




'''simple docstring'''





from __future__ import annotations

from sys import maxsize
from typing import Generic, TypeVar

_UpperCAmelCase	:						Tuple			=     TypeVar("T")



def       UpperCAmelCase__  (     lowerCamelCase   ):
  return (position - 1) // 2



def       UpperCAmelCase__  (     lowerCamelCase   ):
  return (2 * position) + 1



def       UpperCAmelCase__  (     lowerCamelCase   ):
  return (2 * position) + 2




class    __lowerCAmelCase       (							Generic[T]):






       def __init__(   self:					Tuple				):
         lowercase    :list[tuple[T, int]]      	=						[]
         lowercase    :dict[T, int]      	=						{}
         lowercase    :int      	=						0






       def __len__(   self:					Union[str, Any]				):
         return self.elements






       def __repr__(   self:					Any				):
         return str(self.heap				)






       def 					SCREAMING_SNAKE_CASE    (   self:					Dict				):
         return self.elements == 0






       def 					SCREAMING_SNAKE_CASE    (   self:					Tuple       ,					_lowerCAmelCase:					str       ,					_lowerCAmelCase:					Optional[int]				):
         self.heap.append((elem, weight)				)
         lowercase    :Optional[Any]      	=						self.elements
         self.elements += 1
         self._bubble_up(lowercase__				)






       def 					SCREAMING_SNAKE_CASE    (   self:					Optional[int]				):






         if self.elements > 1:
           self._swap_nodes(0       ,					self.elements - 1				)
         lowercase    :int      	=						self.heap.pop()
         del self.position_map[elem]
         self.elements -= 1
         if self.elements > 0:
           lowercase    :List[Any]      	=						self.heap[0]
           self._bubble_down(lowercase__				)
         return elem






       def 					SCREAMING_SNAKE_CASE    (   self:					Tuple       ,					_lowerCAmelCase:					List[str]       ,					_lowerCAmelCase:					List[Any]				):
         lowercase    :Union[str, Any]      	=						self.position_map[elem]
         lowercase    :Tuple      	=						(elem, weight)
         if position > 0:
           lowercase    :Tuple      	=						get_parent_position(lowercase__				)
           lowercase    :List[Any]      	=						self.heap[parent_position]
           if parent_weight > weight:
             self._bubble_up(lowercase__				)
           else:
             self._bubble_down(lowercase__				)
         else:
           self._bubble_down(lowercase__				)






       def 					SCREAMING_SNAKE_CASE    (   self:					str       ,					_lowerCAmelCase:					Union[str, Any]				):
         lowercase    :int      	=						self.position_map[elem]
         if curr_pos == 0:
           return None
         lowercase    :Optional[int]      	=						get_parent_position(lowercase__				)
         lowercase    :List[Any]      	=						self.heap[curr_pos]
         lowercase    :int      	=						self.heap[parent_position]
         if parent_weight > weight:
           self._swap_nodes(lowercase__       ,					lowercase__				)
           return self._bubble_up(lowercase__				)
         return None






       def 					SCREAMING_SNAKE_CASE    (   self:					Dict       ,					_lowerCAmelCase:					Optional[Any]				):
         lowercase    :int      	=						self.position_map[elem]
         lowercase    :Optional[Any]      	=						self.heap[curr_pos]
         lowercase    :int      	=						get_child_left_position(lowercase__				)
         lowercase    :Union[str, Any]      	=						get_child_right_position(lowercase__				)
         if child_left_position < self.elements and child_right_position < self.elements:
           lowercase    :str      	=						self.heap[child_left_position]
           lowercase    :Optional[Any]      	=						self.heap[child_right_position]
           if child_right_weight < child_left_weight and child_right_weight < weight:
             self._swap_nodes(lowercase__       ,					lowercase__				)
             return self._bubble_down(lowercase__				)
         if child_left_position < self.elements:
           lowercase    :Optional[int]      	=						self.heap[child_left_position]
           if child_left_weight < weight:
             self._swap_nodes(lowercase__       ,					lowercase__				)
             return self._bubble_down(lowercase__				)
         else:
           return None
         if child_right_position < self.elements:
           lowercase    :List[Any]      	=						self.heap[child_right_position]
           if child_right_weight < weight:
             self._swap_nodes(lowercase__       ,					lowercase__				)
             return self._bubble_down(lowercase__				)
         return None






