

A_						:     Optional[int]			  =				[
    ['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    (				SCREAMING_SNAKE_CASE ) ->       Union[str, Any]:






    '''simple docstring'''
    __UpperCAmelCase			   =     set()
    for row in edge_array:
        for item in row:
            distinct_edge.add(item[0] )
    return list(SCREAMING_SNAKE_CASE )


def  __a    (				SCREAMING_SNAKE_CASE    ,				SCREAMING_SNAKE_CASE ) ->       Any:






    '''simple docstring'''
    __UpperCAmelCase			   =     ['''0'''] * len(SCREAMING_SNAKE_CASE )
    for i, row in enumerate(SCREAMING_SNAKE_CASE ):
        for item in row:
            if distinct_edge in item[0]:
                __UpperCAmelCase			   =     '''1'''
                break
    return "".join(SCREAMING_SNAKE_CASE )


def  __a    (				SCREAMING_SNAKE_CASE ) ->       Optional[int]:






    '''simple docstring'''
    __UpperCAmelCase			   =     get_distinct_edge(SCREAMING_SNAKE_CASE )
    __UpperCAmelCase			   =     {}

    for item in distinct_edge:
        __UpperCAmelCase			   =     get_bitcode(SCREAMING_SNAKE_CASE    ,				SCREAMING_SNAKE_CASE )
        # print('bit',bit)
        # bt=''.join(bit)
        __UpperCAmelCase			   =     bit.count('''1''' )
        __UpperCAmelCase			   =     [s, bit]
    # Store [Distinct edge, WT(Bitcode), Bitcode] in descending order
    __UpperCAmelCase			   =     [
        [k, v[0], v[1]]
        for k, v in sorted(frequency_table.items()    ,				key=lambda SCREAMING_SNAKE_CASE : v[1][0]    ,				reverse=SCREAMING_SNAKE_CASE )
    ]
    return sorted_frequency_table


def  __a    (				SCREAMING_SNAKE_CASE ) ->       Tuple:






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


def  __a    (				SCREAMING_SNAKE_CASE ) ->       Union[str, Any]:






    '''simple docstring'''
    __UpperCAmelCase			   =     {}
    for key, value in nodes.items():
        __UpperCAmelCase			   =     value
    return cluster


def  __a    (				SCREAMING_SNAKE_CASE ) ->       Any:






    '''simple docstring'''
    return [i * 1_0_0 / len(SCREAMING_SNAKE_CASE ) for i in cluster]


def  __a    (				) ->       None:






    '''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    (				SCREAMING_SNAKE_CASE    ,				SCREAMING_SNAKE_CASE    ,				SCREAMING_SNAKE_CASE    ,				SCREAMING_SNAKE_CASE ) ->       List[str]:






    '''simple docstring'''
    for i in cluster[ca]:
        __UpperCAmelCase			   =     0
        __UpperCAmelCase			   =     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:
                        __UpperCAmelCase			   =     [nodes[j]]
                    count += 1
            if count == 0:
                __UpperCAmelCase			   =     ca + 1
            else:
                break


def  __a    (				SCREAMING_SNAKE_CASE    ,				SCREAMING_SNAKE_CASE ) ->       List[Any]:






    '''simple docstring'''
    __UpperCAmelCase			   =     cluster[max(cluster.keys() )]
    __UpperCAmelCase			   =     '''Header'''
    __UpperCAmelCase			   =     {}
    for i in x:
        if (["Header"],) in graph:
            graph[(["Header"],)].append(x[i] )
        else:
            __UpperCAmelCase			   =     [x[i]]
    for i in x:
        __UpperCAmelCase			   =     [['''Header''']]
    __UpperCAmelCase			   =     1
    while i < max(SCREAMING_SNAKE_CASE ) - 1:
        create_edge(SCREAMING_SNAKE_CASE    ,				SCREAMING_SNAKE_CASE    ,				SCREAMING_SNAKE_CASE    ,				SCREAMING_SNAKE_CASE )
        __UpperCAmelCase			   =     i + 1
    return graph


def  __a    (				SCREAMING_SNAKE_CASE    ,				SCREAMING_SNAKE_CASE    ,				SCREAMING_SNAKE_CASE    ,				SCREAMING_SNAKE_CASE=None ) ->       Tuple:






