# A Bipartite Graph is a graph whose vertices can be divided into two independent sets,
# U and V such that every edge (u, v) either connects a vertex from U to V or a vertex
# from V to U. In other words, for every edge (u, v), either u belongs to U and v to V,
# or u belongs to V and v to U. We can also say that there is no edge that connects
# vertices of same set.
from queue import Queue

def     lowercase_       (    _lowerCamelCase							: Optional[int]):
    lowercase__				:     str					      =       Queue()
    lowercase__				:     str					      =       [False] * len(_lowerCamelCase)
    lowercase__				:     Tuple					      =       [-1] * len(_lowerCamelCase)

    def bfs():
        while not queue.empty():
            lowercase__				:     Union[str, Any]					      =       queue.get()
            lowercase__				:     Dict					      =       True

            for neighbour in graph[u]:
                if neighbour == u:
                    return False

                if color[neighbour] == -1:
                    lowercase__				:     Optional[Any]					      =       1 - color[u]
                    queue.put(_lowerCamelCase)

                elif color[neighbour] == color[u]:
                    return False

        return True

    for i in range(len(_lowerCamelCase)):
        if not visited[i]:
            queue.put(_lowerCamelCase)
            lowercase__				:     str					      =       0
            if bfs() is False:
                return False

    return True


if __name__ == "__main__":
      # Adjacency List of graph
      print(check_bipartite({0: [1, 3], 1: [0, 2], 2: [1, 3], 3: [0, 2]}))




import warnings
from typing import List, Optional, Union

from ...processing_utils import ProcessorMixin
from ...tokenization_utils_base import BatchEncoding, PaddingStrategy, PreTokenizedInput, TextInput, TruncationStrategy
from ...utils import TensorType



class 						snake_case_ (	__A ):
   __A			:	Optional[Any]        =       ["image_processor", "tokenizer"]
   __A			:	Tuple        =       "LayoutLMv2ImageProcessor"
   __A			:	Optional[int]        =       ("LayoutLMv2Tokenizer", "LayoutLMv2TokenizerFast")






   def __init__(   self       :  Tuple			,		lowercase_       :  List[str]=None			,		lowercase_       :  Dict=None			,		**lowercase_       :  List[str]						)      ->		int:
       lowercase__				:     Optional[Any]					      =       None
       if "feature_extractor" in kwargs:
           warnings.warn(
               "The `feature_extractor` argument is deprecated and will be removed in v5, use `image_processor`"
               " instead."			,		lowercase_			,		)
           lowercase__				:     Any					      =       kwargs.pop("feature_extractor"						)

       lowercase__				:     List[str]					      =       image_processor if image_processor is not None else feature_extractor
       if image_processor is None:
           raise ValueError("You need to specify an `image_processor`."						)
       if tokenizer is None:
           raise ValueError("You need to specify a `tokenizer`."						)

       super().__init__(lowercase_			,		lowercase_						)






   def __call__(   self       :  Union[str, Any]			,		lowercase_       :  Optional[Any]			,		lowercase_       :  Union[TextInput, PreTokenizedInput, List[TextInput], List[PreTokenizedInput]] = None			,		lowercase_       :  Optional[Union[PreTokenizedInput, List[PreTokenizedInput]]] = None			,		lowercase_       :  Union[List[List[int]], List[List[List[int]]]] = None			,		lowercase_       :  Optional[Union[List[int], List[List[int]]]] = None			,		lowercase_       :  bool = True			,		lowercase_       :  Union[bool, str, PaddingStrategy] = False			,		lowercase_       :  Union[bool, str, TruncationStrategy] = False			,		lowercase_       :  Optional[int] = None			,		lowercase_       :  int = 0			,		lowercase_       :  Optional[int] = None			,		lowercase_       :  Optional[bool] = None			,		lowercase_       :  Optional[bool] = None			,		lowercase_       :  bool = False			,		lowercase_       :  bool = False			,		lowercase_       :  bool = False			,		lowercase_       :  bool = False			,		lowercase_       :  bool = True			,		lowercase_       :  Optional[Union[str, TensorType]] = None			,		**lowercase_       :  List[str]			,		)      ->		BatchEncoding:
       # verify input
       if self.image_processor.apply_ocr and (boxes is not None):
           raise ValueError(
               "You cannot provide bounding boxes if you initialized the image processor with apply_ocr set to True."						)

       if self.image_processor.apply_ocr and (word_labels is not None):
           raise ValueError(
               "You cannot provide word labels if you initialized the image processor with apply_ocr set to True."						)

       if return_overflowing_tokens is True and return_offsets_mapping is False:
           raise ValueError("You cannot return overflowing tokens without returning the offsets mapping."						)

