"""simple docstring"""


from __future__ import annotations

import random
from collections.abc import Iterable






class        __UpperCAmelCase						:

				def __init__(				self     ,			_lowerCamelCase				):
										lowerCamelCase__ ={literal: None for literal in literals}

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

				def __len__(				self				):
										return len(self.literals				)

				def 		_a     (				self     ,			_lowerCamelCase				):
										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 		_a     (				self     ,			_lowerCamelCase				):
										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        __UpperCAmelCase						:

				def __init__(				self     ,			_lowerCamelCase				):
										lowerCamelCase__ =list(_lowerCamelCase				)






				def __str__(				self				):
										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(__lowerCAmelCase    )
												lowerCamelCase__ =random.randint(0       ,   1    )
												if var_complement == 1:
																		var_name += "'"
												if var_name in literals:
																		i -= 1
												else:
																		literals.append(__lowerCAmelCase    )
												i += 1
						return Clause(__lowerCAmelCase    )





def       lowerCamelCase_			( )							-> Formula:




						'''simple docstring'''



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





def       lowerCamelCase_			( __lowerCAmelCase    )							-> 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(__lowerCAmelCase    )
						return clauses, symbols_set





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




						'''simple docstring'''



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

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

						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(__lowerCAmelCase    )
						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_			( __lowerCAmelCase       ,   __lowerCAmelCase    )							-> tuple[list[str], dict[str, bool | None]]:




						'''simple docstring'''



						lowerCamelCase__ =[]
						for clause in clauses:
												if len(__lowerCAmelCase    ) == 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(__lowerCAmelCase    ) - 1 and n_count == 1:
																								unit_symbols.append(__lowerCAmelCase    )
						lowerCamelCase__ ={}
						for i in unit_symbols:
												lowerCamelCase__ =i[:2]
												lowerCamelCase__ =len(__lowerCAmelCase    ) == 2
						lowerCamelCase__ =[i[:2] for i in unit_symbols]

						return unit_symbols, assignment





def       lowerCamelCase_			( __lowerCAmelCase       ,   __lowerCAmelCase       ,   __lowerCAmelCase    )							-> tuple[bool | None, dict[str, bool | None] | None]:




						'''simple docstring'''



						lowerCamelCase__ =True
						for clause in clauses:
												lowerCamelCase__ =clause.evaluate(__lowerCAmelCase    )
												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(__lowerCAmelCase       ,   __lowerCAmelCase       ,   __lowerCAmelCase    )
						except RecursionError:
												print("raises a RecursionError and is"    )
												return None, {}
						lowerCamelCase__ =None
						if len(__lowerCAmelCase    ) > 0:
												lowerCamelCase__ ,				lowerCamelCase__ =pure_symbols[0], assignment[pure_symbols[0]]

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

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

						return dpll_algorithm(__lowerCAmelCase       ,   __lowerCAmelCase       ,   __lowerCAmelCase    ) or dpll_algorithm(__lowerCAmelCase       ,   __lowerCAmelCase       ,   __lowerCAmelCase    )


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.')



"""simple docstring"""


class        __UpperCAmelCase						:

				def __init__(				self     ,			_lowerCamelCase				):
										lowerCamelCase__ =data
										lowerCamelCase__ =None
										lowerCamelCase__ =None





def       lowerCamelCase_			( __lowerCAmelCase       ,   __lowerCAmelCase    )							-> BinaryTreeNode | None:




						'''simple docstring'''



						if node is None:
												lowerCamelCase__ =BinaryTreeNode(__lowerCAmelCase    )
												return node

						# binary search tree is not empty,
						# so we will insert it into the tree
						# if new_value is less than value of data in node,
						#  add it to left subtree and proceed recursively
						if new_value < node.data:
												lowerCamelCase__ =insert(node.left_child       ,   __lowerCAmelCase    )
						else:
												# if new_value is greater than value of data in node,
												#  add it to right subtree and proceed recursively
												lowerCamelCase__ =insert(node.right_child       ,   __lowerCAmelCase    )
						return node





def       lowerCamelCase_			( __lowerCAmelCase    )							-> list[int]:  # if node is None,return




						'''simple docstring'''



						if node:
												lowerCamelCase__ =inorder(node.left_child    )
												lowerCamelCase__ =[*inorder_array, node.data]
												lowerCamelCase__ =inorder_array + inorder(node.right_child    )
						else:
												lowerCamelCase__ =[]
						return inorder_array





def       lowerCamelCase_			( )							-> BinaryTreeNode | None:




						'''simple docstring'''



						lowerCamelCase__ =insert(__lowerCAmelCase       ,   15    )
						insert(__lowerCAmelCase       ,   10    )
						insert(__lowerCAmelCase       ,   25    )
						insert(__lowerCAmelCase       ,   6    )
						insert(__lowerCAmelCase       ,   14    )
						insert(__lowerCAmelCase       ,   20    )
						insert(__lowerCAmelCase       ,   60    )
						return root





def       lowerCamelCase_			( )							-> None:




						'''simple docstring'''



						lowerCamelCase__ =make_tree()
						print("Printing values of binary search tree in Inorder Traversal."    )
						inorder(__lowerCAmelCase    )


if __name__ == "__main__":
	import doctest

	doctest.testmod()
	main()


