



'''simple docstring'''







import sys
from random import randint

class      lowerCamelCase__     :






	'''simple docstring'''

	def __init__(  self		:  str   ,		__A		:  int   ,		__A		:  str					)     ->			Optional[int]:




								'''simple docstring'''





								lowerCAmelCase__  =   key
								lowerCAmelCase__  =   freq




	def __str__(  self		:  Tuple					)     ->			Union[str, Any]:




								'''simple docstring'''





								return f'''Node(key={self.key}, freq={self.freq})'''





def 			_lowerCAmelCase(      UpperCAmelCase_      :	int					, UpperCAmelCase_      :	Optional[int]					, UpperCAmelCase_      :	Optional[Any]					, UpperCAmelCase_      :	str					, UpperCAmelCase_      :	int					, UpperCAmelCase_      :	Optional[Any]						) ->							Any:







							if i > j or i < 0 or j > len(lowercase_						) - 1:
														return

							lowerCAmelCase__  =   root[i][j]
							if parent == -1:  # root does not have a parent
														print(F'''{key[node]} is the root of the binary search tree.'''						)
							elif is_left:
														print(F'''{key[node]} is the left child of key {parent}.'''						)
							else:
														print(F'''{key[node]} is the right child of key {parent}.'''						)

							print_binary_search_tree(lowercase_					, lowercase_					, lowercase_					, node - 1					, key[node]					, lowercase_						)
							print_binary_search_tree(lowercase_					, lowercase_					, node + 1					, lowercase_					, key[node]					, lowercase_						)
def 			_lowerCAmelCase(      UpperCAmelCase_      :	int						) ->							Tuple:
							nodes.sort(key=lambda UpperCAmelCase_						: node.key						)

							lowerCAmelCase__  =   len(lowercase_						)

							lowerCAmelCase__  =   [nodes[i].key for i in range(lowercase_						)]
							lowerCAmelCase__  =   [nodes[i].freq for i in range(lowercase_						)]

							# This 2D array stores the overall tree cost (which's as minimized as possible);
							# for a single key, cost is equal to frequency of the key.
							lowerCAmelCase__  =   [[freqs[i] if i == j else 0 for j in range(lowercase_						)] for i in range(lowercase_						)]
							# sum[i][j] stores the sum of key frequencies between i and j inclusive in nodes
							# array
							lowerCAmelCase__  =   [[freqs[i] if i == j else 0 for j in range(lowercase_						)] for i in range(lowercase_						)]
							# stores tree roots that will be used later for constructing binary search tree
							lowerCAmelCase__  =   [[i if i == j else 0 for j in range(lowercase_						)] for i in range(lowercase_						)]

							for interval_length in range(2					, n + 1						):
														for i in range(n - interval_length + 1						):
																					lowerCAmelCase__  =   i + interval_length - 1

																					lowerCAmelCase__  =   sys.maxsize  # set the value to "infinity"
																					lowerCAmelCase__  =   total[i][j - 1] + freqs[j]

																					# Apply Knuth's optimization
																					# Loop without optimization: for r in range(i, j + 1):
																					for r in range(root[i][j - 1]					, root[i + 1][j] + 1						):  # r is a temporal root
																												lowerCAmelCase__  =   dp[i][r - 1] if r != i else 0  # optimal cost for left subtree
																												lowerCAmelCase__  =   dp[r + 1][j] if r != j else 0  # optimal cost for right subtree
																												lowerCAmelCase__  =   left + total[i][j] + right

																												if dp[i][j] > cost:
																																			lowerCAmelCase__  =   cost
																																			lowerCAmelCase__  =   r

							print("""Binary search tree nodes:"""						)
							for node in nodes:
														print(lowercase_						)

							print(F'''\nThe cost of optimal BST for given tree nodes is {dp[0][n - 1]}.'''						)
							print_binary_search_tree(lowercase_					, lowercase_					, 0					, n - 1					, -1					, lowercase_						)
def 			_lowerCAmelCase(      ) ->							str:
							lowerCAmelCase__  =   [Node(lowercase_					, randint(1					, 50						)						) for i in range(10					, 0					, -1						)]
							find_optimal_binary_search_tree(lowercase_						)


if __name__ == "__main__":
		main()











'''simple docstring'''







import datasets

from .evaluate import (
    apply_no_ans_threshold,
    find_all_best_thresh,
    get_raw_scores,
    make_eval_dict,
    make_qid_to_has_ans,
    merge_eval,
)


_lowerCamelCase				:		str				      =    '\\n@inproceedings{Rajpurkar2016SQuAD10,\n  title={SQuAD: 100, 000+ Questions for Machine Comprehension of Text},\n  author={Pranav Rajpurkar and Jian Zhang and Konstantin Lopyrev and Percy Liang},\n  booktitle={EMNLP},\n  year={2016}\n}\n'

_lowerCamelCase				:		Union[str, Any]				      =    '\nThis metric wrap the official scoring script for version 2 of the Stanford Question\nAnswering Dataset (SQuAD).\n\nStanford Question Answering Dataset (SQuAD) is a reading comprehension dataset, consisting of questions posed by\ncrowdworkers on a set of Wikipedia articles, where the answer to every question is a segment of text, or span,\nfrom the corresponding reading passage, or the question might be unanswerable.\n\nSQuAD2.0 combines the 100,000 questions in SQuAD1.1 with over 50,000 unanswerable questions\nwritten adversarially by crowdworkers to look similar to answerable ones.\nTo do well on SQuAD2.0, systems must not only answer questions when possible, but also\ndetermine when no answer is supported by the paragraph and abstain from answering.\n'

