



import math





class    __lowerCAmelCase					:




				def __init__(				self		,							_snake_case		,							_snake_case		,							_snake_case		,							_snake_case						):



									"""simple docstring"""





									_lowerCAmelCase         =       x
									_lowerCAmelCase         =       y
									_lowerCAmelCase         =       step_size
									_lowerCAmelCase         =       function_to_optimize




				def 				snake_case  (				self						):



									"""simple docstring"""





									return self.function(self.x		,							self.y						)




				def 				snake_case  (				self						):



									"""simple docstring"""





									_lowerCAmelCase         =       self.step_size
									return [
									    SearchProblem(_snake_case		,							_snake_case		,							_snake_case		,							self.function						)
									    for x, y in (
									        (self.x - step_size, self.y - step_size),
									        (self.x - step_size, self.y),
									        (self.x - step_size, self.y + step_size),
									        (self.x, self.y - step_size),
									        (self.x, self.y + step_size),
									        (self.x + step_size, self.y - step_size),
									        (self.x + step_size, self.y),
									        (self.x + step_size, self.y + step_size),
									    )
									]




				def __hash__(				self						):



									"""simple docstring"""





									return hash(str(self						)						)




				def __eq__(				self		,							_snake_case						):



									"""simple docstring"""





									if isinstance(_snake_case		,							_snake_case						):
														return hash(str(self						)						) == hash(str(_snake_case						)						)
									return False




				def __str__(				self						):



									"""simple docstring"""





									return F'x: {self.x} y: {self.y}'


def 						_UpperCAmelCase							( snake_case      ,		snake_case = True      ,		snake_case = math.inf      ,		snake_case = -math.inf      ,		snake_case = math.inf      ,		snake_case = -math.inf      ,		snake_case = False      ,		snake_case = 1_00_00      ,		):





					"""simple docstring"""

					_lowerCAmelCase         =       search_prob
					_lowerCAmelCase         =       []  # list to store the current score at each iteration
					_lowerCAmelCase         =       0
					_lowerCAmelCase         =       False
					_lowerCAmelCase         =       set()
					while not solution_found and iterations < max_iter:
										visited.add(snake_case     )
										iterations += 1
										_lowerCAmelCase         =       current_state.score()
										scores.append(snake_case     )
										_lowerCAmelCase         =       current_state.get_neighbors()
										_lowerCAmelCase         =       -math.inf
										_lowerCAmelCase         =       math.inf
										_lowerCAmelCase         =       None  # to hold the next best neighbor
										for neighbor in neighbors:
															if neighbor in visited:
																				continue  # do not want to visit the same state again
															if (
															    neighbor.x > max_x
															    or neighbor.x < min_x
															    or neighbor.y > max_y
															    or neighbor.y < min_y
															):
																				continue  # neighbor outside our bounds
															_lowerCAmelCase         =       neighbor.score() - current_score
															if find_max:  # finding max
																				# going to direction with greatest ascent
																				if change > max_change and change > 0:
																									_lowerCAmelCase         =       change
																									_lowerCAmelCase         =       neighbor
															else:  # finding min
																				# to direction with greatest descent
																				if change < min_change and change < 0:
																									_lowerCAmelCase         =       change
																									_lowerCAmelCase         =       neighbor
										if next_state is not None:
															# we found at least one neighbor which improved the current state
															_lowerCAmelCase         =       next_state
										else:
															# since we have no neighbor that improves the solution we stop the search
															_lowerCAmelCase         =       True

					if visualization:
										from matplotlib import pyplot as plt

										plt.plot(range(snake_case     )      ,		snake_case     )
										plt.xlabel("""Iterations"""     )
										plt.ylabel("""Function values"""     )
										plt.show()

					return current_state


if __name__ == "__main__":
	import doctest

	doctest.testmod()


	def 						_UpperCAmelCase							( snake_case      ,		snake_case     ):





						"""simple docstring"""

						return (x**2) + (y**2)

