



from __future__ import annotations

from collections.abc import Sequence
from typing import Literal

def        a						(      _UpperCAmelCase							:					str ,   _UpperCAmelCase							:					str						):







		'''simple docstring'''





		__UpperCAmelCase    :     str													=	list(_UpperCAmelCase						)
		__UpperCAmelCase    :     Optional[Any]													=	list(_UpperCAmelCase						)
		__UpperCAmelCase    :     Optional[Any]													=	0
		for i in range(len(_UpperCAmelCase						)						):
				if lista[i] != lista[i]:
						count += 1
						__UpperCAmelCase    :     Dict													=	'''_'''
		if count > 1:
				return False
		else:
				return "".join(_UpperCAmelCase						)

def        a						(      _UpperCAmelCase							:					list[str]						):







		'''simple docstring'''





		__UpperCAmelCase    :     str													=	[]
		while True:
				__UpperCAmelCase    :     List[Any]													=	['''$'''] * len(_UpperCAmelCase						)
				__UpperCAmelCase    :     int													=	[]
				for i in range(len(_UpperCAmelCase						)						):
						for j in range(i + 1 ,   len(_UpperCAmelCase						)						):
								__UpperCAmelCase    :     List[Any]													=	compare_string(binary[i] ,   binary[j]						)
								if k is False:
										__UpperCAmelCase    :     List[Any]													=	'''*'''
										__UpperCAmelCase    :     Any													=	'''*'''
										temp.append('''X'''						)
				for i in range(len(_UpperCAmelCase						)						):
						if checka[i] == "$":
								pi.append(binary[i]						)
				if len(_UpperCAmelCase						) == 0:
						return pi
				__UpperCAmelCase    :     List[str]													=	list(set(_UpperCAmelCase						)						)

def        a						(      _UpperCAmelCase							:					int ,   _UpperCAmelCase							:					Sequence[float]						):







		'''simple docstring'''





		__UpperCAmelCase    :     Optional[int]													=	[]
		for minterm in minterms:
				__UpperCAmelCase    :     int													=	''''''
				for _ in range(_UpperCAmelCase						):
						__UpperCAmelCase    :     Union[str, Any]													=	str(minterm % 2						) + string
						minterm //= 2
				temp.append(_UpperCAmelCase						)
		return temp

def        a						(      _UpperCAmelCase							:					str ,   _UpperCAmelCase							:					str ,   _UpperCAmelCase							:					int						):







		'''simple docstring'''





		__UpperCAmelCase    :     str													=	list(_UpperCAmelCase						)
		__UpperCAmelCase    :     List[str]													=	list(_UpperCAmelCase						)
		__UpperCAmelCase    :     int													=	0
		for i in range(len(_UpperCAmelCase						)						):
				if lista[i] != lista[i]:
						count_n += 1
		return count_n == count

def        a						(      _UpperCAmelCase							:					list[list[int]] ,   _UpperCAmelCase							:					list[str]						):







		'''simple docstring'''





		__UpperCAmelCase    :     List[Any]													=	[]
		__UpperCAmelCase    :     Dict													=	[0] * len(_UpperCAmelCase						)
		for i in range(len(chart[0]						)						):
				__UpperCAmelCase    :     str													=	0
				__UpperCAmelCase    :     Optional[Any]													=	-1
				for j in range(len(_UpperCAmelCase						)						):
						if chart[j][i] == 1:
								count += 1
								__UpperCAmelCase    :     Optional[Any]													=	j
				if count == 1:
						__UpperCAmelCase    :     Optional[Any]													=	1
		for i in range(len(_UpperCAmelCase						)						):
				if select[i] == 1:
						for j in range(len(chart[0]						)						):
								if chart[i][j] == 1:
										for k in range(len(_UpperCAmelCase						)						):
												__UpperCAmelCase    :     int													=	0
						temp.append(prime_implicants[i]						)
		while True:
				__UpperCAmelCase    :     int													=	0
				__UpperCAmelCase    :     Tuple													=	-1
				__UpperCAmelCase    :     Dict													=	0
				for i in range(len(_UpperCAmelCase						)						):
						__UpperCAmelCase    :     Any													=	chart[i].count(1						)
						if count_n > max_n:
								__UpperCAmelCase    :     Optional[Any]													=	count_n
								__UpperCAmelCase    :     Optional[Any]													=	i

				if max_n == 0:
						return temp

				temp.append(prime_implicants[rem]						)

				for i in range(len(chart[0]						)						):
						if chart[rem][i] == 1:
								for j in range(len(_UpperCAmelCase						)						):
										__UpperCAmelCase    :     Tuple													=	0

def        a						(      _UpperCAmelCase							:					list[str] ,   _UpperCAmelCase							:					list[str]						):







		'''simple docstring'''





		__UpperCAmelCase    :     List[Any]													=	[[0 for x in range(len(_UpperCAmelCase						)						)] for x in range(len(_UpperCAmelCase						)						)]
		for i in range(len(_UpperCAmelCase						)						):
				__UpperCAmelCase    :     Union[str, Any]													=	prime_implicants[i].count('''_'''						)
				for j in range(len(_UpperCAmelCase						)						):
						if is_for_table(prime_implicants[i] ,   binary[j] ,   _UpperCAmelCase						):
								__UpperCAmelCase    :     Dict													=	1

		return chart

def        a						(      ):







		'''simple docstring'''