    '''simple docstring'''
    __UpperCAmelCase			   =     (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    (				SCREAMING_SNAKE_CASE    ,				SCREAMING_SNAKE_CASE    ,				SCREAMING_SNAKE_CASE ) ->       str:






    '''simple docstring'''
    __UpperCAmelCase			   =     int(s / 1_0_0 * (len(SCREAMING_SNAKE_CASE ) - 1) )
    for i in cluster[k]:
        my_dfs(SCREAMING_SNAKE_CASE    ,				tuple(cluster[k][i] )    ,				(['''Header'''],) )


def  __a    (				SCREAMING_SNAKE_CASE ) ->       Any:






    '''simple docstring'''
    __UpperCAmelCase			   =     []
    for edges in paths:
        __UpperCAmelCase			   =     []
        for j in range(len(SCREAMING_SNAKE_CASE ) - 1 ):
            __UpperCAmelCase			   =     list(edges[j] )
            for e in temp:
                __UpperCAmelCase			   =     (e[0], e[1])
                el.append(SCREAMING_SNAKE_CASE )
        freq_sub_el.append(SCREAMING_SNAKE_CASE )
    return freq_sub_el


def  __a    (				SCREAMING_SNAKE_CASE ) ->       Any:






    '''simple docstring'''
    for i in range(len(SCREAMING_SNAKE_CASE ) ):
        for j in range(len(edge_array[i] ) ):
            __UpperCAmelCase			   =     edge_array[i][j].split('''-''' )
            __UpperCAmelCase			   =     t


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






def  __a    (				SCREAMING_SNAKE_CASE ) ->       float:






    '''simple docstring'''
    return -num if num < 0 else num


def  __a    (				SCREAMING_SNAKE_CASE ) ->       int:






    '''simple docstring'''
    if len(SCREAMING_SNAKE_CASE ) == 0:
        raise ValueError('''abs_min() arg is an empty sequence''' )
    __UpperCAmelCase			   =     x[0]
    for i in x:
        if abs_val(SCREAMING_SNAKE_CASE ) < abs_val(SCREAMING_SNAKE_CASE ):
            __UpperCAmelCase			   =     i
    return j


def  __a    (				SCREAMING_SNAKE_CASE ) ->       int:






    '''simple docstring'''
    if len(SCREAMING_SNAKE_CASE ) == 0:
        raise ValueError('''abs_max() arg is an empty sequence''' )
    __UpperCAmelCase			   =     x[0]
    for i in x:
        if abs(SCREAMING_SNAKE_CASE ) > abs(SCREAMING_SNAKE_CASE ):
            __UpperCAmelCase			   =     i
    return j


def  __a    (				SCREAMING_SNAKE_CASE ) ->       int:






    '''simple docstring'''
    if len(SCREAMING_SNAKE_CASE ) == 0:
        raise ValueError('''abs_max_sort() arg is an empty sequence''' )
    return sorted(SCREAMING_SNAKE_CASE    ,				key=SCREAMING_SNAKE_CASE )[-1]


def  __a    (				) ->       Union[str, Any]:






    '''simple docstring'''
    assert abs_val(0 ) == 0
    assert abs_val(3_4 ) == 3_4
    assert abs_val(-1_0_0_0_0_0_0_0_0_0_0_0 ) == 1_0_0_0_0_0_0_0_0_0_0_0

    __UpperCAmelCase			   =     [-3, -1, 2, -1_1]
    assert abs_max(SCREAMING_SNAKE_CASE ) == -1_1
    assert abs_max_sort(SCREAMING_SNAKE_CASE ) == -1_1
    assert abs_min(SCREAMING_SNAKE_CASE ) == -1


if __name__ == "__main__":
       import doctest

       doctest.testmod()

       test_abs_val()
       print(abs_val(-34))  # --> 34