	# starting the problem with initial coordinates (3, 4)
	A__       =			SearchProblem(x=3, y=4, step_size=1, function_to_optimize=test_fa)
	A__       =			hill_climbing(prob, find_max=False)
	print(
	    """The minimum score for f(x, y) = x^2 + y^2 found via hill climbing: """
	    f"{local_min.score()}"
	)

	# starting the problem with initial coordinates (12, 47)
	A__       =			SearchProblem(x=12, y=47, step_size=1, function_to_optimize=test_fa)
	A__       =			hill_climbing(
	    prob, find_max=False, max_x=1_00, min_x=5, max_y=50, min_y=-5, visualization=True
	)
	print(
	    """The minimum score for f(x, y) = x^2 + y^2 with the domain 100 > x > 5 """
	    f"and 50 > y > - 5 found via hill climbing: {local_min.score()}"
	)


	def 						_UpperCAmelCase							( snake_case      ,		snake_case     ):





						"""simple docstring"""

						return (3 * x**2) - (6 * y)

	A__       =			SearchProblem(x=3, y=4, step_size=1, function_to_optimize=test_fa)
	A__       =			hill_climbing(prob, find_max=True)
	print(
	    """The maximum score for f(x, y) = x^2 + y^2 found via hill climbing: """
	    f"{local_min.score()}"
	)




"""simple docstring"""







import dataclasses
import enum
import functools
import math
import re

# The following script is adapted from the script of TaPas.
# Original: https://github.com/google-research/tapas/master/wikisql_utils.py
from typing import Any, List, Text


_a	:	List[Any]=					"none"
_a	:	List[str]=					"none"
def     __UpperCAmelCase							(       UpperCAmelCase_       :							Optional[int]     ,				UpperCAmelCase_       :							Tuple    )				->     Dict:

	'''simple docstring'''





	__snake_case     :				int 						=					value.split(UpperCAmelCase_    )
	return len(UpperCAmelCase_    ) > 1 and any((len(UpperCAmelCase_    ) == 3 for x in split)    )
def     __UpperCAmelCase							(       UpperCAmelCase_       :							Optional[Any]    )				->     Tuple:

	'''simple docstring'''





	if isinstance(UpperCAmelCase_     ,				UpperCAmelCase_    ):
		return value
	if isinstance(UpperCAmelCase_     ,				UpperCAmelCase_    ):
		return float(UpperCAmelCase_    )
	if not isinstance(UpperCAmelCase_     ,				UpperCAmelCase_    ):
		raise ValueError('Argument value is not a string. Can\'t parse it as float'    )
	__snake_case     :				Any 						=					value

	try:
		# Example: 1,000.7
		if "." in sanitized and "," in sanitized:
			return float(sanitized.replace(','     ,				''    )    )
		# 1,000
		if "," in sanitized and _split_thousands(','     ,				UpperCAmelCase_    ):
			return float(sanitized.replace(','     ,				''    )    )
		# 5,5556
		if "," in sanitized and sanitized.count(','    ) == 1 and not _split_thousands(','     ,				UpperCAmelCase_    ):
			return float(sanitized.replace(','     ,				'.'    )    )
		# 0.0.0.1
		if sanitized.count('.'    ) > 1:
			return float(sanitized.replace('.'     ,				''    )    )
		# 0,0,0,1
		if sanitized.count(','    ) > 1:
			return float(sanitized.replace(','     ,				''    )    )
		return float(UpperCAmelCase_    )
	except ValueError:
		# Avoid adding the sanitized value in the error message.
		raise ValueError('Unable to convert value to float'    )
def     __UpperCAmelCase							(       UpperCAmelCase_       :							str    )				->     Any:

	'''simple docstring'''





	if answer is None:
		return None
	try:
		__snake_case     :				Dict 						=					convert_to_float(UpperCAmelCase_    )
		if isinstance(UpperCAmelCase_     ,				UpperCAmelCase_    ) and math.isnan(UpperCAmelCase_    ):
			return None
		return value
	except ValueError:
		return answer.lower()


