





from __future__ import annotations

import random
from collections.abc import Iterable






class  __A   :

			'''simple docstring'''







			def __init__(   self	,  __lowerCAmelCase							):



				'''simple docstring'''







				lowerCamelCase__        =		{literal: None for literal in literals}





			def __str__(   self							):



				'''simple docstring'''







				return "{" + " , ".join(self.literals							) + "}"





			def __len__(   self							):



				'''simple docstring'''







				return len(self.literals							)





			def 		__lowerCamelCase    (   self	,  __lowerCAmelCase							):



				'''simple docstring'''







				for literal in self.literals:
					lowerCamelCase__        =		literal[:2]
					if symbol in model:
						lowerCamelCase__        =		model[symbol]
					else:
						continue
					if value is not None:
						# Complement assignment if literal is in complemented form
						if literal.endswith('''\''''							):
							lowerCamelCase__        =		not value
					lowerCamelCase__        =		value





			def 		__lowerCamelCase    (   self	,  __lowerCAmelCase							):



				'''simple docstring'''







				for literal in self.literals:
					lowerCamelCase__        =		literal.rstrip('''\''''							) if literal.endswith('''\''''							) else literal + '''\''''
					if symbol in self.literals:
						return True

				self.assign(__lowerCAmelCase							)
				for value in self.literals.values():
					if value in (True, None):
						return value
				return any(self.literals.values()							)






class  __A   :

			'''simple docstring'''







			def __init__(   self	,  __lowerCAmelCase							):



				'''simple docstring'''







				lowerCamelCase__        =		list(__lowerCAmelCase							)





			def __str__(   self							):



				'''simple docstring'''







				return "{" + " , ".join(str(__lowerCAmelCase							) for clause in self.clauses							) + "}"





def lowerCAmelCase__()    ->				Clause:







	'''simple docstring'''







	lowerCamelCase__        =		[]
	lowerCamelCase__        =		random.randint(1	,5							)
	lowerCamelCase__        =		'''A'''
	lowerCamelCase__        =		0
	while i < no_of_literals:
		lowerCamelCase__        =		random.randint(1	,5							)
		lowerCamelCase__        =		base_var + str(__snake_case							)
		lowerCamelCase__        =		random.randint(0	,1							)
		if var_complement == 1:
			var_name += "'"
		if var_name in literals:
			i -= 1
		else:
			literals.append(__snake_case							)
		i += 1
	return Clause(__snake_case							)





def lowerCAmelCase__()    ->				Formula:







	'''simple docstring'''







	lowerCamelCase__        =		set()
	lowerCamelCase__        =		random.randint(1	,10							)
	while len(__snake_case							) < no_of_clauses:
		clauses.add(generate_clause()							)
	return Formula(__snake_case							)





def lowerCAmelCase__(__snake_case							)    ->				tuple[list[Clause], list[str]]:







	'''simple docstring'''







	lowerCamelCase__        =		formula.clauses
	lowerCamelCase__        =		[]
	for clause in formula.clauses:
		for literal in clause.literals:
			lowerCamelCase__        =		literal[:2]
			if symbol not in symbols_set:
				symbols_set.append(__snake_case							)
	return clauses, symbols_set





def lowerCAmelCase__(__snake_case	,__snake_case	,__snake_case							)    ->				tuple[list[str], dict[str, bool | None]]:







	'''simple docstring'''







	lowerCamelCase__        =		[]
	lowerCamelCase__        =		{}
	lowerCamelCase__        =		[]

	for clause in clauses:
		if clause.evaluate(__snake_case							):
			continue
		for literal in clause.literals:
			literals.append(__snake_case							)

	for s in symbols:
		lowerCamelCase__        =		s + '''\''''
		if (s in literals and sym not in literals) or (
		    s not in literals and sym in literals
		):
			pure_symbols.append(__snake_case							)
	for p in pure_symbols:
		lowerCamelCase__        =		None
	for s in pure_symbols:
		lowerCamelCase__        =		s + '''\''''
		if s in literals:
			lowerCamelCase__        =		True
		elif sym in literals:
			lowerCamelCase__        =		False
	return pure_symbols, assignment





def lowerCAmelCase__(__snake_case	,__snake_case							)    ->				tuple[list[str], dict[str, bool | None]]:







	'''simple docstring'''







	lowerCamelCase__        =		[]
	for clause in clauses:
		if len(__snake_case							) == 1:
			unit_symbols.append(list(clause.literals.keys()							)[0]							)
		else:
			lowerCamelCase__    ,     lowerCamelCase__        =		0, 0
			for literal, value in clause.literals.items():
				if value is False:
					f_count += 1
				elif value is None:
					lowerCamelCase__        =		literal
					n_count += 1
			if f_count == len(__snake_case							) - 1 and n_count == 1:
				unit_symbols.append(__snake_case							)
	lowerCamelCase__        =		{}
	for i in unit_symbols:
		lowerCamelCase__        =		i[:2]
		lowerCamelCase__        =		len(__snake_case							) == 2
	lowerCamelCase__        =		[i[:2] for i in unit_symbols]

	return unit_symbols, assignment





def lowerCAmelCase__(__snake_case	,__snake_case	,__snake_case							)    ->				tuple[bool | None, dict[str, bool | None] | None]:







	'''simple docstring'''







	lowerCamelCase__        =		True
	for clause in clauses:
		lowerCamelCase__        =		clause.evaluate(__snake_case							)
		if clause_check is False:
			return False, None
		elif clause_check is None:
			lowerCamelCase__        =		False
			continue

	if check_clause_all_true:
		return True, model

	try:
		lowerCamelCase__    ,     lowerCamelCase__        =		find_pure_symbols(__snake_case	,__snake_case	,__snake_case							)
	except RecursionError:
		print('''raises a RecursionError and is'''							)
		return None, {}
	lowerCamelCase__        =		None
	if len(__snake_case							) > 0:
		lowerCamelCase__    ,     lowerCamelCase__        =		pure_symbols[0], assignment[pure_symbols[0]]

	if p:
		lowerCamelCase__        =		model
		lowerCamelCase__        =		value
		lowerCamelCase__        =		list(__snake_case							)
		if p in tmp_symbols:
			tmp_symbols.remove(__snake_case							)
		return dpll_algorithm(__snake_case	,__snake_case	,__snake_case							)

	lowerCamelCase__    ,     lowerCamelCase__        =		find_unit_clauses(__snake_case	,__snake_case							)
	lowerCamelCase__        =		None
	if len(__snake_case							) > 0:
		lowerCamelCase__    ,     lowerCamelCase__        =		unit_symbols[0], assignment[unit_symbols[0]]
	if p:
		lowerCamelCase__        =		model
		lowerCamelCase__        =		value
		lowerCamelCase__        =		list(__snake_case							)
		if p in tmp_symbols:
			tmp_symbols.remove(__snake_case							)
		return dpll_algorithm(__snake_case	,__snake_case	,__snake_case							)
	lowerCamelCase__        =		symbols[0]
	lowerCamelCase__        =		symbols[1:]
	lowerCamelCase__    ,     lowerCamelCase__        =		model, model
	lowerCamelCase__    ,     lowerCamelCase__        =		True, False

	return dpll_algorithm(__snake_case	,__snake_case	,__snake_case							) or dpll_algorithm(__snake_case	,__snake_case	,__snake_case							)


if __name__ == "__main__":
			import doctest

			doctest.testmod()

			_a									=				generate_formula()
			print(f"""The formula {formula} is""", end=" ")

			_a						,		_a									=				generate_parameters(formula)
			_a						,		_a									=				dpll_algorithm(clauses, symbols, {})

			if solution:
						print(f"""satisfiable with the assignment {model}.""")
			else:
						print("not satisfiable.")










import unittest

import numpy as np

from transformers.testing_utils import require_torch, require_vision
from transformers.utils import is_torch_available, is_vision_available

from ...test_image_processing_common import ImageProcessingSavingTestMixin, prepare_image_inputs


if is_torch_available():
			import torch

if is_vision_available():
			from PIL import Image

			from transformers import ViltImageProcessor






class  __A   (   unittest.TestCase			):

			'''simple docstring'''







			def __init__(   self	,  __lowerCAmelCase	,  __lowerCAmelCase=7	,  __lowerCAmelCase=3	,  __lowerCAmelCase=1_8	,  __lowerCAmelCase=3_0	,  __lowerCAmelCase=4_0_0	,  __lowerCAmelCase=True	,  __lowerCAmelCase=None	,  __lowerCAmelCase=2	,  __lowerCAmelCase=True	,  __lowerCAmelCase=[0.5, 0.5, 0.5]	,  __lowerCAmelCase=[0.5, 0.5, 0.5]	,  ):



