




from __future__ import annotations

import random

# Adjacency list representation of this graph:
# https://en.wikipedia.org/wiki/File:Single_run_of_Karger%E2%80%99s_Mincut_algorithm.svg
a_ 		=  {
    '''1''': ['''2''', '''3''', '''4''', '''5'''],
    '''2''': ['''1''', '''3''', '''4''', '''5'''],
    '''3''': ['''1''', '''2''', '''4''', '''5''', '''10'''],
    '''4''': ['''1''', '''2''', '''3''', '''5''', '''6'''],
    '''5''': ['''1''', '''2''', '''3''', '''4''', '''7'''],
    '''6''': ['''7''', '''8''', '''9''', '''10''', '''4'''],
    '''7''': ['''6''', '''8''', '''9''', '''10''', '''5'''],
    '''8''': ['''6''', '''7''', '''9''', '''10'''],
    '''9''': ['''6''', '''7''', '''8''', '''10'''],
    '''10''': ['''6''', '''7''', '''8''', '''9''', '''3'''],
}




def        __SCREAMING_SNAKE_CASE (	lowercase_   )							->						set[tuple[str, str]]:

    """simple docstring"""


    __UpperCamelCase			=    {node: {node} for node in graph}

    __UpperCamelCase			=    {node: graph[node][:] for node in graph}

    while len(_UpperCAmelCase   ) > 2:
        # Choose a random edge.
        __UpperCamelCase			=    random.choice(list(graph_copy.keys()   )   )
        __UpperCamelCase			=    random.choice(graph_copy[u]   )

        # Contract edge (u, v) to new node uv
        __UpperCamelCase			=    u + v
        __UpperCamelCase			=    list(set(graph_copy[u] + graph_copy[v]   )   )
        uv_neighbors.remove(_UpperCAmelCase   )
        uv_neighbors.remove(_UpperCAmelCase   )
        __UpperCamelCase			=    uv_neighbors
        for neighbor in uv_neighbors:
            graph_copy[neighbor].append(_UpperCAmelCase   )

        __UpperCamelCase			=    set(contracted_nodes[u].union(contracted_nodes[v]   )   )

        # Remove nodes u and v.
        del graph_copy[u]
        del graph_copy[v]
        for neighbor in uv_neighbors:
            if u in graph_copy[neighbor]:
                graph_copy[neighbor].remove(_UpperCAmelCase   )
            if v in graph_copy[neighbor]:
                graph_copy[neighbor].remove(_UpperCAmelCase   )

    # Find cutset.
    __UpperCamelCase			=    [contracted_nodes[node] for node in graph_copy]
    return {
        (node, neighbor)
        for node in groups[0]
        for neighbor in graph[node]
        if neighbor in groups[1]
    }


if __name__ == "__main__":
 print(partition_graph(TEST_GRAPH))













import json
from typing import List, Optional, Tuple

from tokenizers import normalizers

from ...tokenization_utils_fast import PreTrainedTokenizerFast
from ...utils import logging
from .tokenization_layoutlm import LayoutLMTokenizer


UpperCAmelCase__    :      int       					=logging.get_logger(__name__)

UpperCAmelCase__    :      Optional[Any]       					={'''vocab_file''': '''vocab.txt''', '''tokenizer_file''': '''tokenizer.json'''}

UpperCAmelCase__    :      List[str]       					={
    '''vocab_file''': {
        '''microsoft/layoutlm-base-uncased''': (
            '''https://huggingface.co/microsoft/layoutlm-base-uncased/resolve/main/vocab.txt'''
        ),
        '''microsoft/layoutlm-large-uncased''': (
            '''https://huggingface.co/microsoft/layoutlm-large-uncased/resolve/main/vocab.txt'''
        ),
    },
    '''tokenizer_file''': {
        '''microsoft/layoutlm-base-uncased''': (
            '''https://huggingface.co/microsoft/layoutlm-base-uncased/resolve/main/tokenizer.json'''
        ),
        '''microsoft/layoutlm-large-uncased''': (
            '''https://huggingface.co/microsoft/layoutlm-large-uncased/resolve/main/tokenizer.json'''
        ),
    },
}

