




'''simple docstring'''

import math


def 						__magic_name__       (      __UpperCAmelCase, __UpperCAmelCase      )						->   float:

					'''simple docstring'''

					if (
					    not isinstance(__UpperCAmelCase, (int, float)      )
					    or power_factor < -1
					    or power_factor > 1
					):
										raise ValueError('''power_factor must be a valid float value between -1 and 1.'''      )
					return apparent_power * power_factor


def 						__magic_name__       (      __UpperCAmelCase, __UpperCAmelCase      )						->   float:

					'''simple docstring'''

					if (
					    not isinstance(__UpperCAmelCase, (int, float)      )
					    or power_factor < -1
					    or power_factor > 1
					):
										raise ValueError('''power_factor must be a valid float value between -1 and 1.'''      )
					return apparent_power * math.sqrt(1 - power_factor**2      )


if __name__ == "__main__":
							import doctest

							doctest.testmod()







'''simple docstring'''

import heapq
import sys

import numpy as np

a    :							Dict										=    tuple[int, int]






class 		a							:


				def __init__(						self       :   Dict   ):
									snake_case_		     =							[]
									snake_case_		     =							set()


				def     A_					(						self       :   int   ):
									if not self.empty():
														return self.elements[0][0]
									else:
														return float('''inf'''   )


				def     A_					(						self       :   List[str]   ):
									return len(self.elements   ) == 0


				def     A_					(						self       :   Union[str, Any]			,							lowercase_       :   str			,							lowercase_       :   List[str]   ):
									if item not in self.set:
														heapq.heappush(self.elements			,							(priority, item)   )
														self.set.add(lowercase_   )
									else:
														# update
														# print("update", item)
														snake_case_		     =							[]
														((snake_case_)     ,(snake_case_))		     =							heapq.heappop(self.elements   )
														while x != item:
																			temp.append((pri, x)   )
																			((snake_case_)     ,(snake_case_))		     =							heapq.heappop(self.elements   )
														temp.append((priority, item)   )
														for pro, xxx in temp:
																			heapq.heappush(self.elements			,							(pro, xxx)   )


				def     A_					(						self       :   Union[str, Any]			,							lowercase_       :   List[Any]   ):
									if item in self.set:
														self.set.remove(lowercase_   )
														snake_case_		     =							[]
														((snake_case_)     ,(snake_case_))		     =							heapq.heappop(self.elements   )
														while x != item:
																			temp.append((pro, x)   )
																			((snake_case_)     ,(snake_case_))		     =							heapq.heappop(self.elements   )
														for prito, yyy in temp:
																			heapq.heappush(self.elements			,							(prito, yyy)   )


				def     A_					(						self       :   Optional[int]   ):
									return self.elements[0][1]


				def     A_					(						self       :   Tuple   ):
									((snake_case_)     ,(snake_case_))		     =							heapq.heappop(self.elements   )
									self.set.remove(lowercase_   )
									return (priority, item)







def 						__magic_name__       (      __UpperCAmelCase, __UpperCAmelCase      )						->   Any:

					'''simple docstring'''

					snake_case_		     =							np.array(__UpperCAmelCase      )
					snake_case_		     =							np.array(__UpperCAmelCase      )
					return np.linalg.norm(a - b      )


def 						__magic_name__       (      __UpperCAmelCase, __UpperCAmelCase      )						->   int:

					'''simple docstring'''

					return consistent_heuristic(__UpperCAmelCase, __UpperCAmelCase      ) // t


def 						__magic_name__       (      __UpperCAmelCase, __UpperCAmelCase      )						->   List[str]:

					'''simple docstring'''

					return abs(p[0] - goal[0]      ) + abs(p[1] - goal[1]      )


def 						__magic_name__       (      __UpperCAmelCase, __UpperCAmelCase, __UpperCAmelCase, __UpperCAmelCase      )						->   Optional[int]:

					'''simple docstring'''

					snake_case_		     =							g_function[start] + Wa * heuristics[i](__UpperCAmelCase, __UpperCAmelCase      )
					return ans


def 						__magic_name__       (      __UpperCAmelCase, __UpperCAmelCase, __UpperCAmelCase      )						->   Optional[Any]:

