



'''simple docstring'''
class 				lowercase__      :





	def __init__(					self   :							int					,lowerCamelCase__   :							Union[str, Any]					,lowerCamelCase__   :							List[Any]					):







							'''simple docstring'''
							_UpperCamelCase   :						List[Any]												=  name
							_UpperCamelCase   :						str												=  val





	def __str__(					self   :							Union[str, Any]					):







							'''simple docstring'''
							return F'{self.__class__.__name__}({self.name}, {self.val})'





	def __lt__(					self   :							Dict					,lowerCamelCase__   :							Union[str, Any]					):







							'''simple docstring'''
							return self.val < other.val






class 				lowercase__      :





	def __init__(					self   :							Optional[Any]					,lowerCamelCase__   :							Tuple					):







							'''simple docstring'''
							_UpperCamelCase   :						List[Any]												=  {}
							_UpperCamelCase   :						Optional[Any]												=  {}
							_UpperCamelCase   :						str												=  self.build_heap(lowerCamelCase__					)





	def __getitem__(					self   :							List[str]					,lowerCamelCase__   :							List[str]					):







							'''simple docstring'''
							return self.get_value(lowerCamelCase__					)





	def       UpperCamelCase_    (					self   :							List[Any]					,lowerCamelCase__   :							Optional[Any]					):







							'''simple docstring'''
							return (idx - 1) // 2





	def       UpperCamelCase_    (					self   :							str					,lowerCamelCase__   :							List[str]					):







							'''simple docstring'''
							return idx * 2 + 1





	def       UpperCamelCase_    (					self   :							Optional[Any]					,lowerCamelCase__   :							List[str]					):







							'''simple docstring'''
							return idx * 2 + 2





	def       UpperCamelCase_    (					self   :							Dict					,lowerCamelCase__   :							Union[str, Any]					):







							'''simple docstring'''
							return self.heap_dict[key]





	def       UpperCamelCase_    (					self   :							int					,lowerCamelCase__   :							Any					):







							'''simple docstring'''
							_UpperCamelCase   :						Union[str, Any]												=  len(lowerCamelCase__					) - 1
							_UpperCamelCase   :						Tuple												=  self.get_parent_idx(lowerCamelCase__					)

							for idx, i in enumerate(lowerCamelCase__					):
													_UpperCamelCase   :						Optional[int]												=  idx
													_UpperCamelCase   :						Any												=  i.val

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





	def       UpperCamelCase_    (					self   :							Tuple					,lowerCamelCase__   :							List[Any]					,lowerCamelCase__   :							Optional[int]					):







							'''simple docstring'''
							while True:
													_UpperCamelCase   :						Union[str, Any]												=  self.get_left_child_idx(lowerCamelCase__					)  # noqa: E741
													_UpperCamelCase   :						Union[str, Any]												=  self.get_right_child_idx(lowerCamelCase__					)

													_UpperCamelCase   :						Optional[int]												=  idx
													if l < len(lowerCamelCase__					) and array[l] < array[idx]:
																			_UpperCamelCase   :						Optional[Any]												=  l
													if r < len(lowerCamelCase__					) and array[r] < array[smallest]:
																			_UpperCamelCase   :						str												=  r

													if smallest != idx:
																			_UpperCamelCase							,     _UpperCamelCase   :						List[Any]												=  array[smallest], array[idx]
																			(
																			    (
																			    _UpperCamelCase
																			)							,     (
																			    _UpperCamelCase
																			)							,     
																			)   :						Union[str, Any]												=  (
																			    self.idx_of_element[array[smallest]],
																			    self.idx_of_element[array[idx]],
																			)
																			_UpperCamelCase   :						str												=  smallest
													else:
																			break





	def       UpperCamelCase_    (					self   :							List[str]					,lowerCamelCase__   :							Tuple					):







							'''simple docstring'''
							_UpperCamelCase   :						List[str]												=  self.get_parent_idx(lowerCamelCase__					)
							while p >= 0 and self.heap[p] > self.heap[idx]:
													_UpperCamelCase							,     _UpperCamelCase   :						List[Any]												=  self.heap[idx], self.heap[p]
													_UpperCamelCase							,     _UpperCamelCase   :						Dict												=  (
													    self.idx_of_element[self.heap[idx]],
													    self.idx_of_element[self.heap[p]],
													)
													_UpperCamelCase   :						Dict												=  p
													_UpperCamelCase   :						Union[str, Any]												=  self.get_parent_idx(lowerCamelCase__					)





	def       UpperCamelCase_    (					self   :							Optional[Any]					):







							'''simple docstring'''
							return self.heap[0]





	def       UpperCamelCase_    (					self   :							Optional[Any]					):







							'''simple docstring'''
							_UpperCamelCase							,     _UpperCamelCase   :						List[str]												=  self.heap[-1], self.heap[0]
							_UpperCamelCase							,     _UpperCamelCase   :						Optional[int]												=  (
							    self.idx_of_element[self.heap[-1]],
							    self.idx_of_element[self.heap[0]],
							)

							_UpperCamelCase   :						Optional[Any]												=  self.heap.pop()
							del self.idx_of_element[x]
							self.sift_down(0					,self.heap					)
							return x





	def       UpperCamelCase_    (					self   :							Union[str, Any]					,lowerCamelCase__   :							Union[str, Any]					):







