





def   lowerCamelCase__       (       UpperCamelCase__     :    Optional[int]    ,      UpperCamelCase__     :    str  )     ->	int:



					'''simple docstring'''




					_snake_case													=			0
					_snake_case													=			len(UpperCamelCase__  ) - 1

					while left <= right:
										# avoid divided by 0 during interpolation
										if sorted_collection[left] == sorted_collection[right]:
															if sorted_collection[left] == item:
																				return left
															else:
																				return None

										_snake_case													=			left + ((item - sorted_collection[left]) * (right - left)) // (
										    sorted_collection[right] - sorted_collection[left]
										)

										# out of range check
										if point < 0 or point >= len(UpperCamelCase__  ):
															return None

										_snake_case													=			sorted_collection[point]
										if current_item == item:
															return point
										else:
															if point < left:
																				_snake_case													=			left
																				_snake_case													=			point
															elif point > right:
																				_snake_case													=			right
																				_snake_case													=			point
															else:
																				if item < current_item:
																									_snake_case													=			point - 1
																				else:
																									_snake_case													=			point + 1
					return None





def   lowerCamelCase__       (       UpperCamelCase__     :    Any    ,      UpperCamelCase__     :    Optional[int]    ,      UpperCamelCase__     :    Optional[int]    ,      UpperCamelCase__     :    int  )     ->	Dict:



					'''simple docstring'''




					if sorted_collection[left] == sorted_collection[right]:
										if sorted_collection[left] == item:
															return left
										else:
															return None

					_snake_case													=			left + ((item - sorted_collection[left]) * (right - left)) // (
					    sorted_collection[right] - sorted_collection[left]
					)

					# out of range check
					if point < 0 or point >= len(UpperCamelCase__  ):
										return None

					if sorted_collection[point] == item:
										return point
					elif point < left:
										return interpolation_search_by_recursion(UpperCamelCase__    ,      UpperCamelCase__    ,      UpperCamelCase__    ,      UpperCamelCase__  )
					elif point > right:
										return interpolation_search_by_recursion(UpperCamelCase__    ,      UpperCamelCase__    ,      UpperCamelCase__    ,      UpperCamelCase__  )
					else:
										if sorted_collection[point] > item:
															return interpolation_search_by_recursion(
															    UpperCamelCase__    ,      UpperCamelCase__    ,      UpperCamelCase__    ,      point - 1  )
										else:
															return interpolation_search_by_recursion(
															    UpperCamelCase__    ,      UpperCamelCase__    ,      point + 1    ,      UpperCamelCase__  )





def   lowerCamelCase__       (       UpperCamelCase__     :    Optional[int]  )     ->	Optional[int]:



					'''simple docstring'''




					if collection != sorted(UpperCamelCase__  ):
										raise ValueError('Collection must be ascending sorted'  )
					return True


if __name__ == "__main__":
					import sys
					UpperCAmelCase_									=       0
					if debug == 1:
										UpperCAmelCase_									=       [10, 30, 40, 45, 50, 66, 77, 93]
										try:
															__assert_sorted(collection)
										except ValueError:
															sys.exit("""Sequence must be ascending sorted to apply interpolation search""")
										UpperCAmelCase_									=       67

					UpperCAmelCase_									=       interpolation_search(collection, target)
					if result is not None:
										print(F"{target} found at positions: {result}")
					else:
										print("""Not found""")










from collections import defaultdict

from graphs.minimum_spanning_tree_prims import prisms_algorithm as mst





def   lowerCamelCase__       (       )     ->	List[str]:



					'''simple docstring'''




					_snake_case							,       _snake_case													=			9, 14  # noqa: F841
					_snake_case													=			[
					    [0, 1, 4],
					    [0, 7, 8],
					    [1, 2, 8],
					    [7, 8, 7],
					    [7, 6, 1],
					    [2, 8, 2],
					    [8, 6, 6],
					    [2, 3, 7],
					    [2, 5, 4],
					    [6, 5, 2],
					    [3, 5, 14],
					    [3, 4, 9],
					    [5, 4, 10],
					    [1, 7, 11],
					]

					_snake_case													=			defaultdict(UpperCamelCase__  )
					for nodea, nodea, cost in edges:
										adjancency[nodea].append([nodea, cost]  )
										adjancency[nodea].append([nodea, cost]  )

					_snake_case													=			mst(UpperCamelCase__  )

					_snake_case													=			[
					    [7, 6, 1],
					    [2, 8, 2],
					    [6, 5, 2],
					    [0, 1, 4],
					    [2, 5, 4],
					    [2, 3, 7],
					    [0, 7, 8],
					    [3, 4, 9],
					]

					for answer in expected:
										_snake_case													=			tuple(answer[:2]  )
										_snake_case													=			tuple(edge[::-1]  )
										assert edge in result or reverse in result