					'''simple docstring'''

					snake_case_		     =							np.chararray((n, n)      )
					for i in range(__UpperCAmelCase      ):
										for j in range(__UpperCAmelCase      ):
															snake_case_		     =							'''*'''

					for i in range(__UpperCAmelCase      ):
										for j in range(__UpperCAmelCase      ):
															if (j, (n - 1) - i) in blocks:
																				snake_case_		     =							'''#'''

					snake_case_		     =							'''-'''
					snake_case_		     =							back_pointer[goal]
					while x != start:
										((snake_case_)     ,(snake_case_))		     =							x
										# print(x)
										snake_case_		     =							'''-'''
										snake_case_		     =							back_pointer[x]
					snake_case_		     =							'''-'''

					for i in range(__UpperCAmelCase      ):
										for j in range(__UpperCAmelCase      ):
															if (i, j) == (0, n - 1):
																				print(grid[i][j], end=''' '''      )
																				print('''<-- End position''', end=''' '''      )
															else:
																				print(grid[i][j], end=''' '''      )
										print()
					print('''^'''      )
					print('''Start position'''      )
					print()
					print('''# is an obstacle'''      )
					print('''- is the path taken by algorithm'''      )
					print('''PATH TAKEN BY THE ALGORITHM IS:-'''      )
					snake_case_		     =							back_pointer[goal]
					while x != start:
										print(__UpperCAmelCase, end=''' '''      )
										snake_case_		     =							back_pointer[x]
					print(__UpperCAmelCase      )
					sys.exit()


def 						__magic_name__       (      __UpperCAmelCase      )						->   int:

					'''simple docstring'''

					if p[0] < 0 or p[0] > n - 1:
										return False
					if p[1] < 0 or p[1] > n - 1:
										return False
					return True


def 						__magic_name__       (      __UpperCAmelCase, __UpperCAmelCase, __UpperCAmelCase, __UpperCAmelCase, __UpperCAmelCase, __UpperCAmelCase, __UpperCAmelCase, __UpperCAmelCase, )						->   str:

					'''simple docstring'''

					for itera in range(__UpperCAmelCase      ):
										open_list[itera].remove_element(__UpperCAmelCase      )
					# print("s", s)
					# print("j", j)
					((snake_case_)     ,(snake_case_))		     =							s
					snake_case_		     =							(x - 1, y)
					snake_case_		     =							(x + 1, y)
					snake_case_		     =							(x, y + 1)
					snake_case_		     =							(x, y - 1)

					for neighbours in [left, right, up, down]:
										if neighbours not in blocks:
															if valid(__UpperCAmelCase      ) and neighbours not in visited:
																				# print("neighbour", neighbours)
																				visited.add(__UpperCAmelCase      )
																				snake_case_		     =							-1
																				snake_case_		     =							float('''inf'''      )

															if valid(__UpperCAmelCase      ) and g_function[neighbours] > g_function[s] + 1:
																				snake_case_		     =							g_function[s] + 1
																				snake_case_		     =							s
																				if neighbours not in close_list_anchor:
																									open_list[0].put(__UpperCAmelCase, key(__UpperCAmelCase, 0, __UpperCAmelCase, __UpperCAmelCase      )      )
																									if neighbours not in close_list_inad:
																														for var in range(1, __UpperCAmelCase      ):
																																			if key(__UpperCAmelCase, __UpperCAmelCase, __UpperCAmelCase, __UpperCAmelCase      ) <= Wa * key(
																																			    __UpperCAmelCase, 0, __UpperCAmelCase, __UpperCAmelCase      ):
																																								open_list[j].put(
																																								    __UpperCAmelCase, key(__UpperCAmelCase, __UpperCAmelCase, __UpperCAmelCase, __UpperCAmelCase      )      )


def 						__magic_name__       (      )						->   str:

					'''simple docstring'''

					snake_case_		     =							[]
					for x in range(1, 5      ):
										for y in range(1, 6      ):
															some_list.append((x, y)      )

					for x in range(15, 20      ):
										some_list.append((x, 17)      )

					for x in range(10, 19      ):
										for y in range(1, 15      ):
															some_list.append((x, y)      )