				'''simple docstring'''







				lowerCamelCase__        =		size if size is not None else {'''shortest_edge''': 3_0}
				lowerCamelCase__        =		parent
				lowerCamelCase__        =		batch_size
				lowerCamelCase__        =		num_channels
				lowerCamelCase__        =		image_size
				lowerCamelCase__        =		min_resolution
				lowerCamelCase__        =		max_resolution
				lowerCamelCase__        =		do_resize
				lowerCamelCase__        =		size
				lowerCamelCase__        =		size_divisor
				lowerCamelCase__        =		do_normalize
				lowerCamelCase__        =		image_mean
				lowerCamelCase__        =		image_std





			def 		__lowerCamelCase    (   self							):



				'''simple docstring'''







				return {
				    "image_mean": self.image_mean,
				    "image_std": self.image_std,
				    "do_normalize": self.do_normalize,
				    "do_resize": self.do_resize,
				    "size": self.size,
				    "size_divisor": self.size_divisor,
				}





			def 		__lowerCamelCase    (   self	,  __lowerCAmelCase	,  __lowerCAmelCase=False							):



				'''simple docstring'''







				if not batched:
					lowerCamelCase__        =		self.size['''shortest_edge''']
					lowerCamelCase__        =		image_inputs[0]
					if isinstance(__lowerCAmelCase	,  Image.Image							):
						lowerCamelCase__    ,     lowerCamelCase__        =		image.size
					else:
						lowerCamelCase__    ,     lowerCamelCase__        =		image.shape[1], image.shape[2]
					lowerCamelCase__        =		size / min(__lowerCAmelCase	,  __lowerCAmelCase							)
					if h < w:
						lowerCamelCase__    ,     lowerCamelCase__        =		size, scale * w
					else:
						lowerCamelCase__    ,     lowerCamelCase__        =		scale * h, size

					lowerCamelCase__        =		int((1_3_3_3 / 8_0_0) * size							)
					if max(__lowerCAmelCase	,  __lowerCAmelCase							) > max_size:
						lowerCamelCase__        =		max_size / max(__lowerCAmelCase	,  __lowerCAmelCase							)
						lowerCamelCase__        =		newh * scale
						lowerCamelCase__        =		neww * scale

					lowerCamelCase__    ,     lowerCamelCase__        =		int(newh + 0.5							), int(neww + 0.5							)
					lowerCamelCase__    ,     lowerCamelCase__        =		(
					    newh // self.size_divisor * self.size_divisor,
					    neww // self.size_divisor * self.size_divisor,
					)

				else:
					lowerCamelCase__        =		[]
					for image in image_inputs:
						lowerCamelCase__    ,     lowerCamelCase__        =		self.get_expected_values([image]							)
						expected_values.append((expected_height, expected_width)							)
					lowerCamelCase__        =		max(__lowerCAmelCase	,  key=lambda __lowerCAmelCase							: item[0]							)[0]
					lowerCamelCase__        =		max(__lowerCAmelCase	,  key=lambda __lowerCAmelCase							: item[1]							)[1]

				return expected_height, expected_width






@require_torch
@require_vision
class  __A   (   lowerCAmelCase      ,    unittest.TestCase			):

			'''simple docstring'''







			lowerCAmelCase_												=						ViltImageProcessor if is_vision_available() else None





			def 		__lowerCamelCase    (   self							):



				'''simple docstring'''







				lowerCamelCase__        =		ViltImageProcessingTester(self							)





			@property
			def 		__lowerCamelCase    (   self							):



				'''simple docstring'''







				return self.image_processor_tester.prepare_image_processor_dict()





			def 		__lowerCamelCase    (   self							):



				'''simple docstring'''







				lowerCamelCase__        =		self.image_processing_class(**self.image_processor_dict							)
				self.assertTrue(hasattr(__lowerCAmelCase	,  '''image_mean'''							)							)
				self.assertTrue(hasattr(__lowerCAmelCase	,  '''image_std'''							)							)
				self.assertTrue(hasattr(__lowerCAmelCase	,  '''do_normalize'''							)							)
				self.assertTrue(hasattr(__lowerCAmelCase	,  '''do_resize'''							)							)
				self.assertTrue(hasattr(__lowerCAmelCase	,  '''size'''							)							)
				self.assertTrue(hasattr(__lowerCAmelCase	,  '''size_divisor'''							)							)





			def 		__lowerCamelCase    (   self							):



				'''simple docstring'''







				lowerCamelCase__        =		self.image_processing_class.from_dict(self.image_processor_dict							)
				self.assertEqual(image_processor.size	,  {'''shortest_edge''': 3_0}							)

				lowerCamelCase__        =		self.image_processing_class.from_dict(self.image_processor_dict	,  size=4_2							)
				self.assertEqual(image_processor.size	,  {'''shortest_edge''': 4_2}							)





			def 		__lowerCamelCase    (   self							):