       # first, apply the image processor
       lowercase__				:     List[Any]					      =       self.image_processor(images=lowercase_			,		return_tensors=lowercase_						)

       # second, apply the tokenizer
       if text is not None and self.image_processor.apply_ocr and text_pair is None:
           if isinstance(lowercase_			,		lowercase_						):
               lowercase__				:     List[Any]					      =       [text]  # add batch dimension (as the image processor always adds a batch dimension)
           lowercase__				:     Union[str, Any]					      =       features["words"]

       lowercase__				:     List[str]					      =       self.tokenizer(
           text=text if text is not None else features["words"]			,		text_pair=text_pair if text_pair is not None else None			,		boxes=boxes if boxes is not None else features["boxes"]			,		word_labels=lowercase_			,		add_special_tokens=lowercase_			,		padding=lowercase_			,		truncation=lowercase_			,		max_length=lowercase_			,		stride=lowercase_			,		pad_to_multiple_of=lowercase_			,		return_token_type_ids=lowercase_			,		return_attention_mask=lowercase_			,		return_overflowing_tokens=lowercase_			,		return_special_tokens_mask=lowercase_			,		return_offsets_mapping=lowercase_			,		return_length=lowercase_			,		verbose=lowercase_			,		return_tensors=lowercase_			,		**lowercase_			,		)

       # add pixel values
       lowercase__				:     Optional[int]					      =       features.pop("pixel_values"						)
       if return_overflowing_tokens is True:
           lowercase__				:     Tuple					      =       self.get_overflowing_images(lowercase_			,		encoded_inputs["overflow_to_sample_mapping"]						)
       lowercase__				:     str					      =       images

       return encoded_inputs






   def    __UpperCamelCase  (   self       :  Tuple			,		lowercase_       :  Optional[int]			,		lowercase_       :  Union[str, Any]						)      ->		Any:
       # in case there's an overflow, ensure each `input_ids` sample is mapped to its corresponding image
       lowercase__				:     str					      =       []
       for sample_idx in overflow_to_sample_mapping:
           images_with_overflow.append(images[sample_idx]						)

       if len(lowercase_						) != len(lowercase_						):
           raise ValueError(
               "Expected length of images to be the same as the length of `overflow_to_sample_mapping`, but got"
               F''' {len(lowercase_						)} and {len(lowercase_						)}'''						)

       return images_with_overflow






   def    __UpperCamelCase  (   self       :  Any			,		*lowercase_       :  Tuple			,		**lowercase_       :  List[Any]						)      ->		Union[str, Any]:
       return self.tokenizer.batch_decode(*lowercase_			,		**lowercase_						)






   def    __UpperCamelCase  (   self       :  List[Any]			,		*lowercase_       :  Tuple			,		**lowercase_       :  Union[str, Any]						)      ->		List[Any]:
       return self.tokenizer.decode(*lowercase_			,		**lowercase_						)






   @property
   def    __UpperCamelCase  (   self       :  int						)      ->		Optional[Any]:
       return ["input_ids", "bbox", "token_type_ids", "attention_mask", "image"]






   @property
   def    __UpperCamelCase  (   self       :  Optional[int]						)      ->		Tuple:
       warnings.warn(
           "`feature_extractor_class` is deprecated and will be removed in v5. Use `image_processor_class` instead."			,		lowercase_			,		)
       return self.image_processor_class







   @property
   def    __UpperCamelCase  (   self       :  Dict						)      ->		List[Any]:
       warnings.warn(
           "`feature_extractor` is deprecated and will be removed in v5. Use `image_processor` instead."			,		lowercase_			,		)
       return self.image_processor



