
'''simple docstring'''



from __future__ import annotations

# This is the precision for this function which can be altered.
# It is recommended for users to keep this number greater than or equal to 10.
_lowercase    =		10


def A				(__lowerCamelCase				:int			,     __lowerCamelCase				:int			,     __lowerCamelCase				:list[int]			,     __lowerCamelCase				:int		):

						for i in range(__a			,     __a		):
												if array[i] == target:
																		return i
						return -1


def A				(__lowerCamelCase				:list[int]			,     __lowerCamelCase				:int		):
						_lowerCAmelCase  						=			0
						_lowerCAmelCase  						=			len(__a		)
						while left <= right:
												if right - left < precision:
																		return lin_search(__a			,     __a			,     __a			,     __a		)

												_lowerCAmelCase  						=			(left + right) // 3 + 1
												_lowerCAmelCase  						=			2 * (left + right) // 3 + 1

												if array[one_third] == target:
																		return one_third
												elif array[two_third] == target:
																		return two_third

												elif target < array[one_third]:
																		_lowerCAmelCase  						=			one_third - 1
												elif array[two_third] < target:
																		_lowerCAmelCase  						=			two_third + 1

												else:
																		_lowerCAmelCase  						=			one_third + 1
																		_lowerCAmelCase  						=			two_third - 1
						else:
												return -1


def A				(__lowerCamelCase				:int			,     __lowerCamelCase				:int			,     __lowerCamelCase				:list[int]			,     __lowerCamelCase				:int		):

						if left < right:
												if right - left < precision:
																		return lin_search(__a			,     __a			,     __a			,     __a		)
												_lowerCAmelCase  						=			(left + right) // 3 + 1
												_lowerCAmelCase  						=			2 * (left + right) // 3 + 1

												if array[one_third] == target:
																		return one_third
												elif array[two_third] == target:
																		return two_third

												elif target < array[one_third]:
																		return rec_ternary_search(__a			,     one_third - 1			,     __a			,     __a		)
												elif array[two_third] < target:
																		return rec_ternary_search(two_third + 1			,     __a			,     __a			,     __a		)
												else:
																		return rec_ternary_search(one_third + 1			,     two_third - 1			,     __a			,     __a		)
						else:
												return -1


if __name__ == "__main__":
						import doctest

						doctest.testmod()

						_lowercase    =		input("""Enter numbers separated by comma:\n""").strip()
						_lowercase    =		[int(item.strip()) for item in user_input.split(""",""")]
						assert collection == sorted(collection), F"List must be ordered.\n{collection}."
						_lowercase    =		int(input("""Enter the number to be found in the list:\n""").strip())
						_lowercase    =		ite_ternary_search(collection, target)
						_lowercase    =		rec_ternary_search(0, len(collection) - 1, collection, target)
						if resulta != -1:
												print(F"""Iterative search: {target} found at positions: {resulta}""")
												print(F"""Recursive search: {target} found at positions: {resulta}""")
						else:
												print("""Not found""")


'''simple docstring'''



import heapq as hq
import math
from collections.abc import Iterator




class   UpperCAmelCase_					:






						'''simple docstring'''






						def __init__( self   ,       _lowercase				):

												"""simple docstring"""



												_lowerCAmelCase  						=			str(id_				)
												_lowerCAmelCase  						=			None
												_lowerCAmelCase  						=			None
												_lowerCAmelCase  						=			[]
												_lowerCAmelCase  						=			{}  # {vertex:distance}




						def __lt__( self   ,       _lowercase				):

												"""simple docstring"""



												return self.key < other.key




						def __repr__( self				):

												"""simple docstring"""



												return self.id




						def  _lowercase     ( self   ,       _lowercase				):

												"""simple docstring"""



												self.neighbors.append(_lowercase				)




						def  _lowercase     ( self   ,       _lowercase   ,       _lowercase				):

												"""simple docstring"""



												_lowerCAmelCase  						=			weight






def A				(__lowerCamelCase				:List[Any]			,     __lowerCamelCase				:Union[str, Any]			,     __lowerCamelCase				:Dict			,     __lowerCamelCase				:Optional[int]		):
						# add the neighbors:
						graph[a - 1].add_neighbor(graph[b - 1]		)
						graph[b - 1].add_neighbor(graph[a - 1]		)
						# add the edges:
						graph[a - 1].add_edge(graph[b - 1]			,     __lowerCamelCase		)
						graph[b - 1].add_edge(graph[a - 1]			,     __lowerCamelCase		)


def A				(__lowerCamelCase				:list			,     __lowerCamelCase				:Vertex		):
						_lowerCAmelCase  						=			[]
						for u in graph:
												_lowerCAmelCase  						=			math.inf
												_lowerCAmelCase  						=			None
						_lowerCAmelCase  						=			0
						_lowerCAmelCase  						=			graph[:]
						while q:
												_lowerCAmelCase  						=			min(__lowerCamelCase		)
												q.remove(__lowerCamelCase		)
												for v in u.neighbors:
																		if (v in q) and (u.edges[v.id] < v.key):
																								_lowerCAmelCase  						=			u
																								_lowerCAmelCase  						=			u.edges[v.id]
						for i in range(1			,     len(__lowerCamelCase		)		):
												a.append((int(graph[i].id		) + 1, int(graph[i].pi.id		) + 1)		)
						return a


def A				(__lowerCamelCase				:list			,     __lowerCamelCase				:Vertex		):
						for u in graph:
												_lowerCAmelCase  						=			math.inf
												_lowerCAmelCase  						=			None
						_lowerCAmelCase  						=			0

						_lowerCAmelCase  						=			list(__lowerCamelCase		)
						hq.heapify(__lowerCamelCase		)

						while h:
												_lowerCAmelCase  						=			hq.heappop(__lowerCamelCase		)
												for v in u.neighbors:
																		if (v in h) and (u.edges[v.id] < v.key):
																								_lowerCAmelCase  						=			u
																								_lowerCAmelCase  						=			u.edges[v.id]
																								hq.heapify(__lowerCamelCase		)

						for i in range(1			,     len(__lowerCamelCase		)		):
												yield (int(graph[i].id		) + 1, int(graph[i].pi.id		) + 1)


def A				():
						pass


if __name__ == "__main__":
						import doctest

						doctest.testmod()