_a	:	Union[str, Any]=					{
    "text": lambda x: x,
    "real": convert_to_float,
}

class 						UpperCamelCase     (       enum.Enum		):
				UpperCAmelCase							: int       =						0
				UpperCAmelCase							: Optional[Any]       =						1
				UpperCAmelCase							: List[Any]       =						2
				UpperCAmelCase							: Dict       =						3
				UpperCAmelCase							: Union[str, Any]       =						4
				UpperCAmelCase							: int       =						5







class 						UpperCamelCase     (       enum.Enum		):
				UpperCAmelCase							: List[str]       =						0
				UpperCAmelCase							: List[str]       =						1
				UpperCAmelCase							: int       =						2







@dataclasses.dataclass
class 						UpperCamelCase     :
				UpperCAmelCase							: Text
				UpperCAmelCase							: _Operator
				UpperCAmelCase							: Any







_a	:	Union[str, Any]=					re.compile(R"\w+|[^\w\s]+", re.UNICODE | re.MULTILINE | re.DOTALL)
def     __UpperCAmelCase							(       UpperCAmelCase_       :							List[str]    )				->     Optional[Any]:

	'''simple docstring'''





	return list(_TOKENIZER.findall(x.lower()    )    )
def     __UpperCAmelCase							(       UpperCAmelCase_       :							Tuple     ,				UpperCAmelCase_       :							int     ,				UpperCAmelCase_       :							List[Any]    )				->     List[str]:

	'''simple docstring'''





	if operator == _Operator.EQUALS:
		return src == tgt
	elif operator == _Operator.GREATER:
		return src > tgt
	elif operator == _Operator.LESSER:
		return src < tgt
	raise ValueError(F"Unknown operator: {operator}"    )
def     __UpperCAmelCase							(       UpperCAmelCase_       :							List[Any]     ,				UpperCAmelCase_       :							int     ,				UpperCAmelCase_       :							Optional[Any]    )				->     Dict:

	'''simple docstring'''





	__snake_case     :				Optional[Any] 						=					table['types']
	return _TYPE_CONVERTER[types[column]](UpperCAmelCase_    )
def     __UpperCAmelCase							(       UpperCAmelCase_       :							List[Any]    )				->     str:

	'''simple docstring'''





	return isinstance(UpperCAmelCase_     ,				UpperCAmelCase_    )
def     __UpperCAmelCase							(       UpperCAmelCase_       :							Dict     ,				UpperCAmelCase_       :							Union[str, Any]     ,				UpperCAmelCase_       :							int    )				->     List[Any]:

	'''simple docstring'''





	for cond in conditions:
		__snake_case     :				Any 						=					row[cond.column]

		__snake_case     :				Tuple 						=					_parse_value(UpperCAmelCase_     ,				cond.column     ,				cond.cmp_value    )

		if _is_string(UpperCAmelCase_    ) and _is_string(UpperCAmelCase_    ):
			__snake_case     :				str 						=					_normalize_for_match(UpperCAmelCase_    )
			__snake_case     :				Dict 						=					_normalize_for_match(UpperCAmelCase_    )

		if not isinstance(UpperCAmelCase_     ,				type(UpperCAmelCase_    )    ):
			raise ValueError('Type difference {} != {}'.format(type(UpperCAmelCase_    )     ,				type(UpperCAmelCase_    )    )    )

		if not _compare(cond.operator     ,				UpperCAmelCase_     ,				UpperCAmelCase_    ):
			return False
	return True
def     __UpperCAmelCase							(       UpperCAmelCase_       :							Union[str, Any]     ,				UpperCAmelCase_       :							List[str]     ,				UpperCAmelCase_       :							Optional[int]    )				->     Dict:

	'''simple docstring'''





	if not answer_coordinates:
		if aggregation_op == _Aggregation.COUNT:
			return 0.0
		else:
			return EMPTY_ANSWER_AGG

    # Count can support non numeric answers.
	if aggregation_op == _Aggregation.COUNT:
		return float(len(UpperCAmelCase_    )    )