_lowerCamelCase				:		List[Any]				      =    '\nComputes SQuAD v2 scores (F1 and EM).\nArgs:\n    predictions: List of triple for question-answers to score with the following elements:\n        - the question-answer \'id\' field as given in the references (see below)\n        - the text of the answer\n        - the probability that the question has no answer\n    references: List of question-answers dictionaries with the following key-values:\n            - \'id\': id of the question-answer pair (see above),\n            - \'answers\': a list of Dict {\'text\': text of the answer as a string}\n    no_answer_threshold: float\n        Probability threshold to decide that a question has no answer.\nReturns:\n    \'exact\': Exact match (the normalized answer exactly match the gold answer)\n    \'f1\': The F-score of predicted tokens versus the gold answer\n    \'total\': Number of score considered\n    \'HasAns_exact\': Exact match (the normalized answer exactly match the gold answer)\n    \'HasAns_f1\': The F-score of predicted tokens versus the gold answer\n    \'HasAns_total\': Number of score considered\n    \'NoAns_exact\': Exact match (the normalized answer exactly match the gold answer)\n    \'NoAns_f1\': The F-score of predicted tokens versus the gold answer\n    \'NoAns_total\': Number of score considered\n    \'best_exact\': Best exact match (with varying threshold)\n    \'best_exact_thresh\': No-answer probability threshold associated to the best exact match\n    \'best_f1\': Best F1 (with varying threshold)\n    \'best_f1_thresh\': No-answer probability threshold associated to the best F1\nExamples:\n\n    >>> predictions = [{\'prediction_text\': \'1976\', \'id\': \'56e10a3be3433e1400422b22\', \'no_answer_probability\': 0.}]\n    >>> references = [{\'answers\': {\'answer_start\': [97], \'text\': [\'1976\']}, \'id\': \'56e10a3be3433e1400422b22\'}]\n    >>> squad_v2_metric = datasets.load_metric("squad_v2")\n    >>> results = squad_v2_metric.compute(predictions=predictions, references=references)\n    >>> print(results)\n    {\'exact\': 100.0, \'f1\': 100.0, \'total\': 1, \'HasAns_exact\': 100.0, \'HasAns_f1\': 100.0, \'HasAns_total\': 1, \'best_exact\': 100.0, \'best_exact_thresh\': 0.0, \'best_f1\': 100.0, \'best_f1_thresh\': 0.0}\n'





@datasets.utils.file_utils.add_start_docstrings(_DESCRIPTION,			_KWARGS_DESCRIPTION				)
class 	lowerCamelCase_				(			datasets.Metric				):




					'''simple docstring'''






					def 							__SCREAMING_SNAKE_CASE      (       self					):
							return datasets.MetricInfo(
							    description=_DESCRIPTION,    citation=_CITATION,    inputs_description=_KWARGS_DESCRIPTION,    features=datasets.Features(
							        {
							            "predictions": {
							                "id": datasets.Value("string"					),
							                "prediction_text": datasets.Value("string"					),
							                "no_answer_probability": datasets.Value("float32"					),
							            },
							            "references": {
							                "id": datasets.Value("string"					),
							                "answers": datasets.features.Sequence(
							                    {"text": datasets.Value("string"					), "answer_start": datasets.Value("int32"					)}					),
							            },
							        }					),    codebase_urls=["https://rajpurkar.github.io/SQuAD-explorer/"],    reference_urls=["https://rajpurkar.github.io/SQuAD-explorer/"],    )






					def 							__SCREAMING_SNAKE_CASE      (       self,    __UpperCamelCase,    __UpperCamelCase,    __UpperCamelCase=1.0					):
							_snake_case      			=			{p["id"]: p["no_answer_probability"] for p in predictions}
							_snake_case      			=			[{"paragraphs": [{"qas": references}]}]
							_snake_case      			=			{p["id"]: p["prediction_text"] for p in predictions}

							_snake_case      			=			make_qid_to_has_ans(__UpperCamelCase					)  # maps qid to True/False
							_snake_case      			=			[k for k, v in qid_to_has_ans.items() if v]
							_snake_case      			=			[k for k, v in qid_to_has_ans.items() if not v]

							_snake_case			,       _snake_case      			=			get_raw_scores(__UpperCamelCase,    __UpperCamelCase					)
							_snake_case      			=			apply_no_ans_threshold(__UpperCamelCase,    __UpperCamelCase,    __UpperCamelCase,    __UpperCamelCase					)
							_snake_case      			=			apply_no_ans_threshold(__UpperCamelCase,    __UpperCamelCase,    __UpperCamelCase,    __UpperCamelCase					)
							_snake_case      			=			make_eval_dict(__UpperCamelCase,    __UpperCamelCase					)

							if has_ans_qids:
									_snake_case      			=			make_eval_dict(__UpperCamelCase,    __UpperCamelCase,    qid_list=__UpperCamelCase					)
									merge_eval(__UpperCamelCase,    __UpperCamelCase,    "HasAns"					)
							if no_ans_qids:
									_snake_case      			=			make_eval_dict(__UpperCamelCase,    __UpperCamelCase,    qid_list=__UpperCamelCase					)
									merge_eval(__UpperCamelCase,    __UpperCamelCase,    "NoAns"					)
							find_all_best_thresh(__UpperCamelCase,    __UpperCamelCase,    __UpperCamelCase,    __UpperCamelCase,    __UpperCamelCase,    __UpperCamelCase					)
							return dict(__UpperCamelCase					)