							'''simple docstring'''
							self.heap.append(lowerCamelCase__					)
							_UpperCamelCase   :						Tuple												=  len(self.heap					) - 1
							_UpperCamelCase   :						str												=  node.val
							self.sift_up(len(self.heap					) - 1					)





	def       UpperCamelCase_    (					self   :							List[Any]					):







							'''simple docstring'''
							return len(self.heap					) == 0





	def       UpperCamelCase_    (					self   :							Optional[int]					,lowerCamelCase__   :							Optional[Any]					,lowerCamelCase__   :							int					):







							'''simple docstring'''
							assert (
							    self.heap[self.idx_of_element[node]].val > new_value
							), "newValue must be less that current value"
							_UpperCamelCase   :						List[str]												=  new_value
							_UpperCamelCase   :						Optional[Any]												=  new_value
							self.sift_up(self.idx_of_element[node]					)
snake_case_					:      List[Any]    			=    Node('R', -1)
snake_case_					:      Optional[int]    			=    Node('B', 6)
snake_case_					:      int    			=    Node('A', 3)
snake_case_					:      List[Any]    			=    Node('X', 1)
snake_case_					:      Optional[Any]    			=    Node('E', 4)

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

# Generating Min-Heap from array
snake_case_					:      Optional[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, -17)

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

if __name__ == "__main__":
					import doctest

					doctest.testmod()







'''simple docstring'''
from typing import List

import numpy as np






def A__       (	UpperCAmelCase_				):
						_UpperCamelCase   :						Any												=  {key: len(UpperCAmelCase_				) for key, value in gen_kwargs.items() if isinstance(UpperCAmelCase_    ,    UpperCAmelCase_				)}
						if len(set(lists_lengths.values()				)				) > 1:
												raise RuntimeError(
												    (
												        'Sharding is ambiguous for this dataset: '
												        + 'we found several data sources lists of different lengths, and we don\'t know over which list we should parallelize:\n'
												        + '\n'.join(f'\t- key {key} has length {length}' for key, length in lists_lengths.items()				)
												        + '\nTo fix this, check the \'gen_kwargs\' and make sure to use lists only for data sources, '
												        + 'and use tuples otherwise. In the end there should only be one single list, or several lists with the same length.'
												    )				)
						_UpperCamelCase   :						Tuple												=  max(lists_lengths.values()    ,    default=0				)
						return max(1    ,    UpperCAmelCase_				)






def A__       (	UpperCAmelCase_    ,    UpperCAmelCase_				):
						_UpperCamelCase   :						Dict												=  []
						for group_idx in range(UpperCAmelCase_				):
												_UpperCamelCase   :						int												=  num_shards // max_num_jobs + (group_idx < (num_shards % max_num_jobs))
												if num_shards_to_add == 0:
																		break
												_UpperCamelCase   :						Tuple												=  shards_indices_per_group[-1].stop if shards_indices_per_group else 0
												_UpperCamelCase   :						Tuple												=  range(UpperCAmelCase_    ,    start + num_shards_to_add				)
												shards_indices_per_group.append(UpperCAmelCase_				)
						return shards_indices_per_group






def A__       (	UpperCAmelCase_    ,    UpperCAmelCase_				):
						_UpperCamelCase   :						Tuple												=  _number_of_shards_in_gen_kwargs(UpperCAmelCase_				)
						if num_shards == 1:
												return [dict(UpperCAmelCase_				)]
						else:
												_UpperCamelCase   :						str												=  _distribute_shards(num_shards=UpperCAmelCase_    ,    max_num_jobs=UpperCAmelCase_				)
												return [
												    {
												        key: [value[shard_idx] for shard_idx in shard_indices_per_group[group_idx]]
												        if isinstance(UpperCAmelCase_    ,    UpperCAmelCase_				)
												        else value
												        for key, value in gen_kwargs.items()
												    }
												    for group_idx in range(len(UpperCAmelCase_				)				)
												]






def A__       (	UpperCAmelCase_				):
						return {
						    key: [value for gen_kwargs in gen_kwargs_list for value in gen_kwargs[key]]
						    if isinstance(gen_kwargs_list[0][key]    ,    UpperCAmelCase_				)
						    else gen_kwargs_list[0][key]
						    for key in gen_kwargs_list[0]
						}






def A__       (	UpperCAmelCase_    ,    UpperCAmelCase_				):
						_UpperCamelCase   :						int												=  {len(UpperCAmelCase_				) for value in gen_kwargs.values() if isinstance(UpperCAmelCase_    ,    UpperCAmelCase_				)}
						_UpperCamelCase   :						Union[str, Any]												=  {}
						for size in list_sizes:
												_UpperCamelCase   :						str												=  list(range(UpperCAmelCase_				)				)
												rng.shuffle(indices_per_size[size]				)
						# Now let's copy the gen_kwargs and shuffle the lists based on their sizes
						_UpperCamelCase   :						Union[str, Any]												=  dict(UpperCAmelCase_				)
						for key, value in shuffled_kwargs.items():
												if isinstance(UpperCAmelCase_    ,    UpperCAmelCase_				):
																		_UpperCamelCase   :						Dict												=  [value[i] for i in indices_per_size[len(UpperCAmelCase_				)]]
						return shuffled_kwargs