	# If we have just one answer, if float returns it or try a conversion.
	__snake_case     :				Any 						=					[table['rows'][i][j] for (i, j) in answer_coordinates]
	if len(UpperCAmelCase_    ) == 1:
		try:
			return convert_to_float(values[0]    )
		except ValueError as e:
			if aggregation_op != _Aggregation.NONE:
				raise e

	if aggregation_op == _Aggregation.NONE:
		return None

	# Other aggregation only support numeric values. Bail out if we have strings.
	if not all((isinstance(UpperCAmelCase_     ,				(int, float)    ) for v in values)    ):
		return None

	if aggregation_op == _Aggregation.SUM:
		return float(sum(UpperCAmelCase_    )    )
	elif aggregation_op == _Aggregation.AVERAGE:
		return sum(UpperCAmelCase_    ) / len(UpperCAmelCase_    )
	else:
		raise ValueError(F"Unknown aggregation: {aggregation_op}"    )
def     __UpperCAmelCase							(       UpperCAmelCase_       :							Optional[Any]     ,				UpperCAmelCase_       :							int    )				->     str:

	'''simple docstring'''





	__snake_case     :				int 						=					sql_query['agg']
	if aggregation_op_index >= 3:
		__snake_case     :				Optional[Any] 						=					_Aggregation(UpperCAmelCase_    )
	else:
		__snake_case     :				Any 						=					_Aggregation.NONE

	__snake_case     :				Dict 						=					sql_query['sel']
	__snake_case     :				Dict 						=					[
	    _Condition(UpperCAmelCase_     ,				_Operator(UpperCAmelCase_    )     ,				UpperCAmelCase_    )
	    for column, operator, cmp_value in zip(
	        sql_query['conds']['column_index']     ,				sql_query['conds']['operator_index']     ,				sql_query['conds']['condition']    )
	]

	__snake_case     :				str 						=					[]
	for row in range(len(table['rows']    )    ):
		if _respect_conditions(UpperCAmelCase_     ,				table['rows'][row]     ,				UpperCAmelCase_    ):
			indices.append((row, target_column)    )

	if not indices:
		return [], aggregation_op

	if len(UpperCAmelCase_    ) == 1:
		return indices, aggregation_op

	# Parsing of MIN/MAX.
	if aggregation_op_index in (1, 2):
		__snake_case     :				Union[str, Any] 						=					{2: min, 1: max}
		__snake_case     :				Optional[Any] 						=					[(table['rows'][i][j], index) for index, (i, j) in enumerate(UpperCAmelCase_    )]
		__snake_case     :				Tuple 						=					functools.reduce(operators[sql_query['agg']]     ,				UpperCAmelCase_    )

		__snake_case     :				str 						=					[indices[reduced[1]]]
		return ret, _Aggregation.NONE

	return indices, aggregation_op
def     __UpperCAmelCase							(       UpperCAmelCase_       :							Dict     ,				UpperCAmelCase_       :							List[Any]     ,				UpperCAmelCase_       :							Any    )				->     Optional[Any]:

	'''simple docstring'''





	if float_answer is not None:
		return [str(UpperCAmelCase_    )]
	return [str(table['real_rows'][r][c]    ) for r, c in answer_coordinates]

def     __UpperCAmelCase							(       UpperCAmelCase_       :							int     ,				UpperCAmelCase_       :							Tuple    )				->     List:

	'''simple docstring'''





	__snake_case						,							__snake_case     :				List[Any] 						=					_get_answer_coordinates(UpperCAmelCase_     ,				UpperCAmelCase_    )
	__snake_case     :				Optional[int] 						=					_get_float_answer(UpperCAmelCase_     ,				UpperCAmelCase_     ,				UpperCAmelCase_    )
	__snake_case     :				Union[str, Any] 						=					_get_answer_text(UpperCAmelCase_     ,				UpperCAmelCase_     ,				UpperCAmelCase_    )
	# keep the original data the same with TaPas
	if len(UpperCAmelCase_    ) == 0:
		__snake_case     :				List[str] 						=					[EMPTY_ANSWER]
	return answer_text





