuple(cluster[k][i]						) ,			(["""Header"""],)						)







def     A__	(       __A						):







    '''simple docstring'''
    _lowerCamelCase  :		int			    =    []
    for edges in paths:
        _lowerCamelCase  :		Any			    =    []
        for j in range(len(_SCREAMING_SNAKE_CASE						) - 1						):
            _lowerCamelCase  :		List[Any]			    =    list(edges[j]						)
            for e in temp:
                _lowerCamelCase  :		str			    =    (e[0], e[1])
                el.append(_SCREAMING_SNAKE_CASE						)
        freq_sub_el.append(_SCREAMING_SNAKE_CASE						)
    return freq_sub_el







def     A__	(       __A						):







    '''simple docstring'''


    for i in range(len(_SCREAMING_SNAKE_CASE						)						):
        for j in range(len(edge_array[i]						)						):
            _lowerCamelCase  :		Tuple			    =    edge_array[i][j].split("""-"""						)
            _lowerCamelCase  :		Dict			    =    t


if __name__ == "__main__":
    preprocess(edge_array)
    lowerCAmelCase      :				str     			=get_frequency_table(edge_array)
    lowerCAmelCase      :				Tuple     			=get_nodes(frequency_table)
    lowerCAmelCase      :				Tuple     			=get_cluster(nodes)
    lowerCAmelCase      :				Dict     			=get_support(cluster)
    lowerCAmelCase      :				Optional[int]     			=construct_graph(cluster, nodes)
    find_freq_subgraph_given_support(60, cluster, graph)
    lowerCAmelCase      :				list     			=[]
    lowerCAmelCase      :				int     			=freq_subgraphs_edge_list(paths)
    print_all()





"""simple docstring"""







from typing import Dict, Optional, Tuple

import torch




def 						_lowercase				(  _SCREAMING_SNAKE_CASE				:				torch.Tensor						)    ->     torch.Tensor:







     '''simple docstring'''


     __A					:					List[str]								=		boundaries[1] - boundaries[0]
     __A					:					int								=		boundaries + step / 2
     __A					:					Union[str, Any]								=		torch.cat([bin_centers, (bin_centers[-1] + step).unsqueeze(-1						)]  ,       dim=0						)
     return bin_centers




def 						_lowercase				(  _SCREAMING_SNAKE_CASE				:				torch.Tensor  ,       _SCREAMING_SNAKE_CASE				:				torch.Tensor  ,       )    ->     Tuple[torch.Tensor, torch.Tensor]:







     '''simple docstring'''


     __A					:					str								=		_calculate_bin_centers(_SCREAMING_SNAKE_CASE						)
     return (
         torch.sum(aligned_distance_error_probs * bin_centers  ,       dim=-1						),
         bin_centers[-1],
     )




def 						_lowercase				(  _SCREAMING_SNAKE_CASE				:				torch.Tensor  ,       _SCREAMING_SNAKE_CASE				:				int = 31  ,       _SCREAMING_SNAKE_CASE				:				int = 64  ,       **_SCREAMING_SNAKE_CASE				:				Optional[Any]  ,       )    ->     Dict[str, torch.Tensor]:







     '''simple docstring'''


     __A					:					int								=		torch.linspace(0  ,       _SCREAMING_SNAKE_CASE  ,       steps=(no_bins - 1)  ,       device=logits.device						)

     __A					:					Any								=		torch.nn.functional.softmax(_SCREAMING_SNAKE_CASE  ,       dim=-1						)
     __A						,		__A					:					Tuple								=		_calculate_expected_aligned_error(
         alignment_confidence_breaks=_SCREAMING_SNAKE_CASE  ,       aligned_distance_error_probs=_SCREAMING_SNAKE_CASE  ,       )

     return {
         "aligned_confidence_probs": aligned_confidence_probs,
         "predicted_aligned_error": predicted_aligned_error,
         "max_predicted_aligned_error": max_predicted_aligned_error,
     }




def 						_lowercase				(  _SCREAMING_SNAKE_CASE				:				torch.Tensor  ,       _SCREAMING_SNAKE_CASE				:				Optional[torch.Tensor] = None  ,       _SCREAMING_SNAKE_CASE				:				int = 31  ,       _SCREAMING_SNAKE_CASE				:				int = 64  ,       _SCREAMING_SNAKE_CASE				:				float = 1E-8  ,       **_SCREAMING_SNAKE_CASE				:				Union[str, Any]  ,       )    ->     torch.Tensor:







     '''simple docstring'''


     if residue_weights is None:
          __A					:					Optional[int]								=		logits.new_ones(logits.shape[-2]						)

     __A					:					List[str]								=		torch.linspace(0  ,       _SCREAMING_SNAKE_CASE  ,       steps=(no_bins - 1)  ,       device=logits.device						)

     __A					:					Tuple								=		_calculate_bin_centers(_SCREAMING_SNAKE_CASE						)
     torch.sum(_SCREAMING_SNAKE_CASE						)
     __A					:					int								=		logits.shape[-2]
     __A					:					str								=		max(_SCREAMING_SNAKE_CASE  ,       19						)

     __A					:					Tuple								=		1.24 * (clipped_n - 15) ** (1.0 / 3) - 1.8

     __A					:					Tuple								=		torch.nn.functional.softmax(_SCREAMING_SNAKE_CASE  ,       dim=-1						)

     __A					:					List[str]								=		1.0 / (1 + (bin_centers**2) / (da**2))
     __A					:					int								=		torch.sum(probs * tm_per_bin  ,       dim=-1						)

     __A					:					Any								=		residue_weights / (eps + residue_weights.sum())
     __A					:					List[Any]								=		torch.sum(predicted_tm_term * normed_residue_mask  ,       dim=-1						)

     __A					:					int								=		per_alignment * residue_weights

     __A					:					Optional[int]								=		(weighted == torch.max(_SCREAMING_SNAKE_CASE						)).nonzero()[0]
     return per_alignment[tuple(_SCREAMING_SNAKE_CASE						)]