		__UpperCAmelCase    :     Any													=	int(input('''Enter the no. of variables\n'''						)						)
		__UpperCAmelCase    :     Union[str, Any]													=	[
		    float(_UpperCAmelCase						)
		    for x in input(
		        '''Enter the decimal representation of Minterms \'Spaces Separated\'\n'''						).split()
		]
		__UpperCAmelCase    :     Optional[int]													=	decimal_to_binary(_UpperCAmelCase ,   _UpperCAmelCase						)

		__UpperCAmelCase    :     List[str]													=	check(_UpperCAmelCase						)
		print('''Prime Implicants are:'''						)
		print(_UpperCAmelCase						)
		__UpperCAmelCase    :     List[str]													=	prime_implicant_chart(_UpperCAmelCase ,   _UpperCAmelCase						)

		__UpperCAmelCase    :     Optional[int]													=	selection(_UpperCAmelCase ,   _UpperCAmelCase						)
		print('''Essential Prime Implicants are:'''						)
		print(_UpperCAmelCase						)


if __name__ == "__main__":
				import doctest

				doctest.testmod()
				main()










import numpy as np

class 		UpperCAmelCase__			:




			'''simple docstring'''






			def __init__(   self							: List[Any] ):
					'''simple docstring'''





					__UpperCAmelCase    :     Optional[Any]													=	(0, 0)
					__UpperCAmelCase    :     List[str]													=	None
					__UpperCAmelCase    :     int													=	0
					__UpperCAmelCase    :     Union[str, Any]													=	0
					__UpperCAmelCase    :     List[Any]													=	0




			def __eq__(   self							: Optional[int]       ,       a_							: List[Any] ):
					'''simple docstring'''





					return self.position == cell.position




			def  snake_case__     (   self							: List[Any] ):
					'''simple docstring'''





					print(self.position )

class 		UpperCAmelCase__			:




			'''simple docstring'''






			def __init__(   self							: str       ,       a_							: Dict=(5, 5) ):
					'''simple docstring'''





					__UpperCAmelCase    :     str													=	np.zeros(a_ )
					__UpperCAmelCase    :     List[Any]													=	world_size[0]
					__UpperCAmelCase    :     List[str]													=	world_size[1]




			def  snake_case__     (   self							: Tuple ):
					'''simple docstring'''





					print(self.w )




			def  snake_case__     (   self							: Union[str, Any]       ,       a_							: Tuple ):
					'''simple docstring'''





					__UpperCAmelCase    :     Optional[Any]													=	[
					    (-1, -1),
					    (-1, 0),
					    (-1, 1),
					    (0, -1),
					    (0, 1),
					    (1, -1),
					    (1, 0),
					    (1, 1),
					]
					__UpperCAmelCase    :     str													=	cell.position[0]
					__UpperCAmelCase    :     List[Any]													=	cell.position[1]
					__UpperCAmelCase    :     str													=	[]
					for n in neughbour_cord:
							__UpperCAmelCase    :     Optional[Any]													=	current_x + n[0]
							__UpperCAmelCase    :     Any													=	current_y + n[1]
							if 0 <= x < self.world_x_limit and 0 <= y < self.world_y_limit:
									__UpperCAmelCase    :     int													=	Cell()
									__UpperCAmelCase    :     List[str]													=	(x, y)
									__UpperCAmelCase    :     List[Any]													=	cell
									neighbours.append(a_ )
					return neighbours

def        a						(      _UpperCAmelCase							:					List[Any] ,   _UpperCAmelCase							:					Any ,   _UpperCAmelCase							:					int						):







		'''simple docstring'''





		__UpperCAmelCase    :     List[Any]													=	[]
		__UpperCAmelCase    :     Optional[Any]													=	[]
		_open.append(_UpperCAmelCase						)

		while _open:
				__UpperCAmelCase    :     str													=	np.argmin([n.f for n in _open]						)
				__UpperCAmelCase    :     Optional[Any]													=	_open[min_f]
				_closed.append(_open.pop(_UpperCAmelCase						)						)
				if current == goal:
						break
				for n in world.get_neigbours(_UpperCAmelCase						):
						for c in _closed:
								if c == n:
										continue
						__UpperCAmelCase    :     Optional[Any]													=	current.g + 1
						__UpperCAmelCase							,					__UpperCAmelCase    :     Union[str, Any]													=	n.position
						__UpperCAmelCase							,					__UpperCAmelCase    :     Tuple													=	goal.position
						__UpperCAmelCase    :     Union[str, Any]													=	(ya - ya) ** 2 + (xa - xa) ** 2
						__UpperCAmelCase    :     Optional[Any]													=	n.h + n.g

						for c in _open:
								if c == n and c.f < n.f:
										continue
						_open.append(_UpperCAmelCase						)
		__UpperCAmelCase    :     str													=	[]
		while current.parent is not None:
				path.append(current.position						)
				__UpperCAmelCase    :     int													=	current.parent
		path.append(current.position						)
		return path[::-1]


if __name__ == "__main__":
				__A   			=Gridworld()
				# Start position and goal
				__A   			=Cell()
				__A   			=(0, 0)
				__A   			=Cell()
				__A   			=(4, 4)
				print(f'''path from {start.position} to {goal.position}''')
				__A   			=astar(world, start, goal)
				#   Just for visual reasons.
				for i in s:
								__A   			=1
				print(world.w)