UpperCAmelCase__    :      Dict       					={
    '''microsoft/layoutlm-base-uncased''': 5_12,
    '''microsoft/layoutlm-large-uncased''': 5_12,
}

UpperCAmelCase__    :      List[Any]       					={
    '''microsoft/layoutlm-base-uncased''': {'''do_lower_case''': True},
    '''microsoft/layoutlm-large-uncased''': {'''do_lower_case''': True},
}

class    __A  (    a     ):
				__A  =					VOCAB_FILES_NAMES
				__A  =					PRETRAINED_VOCAB_FILES_MAP
				__A  =					PRETRAINED_INIT_CONFIGURATION
				__A  =					PRETRAINED_POSITIONAL_EMBEDDINGS_SIZES
				__A  =					LayoutLMTokenizer


				def __init__(		self ,			UpperCAmelCase_=None ,			UpperCAmelCase_=None ,			UpperCAmelCase_=True ,			UpperCAmelCase_="[UNK]" ,			UpperCAmelCase_="[SEP]" ,			UpperCAmelCase_="[PAD]" ,			UpperCAmelCase_="[CLS]" ,			UpperCAmelCase_="[MASK]" ,			UpperCAmelCase_=True ,			UpperCAmelCase_=None ,			**UpperCAmelCase_ ,			):
								super().__init__(
								    UpperCAmelCase_ ,			tokenizer_file=UpperCAmelCase_ ,			do_lower_case=UpperCAmelCase_ ,			unk_token=UpperCAmelCase_ ,			sep_token=UpperCAmelCase_ ,			pad_token=UpperCAmelCase_ ,			cls_token=UpperCAmelCase_ ,			mask_token=UpperCAmelCase_ ,			tokenize_chinese_chars=UpperCAmelCase_ ,			strip_accents=UpperCAmelCase_ ,			**UpperCAmelCase_ ,			)

								lowerCamelCase									=json.loads(self.backend_tokenizer.normalizer.__getstate__()				)
								if (
								    normalizer_state.get("""lowercase""" ,			UpperCAmelCase_				) != do_lower_case
								    or normalizer_state.get("""strip_accents""" ,			UpperCAmelCase_				) != strip_accents
								    or normalizer_state.get("""handle_chinese_chars""" ,			UpperCAmelCase_				) != tokenize_chinese_chars
								):
												lowerCamelCase									=getattr(UpperCAmelCase_ ,			normalizer_state.pop("""type"""				)				)
												lowerCamelCase									=do_lower_case
												lowerCamelCase									=strip_accents
												lowerCamelCase									=tokenize_chinese_chars
												lowerCamelCase									=normalizer_class(**UpperCAmelCase_				)

								lowerCamelCase									=do_lower_case


				def _snake_case							(		self ,			UpperCAmelCase_ ,			UpperCAmelCase_=None				):
								lowerCamelCase									=[self.cls_token_id] + token_ids_a + [self.sep_token_id]

								if token_ids_a:
												output += token_ids_a + [self.sep_token_id]

								return output


				def _snake_case							(		self ,			UpperCAmelCase_ ,			UpperCAmelCase_ = None				):
								lowerCamelCase									=[self.sep_token_id]
								lowerCamelCase									=[self.cls_token_id]
								if token_ids_a is None:
												return len(cls + token_ids_a + sep				) * [0]
								return len(cls + token_ids_a + sep				) * [0] + len(token_ids_a + sep				) * [1]


				def _snake_case							(		self ,			UpperCAmelCase_ ,			UpperCAmelCase_ = None				):
								lowerCamelCase									=self._tokenizer.model.save(UpperCAmelCase_ ,			name=UpperCAmelCase_				)
								return tuple(UpperCAmelCase_				)