				'''simple docstring'''







				pass





			def 		__lowerCamelCase    (   self							):



				'''simple docstring'''







				lowerCamelCase__        =		self.image_processing_class(**self.image_processor_dict							)
				# create random PIL images
				lowerCamelCase__        =		prepare_image_inputs(self.image_processor_tester	,  equal_resolution=__lowerCAmelCase							)
				for image in image_inputs:
					self.assertIsInstance(__lowerCAmelCase	,  Image.Image							)

				# Test not batched input
				lowerCamelCase__        =		image_processing(image_inputs[0]	,  return_tensors='''pt'''							).pixel_values

				lowerCamelCase__    ,     lowerCamelCase__        =		self.image_processor_tester.get_expected_values(__lowerCAmelCase							)
				self.assertEqual(
				    encoded_images.shape	,  (1, self.image_processor_tester.num_channels, expected_height, expected_width)	,  )

				# Test batched
				lowerCamelCase__        =		image_processing(__lowerCAmelCase	,  return_tensors='''pt'''							).pixel_values

				lowerCamelCase__    ,     lowerCamelCase__        =		self.image_processor_tester.get_expected_values(__lowerCAmelCase	,  batched=__lowerCAmelCase							)
				self.assertEqual(
				    encoded_images.shape	,  (
				        self.image_processor_tester.batch_size,
				        self.image_processor_tester.num_channels,
				        expected_height,
				        expected_width,
				    )	,  )





			def 		__lowerCamelCase    (   self							):



				'''simple docstring'''







				lowerCamelCase__        =		self.image_processing_class(**self.image_processor_dict							)
				# create random numpy tensors
				lowerCamelCase__        =		prepare_image_inputs(self.image_processor_tester	,  equal_resolution=__lowerCAmelCase	,  numpify=__lowerCAmelCase							)
				for image in image_inputs:
					self.assertIsInstance(__lowerCAmelCase	,  np.ndarray							)

				# Test not batched input
				lowerCamelCase__        =		image_processing(image_inputs[0]	,  return_tensors='''pt'''							).pixel_values

				lowerCamelCase__    ,     lowerCamelCase__        =		self.image_processor_tester.get_expected_values(__lowerCAmelCase							)
				self.assertEqual(
				    encoded_images.shape	,  (1, self.image_processor_tester.num_channels, expected_height, expected_width)	,  )

				# Test batched
				lowerCamelCase__        =		image_processing(__lowerCAmelCase	,  return_tensors='''pt'''							).pixel_values

				lowerCamelCase__    ,     lowerCamelCase__        =		self.image_processor_tester.get_expected_values(__lowerCAmelCase	,  batched=__lowerCAmelCase							)
				self.assertEqual(
				    encoded_images.shape	,  (
				        self.image_processor_tester.batch_size,
				        self.image_processor_tester.num_channels,
				        expected_height,
				        expected_width,
				    )	,  )





			def 		__lowerCamelCase    (   self							):



				'''simple docstring'''







				lowerCamelCase__        =		self.image_processing_class(**self.image_processor_dict							)
				# create random PyTorch tensors
				lowerCamelCase__        =		prepare_image_inputs(self.image_processor_tester	,  equal_resolution=__lowerCAmelCase	,  torchify=__lowerCAmelCase							)
				for image in image_inputs:
					self.assertIsInstance(__lowerCAmelCase	,  torch.Tensor							)

				# Test not batched input
				lowerCamelCase__        =		image_processing(image_inputs[0]	,  return_tensors='''pt'''							).pixel_values

				lowerCamelCase__    ,     lowerCamelCase__        =		self.image_processor_tester.get_expected_values(__lowerCAmelCase							)
				self.assertEqual(
				    encoded_images.shape	,  (1, self.image_processor_tester.num_channels, expected_height, expected_width)	,  )

				# Test batched
				lowerCamelCase__        =		image_processing(__lowerCAmelCase	,  return_tensors='''pt'''							).pixel_values

				lowerCamelCase__    ,     lowerCamelCase__        =		self.image_processor_tester.get_expected_values(__lowerCAmelCase	,  batched=__lowerCAmelCase							)
				self.assertEqual(
				    encoded_images.shape	,  (
				        self.image_processor_tester.batch_size,
				        self.image_processor_tester.num_channels,
				        expected_height,
				        expected_width,
				    )	,  )