    # L block
					for x in range(1, 4      ):
										for y in range(12, 19      ):
															some_list.append((x, y)      )
					for x in range(3, 13      ):
										for y in range(16, 19      ):
															some_list.append((x, y)      )
					return some_list


a    :							Tuple										=    {0: consistent_heuristic, 1: heuristic_a, 2: heuristic_a}

a    :							Dict										=    [
    (0, 1),
    (1, 1),
    (2, 1),
    (3, 1),
    (4, 1),
    (5, 1),
    (6, 1),
    (7, 1),
    (8, 1),
    (9, 1),
    (10, 1),
    (11, 1),
    (12, 1),
    (13, 1),
    (14, 1),
    (15, 1),
    (16, 1),
    (17, 1),
    (18, 1),
    (19, 1),
]
a    :							List[str]										=    make_common_ground()


a    :							Optional[int]										=    blocks_blk
# hyper parameters
a    :							Union[str, Any]										=    1
a    :							str										=    1
a    :							int										=    20
a    :							Optional[int]										=    3  # one consistent and two other inconsistent

# start and end destination
a    :							List[str]										=    (0, 0)
a    :							str										=    (n - 1, n - 1)

a    :							str										=    1


def 						__magic_name__       (      __UpperCAmelCase, __UpperCAmelCase, __UpperCAmelCase      )						->   List[str]:

					'''simple docstring'''

					snake_case_		     =							{start: 0, goal: float('''inf'''      )}
					snake_case_		     =							{start: -1, goal: -1}
					snake_case_		     =							[]
					snake_case_		     =							set()

					for i in range(__UpperCAmelCase      ):
										open_list.append(PriorityQueue()      )
										open_list[i].put(__UpperCAmelCase, key(__UpperCAmelCase, __UpperCAmelCase, __UpperCAmelCase, __UpperCAmelCase      )      )

					snake_case_		     =							[]
					snake_case_		     =							[]
					while open_list[0].minkey() < float('''inf'''      ):
										for i in range(1, __UpperCAmelCase      ):
															# print(open_list[0].minkey(), open_list[i].minkey())
															if open_list[i].minkey() <= Wa * open_list[0].minkey():
																				global t
																				t += 1
																				if g_function[goal] <= open_list[i].minkey():
																									if g_function[goal] < float('''inf'''      ):
																														do_something(__UpperCAmelCase, __UpperCAmelCase, __UpperCAmelCase      )
																				else:
																									snake_case_     ,snake_case_		     =							open_list[i].top_show()
																									visited.add(__UpperCAmelCase      )
																									expand_state(
																									    __UpperCAmelCase, __UpperCAmelCase, __UpperCAmelCase, __UpperCAmelCase, __UpperCAmelCase, __UpperCAmelCase, __UpperCAmelCase, __UpperCAmelCase, )
																									close_list_inad.append(__UpperCAmelCase      )
															else:
																				if g_function[goal] <= open_list[0].minkey():
																									if g_function[goal] < float('''inf'''      ):
																														do_something(__UpperCAmelCase, __UpperCAmelCase, __UpperCAmelCase      )
																				else:
																									snake_case_		     =							open_list[0].top_show()
																									visited.add(__UpperCAmelCase      )
																									expand_state(
																									    __UpperCAmelCase, 0, __UpperCAmelCase, __UpperCAmelCase, __UpperCAmelCase, __UpperCAmelCase, __UpperCAmelCase, __UpperCAmelCase, )
																									close_list_anchor.append(__UpperCAmelCase      )
					print('''No path found to goal'''      )
					print()
					for i in range(n - 1, -1, -1      ):
										for j in range(__UpperCAmelCase      ):
															if (j, i) in blocks:
																				print('''#''', end=''' '''      )
															elif (j, i) in back_pointer:
																				if (j, i) == (n - 1, n - 1):
																									print('''*''', end=''' '''      )
																				else:
																									print('''-''', end=''' '''      )
															else:
																				print('''*''', end=''' '''      )
															if (j, i) == (n - 1, n - 1):
																				print('''<-- End position''', end=''' '''      )
										print()
					print('''^'''      )
					print('''Start position'''      )
					print()
					print('''# is an obstacle'''      )
					print('''- is the path taken by algorithm'''      )


if __name__ == "__main__":
							multi_a_star(start, goal, n_heuristic)

