





from math import factorial







def    __lowerCamelCase					(							__a   :int    ,     __a   :int    ,     __a   :float    )		->				float:






		"""simple docstring"""

		if successes > trials:
				raise ValueError("""successes must be lower or equal to trials"""    )
		if trials < 0 or successes < 0:
				raise ValueError("""the function is defined for non-negative integers"""    )
		if not isinstance(__a    ,     __a    ) or not isinstance(__a    ,     __a    ):
				raise ValueError("""the function is defined for non-negative integers"""    )
		if not 0 < prob < 1:
				raise ValueError("""prob has to be in range of 1 - 0"""    )
		A__        =   (prob**successes) * ((1 - prob) ** (trials - successes))
		# Calculate the binomial coefficient: n! / k!(n-k)!
		A__        =   float(factorial(__a    )    )
		coefficient /= factorial(__a    ) * factorial(trials - successes    )
		return probability * coefficient


if __name__ == "__main__":
					from doctest import testmod

					testmod()
					print('''Probability of 2 successes out of 4 trails''')
					print('''with probability of 0.75 is:''', end=''' ''')
					print(binomial_distribution(2, 4, 0.75))










import argparse
from collections import defaultdict

import yaml


A    :					str =      '''docs/source/en/_toctree.yml'''







def    __lowerCamelCase					(							__a   :str    )		->				List[Any]:






		"""simple docstring"""

		A__        =   defaultdict(__a    )
		A__        =   []
		A__        =   []
		for doc in doc_list:
				if "local" in doc:
						counts[doc["local"]] += 1

				if doc["title"].lower() == "overview":
						overview_doc.append({"""local""": doc["""local"""], """title""": doc["""title"""]}    )
				else:
						new_doc_list.append(__a    )

		A__        =   new_doc_list
		A__        =   [key for key, value in counts.items() if value > 1]

		A__        =   []
		for duplicate_key in duplicates:
				A__        =   list({doc["""title"""] for doc in doc_list if doc["""local"""] == duplicate_key}    )
				if len(__a    ) > 1:
						raise ValueError(
						    F'{duplicate_key} is present several times in the documentation table of content at '
						    """`docs/source/en/_toctree.yml` with different *Title* values. Choose one of those and remove the """
						    """others."""    )
				# Only add this once
				new_doc.append({"""local""": duplicate_key, """title""": titles[0]}    )

		# Add none duplicate-keys
		new_doc.extend([doc for doc in doc_list if """local""" not in counts or counts[doc["""local"""]] == 1]    )
		A__        =   sorted(__a    ,     key=lambda __a    : s["title"].lower()    )

		# "overview" gets special treatment and is always first
		if len(__a    ) > 1:
				raise ValueError("""{doc_list} has two 'overview' docs which is not allowed."""    )

		overview_doc.extend(__a    )

		# Sort
		return overview_doc







def    __lowerCamelCase					(							__a   :Any=False    )		->				List[str]:






		"""simple docstring"""

		with open(__a    ,     encoding="""utf-8"""    ) as f:
				A__        =   yaml.safe_load(f.read()    )

		# Get to the API doc
		A__        =   0
		while content[api_idx]["title"] != "API":
				api_idx += 1
		A__        =   content[api_idx]["""sections"""]

		# Then to the model doc
		A__        =   0
		while api_doc[scheduler_idx]["title"] != "Schedulers":
				scheduler_idx += 1

		A__        =   api_doc[scheduler_idx]["""sections"""]
		A__        =   clean_doc_toc(__a    )

		A__        =   False
		if new_scheduler_doc != scheduler_doc:
				A__        =   True
				if overwrite:
						A__        =   new_scheduler_doc

		if diff:
				if overwrite:
						A__        =   api_doc
						with open(__a    ,     """w"""    ,     encoding="""utf-8"""    ) as f:
								f.write(yaml.dump(__a    ,     allow_unicode=__a    )    )
				else:
						raise ValueError(
						    """The model doc part of the table of content is not properly sorted, run `make style` to fix this."""    )







def    __lowerCamelCase					(							__a   :Optional[int]=False    )		->				Dict:






		"""simple docstring"""

		with open(__a    ,     encoding="""utf-8"""    ) as f:
				A__        =   yaml.safe_load(f.read()    )

		# Get to the API doc
		A__        =   0
		while content[api_idx]["title"] != "API":
				api_idx += 1
		A__        =   content[api_idx]["""sections"""]

		# Then to the model doc
		A__        =   0
		while api_doc[pipeline_idx]["title"] != "Pipelines":
				pipeline_idx += 1

		A__        =   False
		A__        =   api_doc[pipeline_idx]["""sections"""]
		A__        =   []

		# sort sub pipeline docs
		for pipeline_doc in pipeline_docs:
				if "section" in pipeline_doc:
						A__        =   pipeline_doc["""section"""]
						A__        =   clean_doc_toc(__a    )
						if overwrite:
								A__        =   new_sub_pipeline_doc
				new_pipeline_docs.append(__a    )

		# sort overall pipeline doc
		A__        =   clean_doc_toc(__a    )

		if new_pipeline_docs != pipeline_docs:
				A__        =   True
				if overwrite:
						A__        =   new_pipeline_docs

		if diff:
				if overwrite:
						A__        =   api_doc
						with open(__a    ,     """w"""    ,     encoding="""utf-8"""    ) as f:
								f.write(yaml.dump(__a    ,     allow_unicode=__a    )    )
				else:
						raise ValueError(
						    """The model doc part of the table of content is not properly sorted, run `make style` to fix this."""    )


if __name__ == "__main__":
					A    :					Tuple =      argparse.ArgumentParser()
					parser.add_argument('''--fix_and_overwrite''', action='''store_true''', help='''Whether to fix inconsistencies.''')
					A    :					Optional[Any] =      parser.parse_args()

					check_scheduler_doc(args.fix_and_overwrite)
					check_pipeline_doc(args.fix_and_overwrite)