       def 					SCREAMING_SNAKE_CASE    (   self:					Dict       ,					_lowerCAmelCase:					Optional[Any]       ,					_lowerCAmelCase:					Any				):
         lowercase    :List[str]      	=						self.heap[nodea_pos][0]
         lowercase    :List[Any]      	=						self.heap[nodea_pos][0]
         lowercase    :Optional[Any]      	=						(
             self.heap[nodea_pos],
             self.heap[nodea_pos],
         )
         lowercase    :Dict      	=						nodea_pos
         lowercase    :List[str]      	=						nodea_pos







class    __lowerCAmelCase       (							Generic[T]):






       def __init__(   self:					Any				):
         lowercase    :dict[T, dict[T, int]]      	=						{}
         lowercase    :int      	=						0






       def __repr__(   self:					List[str]				):
         return str(self.connections				)






       def __len__(   self:					Tuple				):
         return self.nodes






       def 					SCREAMING_SNAKE_CASE    (   self:					int       ,					_lowerCAmelCase:					Union[str, Any]				):






         if node not in self.connections:
           lowercase    :List[str]      	=						{}
           self.nodes += 1






       def 					SCREAMING_SNAKE_CASE    (   self:					Optional[Any]       ,					_lowerCAmelCase:					Optional[int]       ,					_lowerCAmelCase:					Union[str, Any]       ,					_lowerCAmelCase:					Optional[int]				):
         self.add_node(lowercase__				)
         self.add_node(lowercase__				)
         lowercase    :int      	=						weight
         lowercase    :Any      	=						weight







def       UpperCAmelCase__  (     lowerCamelCase,			):
  lowercase    :dict[T, int]      	=						{node: maxsize for node in graph.connections}
  lowercase    :dict[T, T | None]      	=						{node: None for node in graph.connections}

  lowercase    :MinPriorityQueue[T]      	=						MinPriorityQueue()
  for node, weight in dist.items():
    priority_queue.push(SCREAMING_SNAKE_CASE_,			SCREAMING_SNAKE_CASE_   )

  if priority_queue.is_empty():
    return dist, parent

  # initialization
  lowercase    :Union[str, Any]      	=						priority_queue.extract_min()
  lowercase    :int      	=						0
  for neighbour in graph.connections[node]:
    if dist[neighbour] > dist[node] + graph.connections[node][neighbour]:
      lowercase    :Tuple      	=						dist[node] + graph.connections[node][neighbour]
      priority_queue.update_key(SCREAMING_SNAKE_CASE_,			dist[neighbour]   )
      lowercase    :Dict      	=						node

    # running prim's algorithm
  while not priority_queue.is_empty():
    lowercase    :List[str]      	=						priority_queue.extract_min()
    for neighbour in graph.connections[node]:
      if dist[neighbour] > dist[node] + graph.connections[node][neighbour]:
        lowercase    :Dict      	=						dist[node] + graph.connections[node][neighbour]
        priority_queue.update_key(SCREAMING_SNAKE_CASE_,			dist[neighbour]   )
        lowercase    :List[Any]      	=						node
  return dist, parent









_UpperCAmelCase	:						Union[str, Any]			=     "0.21.0"

from .accelerator import Accelerator
from .big_modeling import (
    cpu_offload,
    cpu_offload_with_hook,
    disk_offload,
    dispatch_model,
    init_empty_weights,
    init_on_device,
    load_checkpoint_and_dispatch,
)
from .data_loader import skip_first_batches
from .launchers import debug_launcher, notebook_launcher
from .state import PartialState
from .utils import (
    DeepSpeedPlugin,
    DistributedDataParallelKwargs,
    DistributedType,
    FullyShardedDataParallelPlugin,
    GradScalerKwargs,
    InitProcessGroupKwargs,
    find_executable_batch_size,
    infer_auto_device_map,
    is_rich_available,
    load_checkpoint_in_model,
    synchronize_rng_states,
)


if is_rich_available():
     from .utils import rich



