
class 			__A:




				def __init__(     self		,     _snake_case		,     _snake_case				)    ->      Optional[int]:


								'''simple docstring'''




								__a										=    name
								__a										=    val




				def __str__(     self				)    ->      List[Any]:


								'''simple docstring'''




								return F"""{self.__class__.__name__}({self.name}, {self.val})"""




				def __lt__(     self		,     _snake_case				)    ->      Optional[Any]:


								'''simple docstring'''




								return self.val < other.val







class 			__A:




				def __init__(     self		,     _snake_case				)    ->      List[str]:


								'''simple docstring'''




								__a										=    {}
								__a										=    {}
								__a										=    self.build_heap(_snake_case				)




				def __getitem__(     self		,     _snake_case				)    ->      Any:


								'''simple docstring'''




								return self.get_value(_snake_case				)




				def 				SCREAMING_SNAKE_CASE_		(     self		,     _snake_case				)    ->      Tuple:


								'''simple docstring'''




								return (idx - 1) // 2




				def 				SCREAMING_SNAKE_CASE_		(     self		,     _snake_case				)    ->      List[str]:


								'''simple docstring'''




								return idx * 2 + 1




				def 				SCREAMING_SNAKE_CASE_		(     self		,     _snake_case				)    ->      Tuple:


								'''simple docstring'''




								return idx * 2 + 2




				def 				SCREAMING_SNAKE_CASE_		(     self		,     _snake_case				)    ->      str:


								'''simple docstring'''




								return self.heap_dict[key]




				def 				SCREAMING_SNAKE_CASE_		(     self		,     _snake_case				)    ->      Dict:


								'''simple docstring'''




								__a										=    len(_snake_case				) - 1
								__a										=    self.get_parent_idx(_snake_case				)

								for idx, i in enumerate(_snake_case				):
												__a										=    idx
												__a										=    i.val

								for i in range(_snake_case		,     -1		,     -1				):
												self.sift_down(_snake_case		,     _snake_case				)
								return array




				def 				SCREAMING_SNAKE_CASE_		(     self		,     _snake_case		,     _snake_case				)    ->      List[Any]:


								'''simple docstring'''




								while True:
												__a										=    self.get_left_child_idx(_snake_case				)  # noqa: E741
												__a										=    self.get_right_child_idx(_snake_case				)

												__a										=    idx
												if l < len(_snake_case				) and array[l] < array[idx]:
																__a										=    l
												if r < len(_snake_case				) and array[r] < array[smallest]:
																__a										=    r

												if smallest != idx:
																__a							,     __a										=    array[smallest], array[idx]
																(
																    (
																    __a
																)							,     (
																    __a
																)							,     
																)										=    (
																    self.idx_of_element[array[smallest]],
																    self.idx_of_element[array[idx]],
																)
																__a										=    smallest
												else:
																break




				def 				SCREAMING_SNAKE_CASE_		(     self		,     _snake_case				)    ->      Union[str, Any]:


								'''simple docstring'''




								__a										=    self.get_parent_idx(_snake_case				)
								while p >= 0 and self.heap[p] > self.heap[idx]:
												__a							,     __a										=    self.heap[idx], self.heap[p]
												__a							,     __a										=    (
												    self.idx_of_element[self.heap[idx]],
												    self.idx_of_element[self.heap[p]],
												)
												__a										=    p
												__a										=    self.get_parent_idx(_snake_case				)




				def 				SCREAMING_SNAKE_CASE_		(     self				)    ->      Optional[Any]:


								'''simple docstring'''




								return self.heap[0]




				def 				SCREAMING_SNAKE_CASE_		(     self				)    ->      List[Any]:


								'''simple docstring'''




								__a							,     __a										=    self.heap[-1], self.heap[0]
								__a							,     __a										=    (
								    self.idx_of_element[self.heap[-1]],
								    self.idx_of_element[self.heap[0]],
								)

								__a										=    self.heap.pop()
								del self.idx_of_element[x]
								self.sift_down(0		,     self.heap				)
								return x




				def 				SCREAMING_SNAKE_CASE_		(     self		,     _snake_case				)    ->      str:


								'''simple docstring'''




								self.heap.append(_snake_case				)
								__a										=    len(self.heap				) - 1
								__a										=    node.val
								self.sift_up(len(self.heap				) - 1				)




				def 				SCREAMING_SNAKE_CASE_		(     self				)    ->      int:


								'''simple docstring'''




								return len(self.heap				) == 0




				def 				SCREAMING_SNAKE_CASE_		(     self		,     _snake_case		,     _snake_case				)    ->      Optional[Any]:


								'''simple docstring'''




								assert (
								    self.heap[self.idx_of_element[node]].val > new_value
								), "newValue must be less that current value"
								__a										=    new_value
								__a										=    new_value
								self.sift_up(self.idx_of_element[node]				)



A     :	Union[str, Any]    = Node('R', -1)
A     :	Union[str, Any]    = Node('B', 6)
A     :	List[Any]    = Node('A', 3)
A     :	List[Any]    = Node('X', 1)
A     :	Union[str, Any]    = Node('E', 4)

# Use one of these two ways to generate Min-Heap

# Generating Min-Heap from array
A     :	Union[str, Any]    = MinHeap([r, b, a, x, e])

# Generating Min-Heap by Insert method
# myMinHeap.insert(a)
# myMinHeap.insert(b)
# myMinHeap.insert(x)
# myMinHeap.insert(r)
# myMinHeap.insert(e)

# Before
print('Min Heap - before decrease key')
for i in my_min_heap.heap:
					print(i)

print('Min Heap - After decrease key of node [B -> -17]')
my_min_heap.decrease_key(b, -1_7)

# After
for i in my_min_heap.heap:
					print(i)

if __name__ == "__main__":
					import doctest

					doctest.testmod()

def     __lowerCAmelCase			(			a__						,    a__  )       ->  float:

				def get_matched_characters(a__						,    a__  ) -> str:
								__a										=    []
								__a										=    min(len(_stra  )						,    len(_stra  )  ) // 2
								for i, l in enumerate(_stra  ):
												__a										=    int(max(0						,    i - limit  )  )
												__a										=    int(min(i + limit + 1						,    len(_stra  )  )  )
												if l in _stra[left:right]:
																matched.append(a__  )
																__a										=    F"""{_stra[0:_stra.index(a__  )]} {_stra[_stra.index(a__  ) + 1:]}"""

								return "".join(a__  )

				# matching characters
				__a										=    get_matched_characters(a__						,    a__  )
				__a										=    get_matched_characters(a__						,    a__  )
				__a										=    len(a__  )

				# transposition
				__a										=    (
				    len([(ca, ca) for ca, ca in zip(a__						,    a__  ) if ca != ca]  ) // 2
				)

				if not match_count:
								__a										=    0.0
				else:
								__a										=    (
								    1
								    / 3
								    * (
								        match_count / len(a__  )
								        + match_count / len(a__  )
								        + (match_count - transpositions) / match_count
								    )
								)

				# common prefix up to 4 characters
				__a										=    0
				for ca, ca in zip(stra[:4]						,    stra[:4]  ):
								if ca == ca:
												prefix_len += 1
								else:
												break

				return jaro + 0.1 * prefix_len * (1 - jaro)


if __name__ == "__main__":
					import doctest

					doctest.testmod()
					print(jaro_winkler('hello', 'world'))