

"""simple docstring"""






import logging
import math
from functools import partial
from typing import Any, Callable, Dict, Iterable, List, Optional, Sequence, Tuple, Union

import torch

from .tensor_utils import tensor_tree_map, tree_map





def 	lowercase      (   __UpperCamelCase						) ->      List[Tuple[int, ...]]:
 __magic_name__     =      []
 if isinstance(__UpperCamelCase      ,   __UpperCamelCase						):
  for v in tree.values():
   shapes.extend(_fetch_dims(__UpperCamelCase						)						)
 elif isinstance(__UpperCamelCase      ,   (list, tuple)						):
  for t in tree:
   shapes.extend(_fetch_dims(__UpperCamelCase						)						)
 elif isinstance(__UpperCamelCase      ,   torch.Tensor						):
  shapes.append(tree.shape						)
 else:
  raise ValueError('''Not supported'''						)

 return shapes





@torch.jit.ignore
def 	lowercase      (   __UpperCamelCase      ,   __UpperCamelCase						) ->      Tuple[int, ...]:
 __magic_name__     =      []
 for d in reversed(__UpperCamelCase						):
  idx.append(flat_idx % d						)
  __magic_name__     =      flat_idx // d

 return tuple(reversed(__UpperCamelCase						)						)





@torch.jit.ignore
def 	lowercase      (   __UpperCamelCase      ,   __UpperCamelCase      ,   __UpperCamelCase      ,   __UpperCamelCase = None      ,   __UpperCamelCase = None      ,   ) ->      List[Tuple[slice, ...]]:

 # start_edges and end_edges both indicate whether, starting from any given
 # dimension, the start/end index is at the top/bottom edge of the
 # corresponding tensor, modeled as a tree
 def reduce_edge_list(__UpperCamelCase						) -> None:
  __magic_name__     =      True
  for i in range(len(__UpperCamelCase						)						):
   __magic_name__     =      -1 * (i + 1)
   l[reversed_idx] &= tally
   __magic_name__     =      l[reversed_idx]

 if start_edges is None:
  __magic_name__     =      [s == 0 for s in start]
  reduce_edge_list(__UpperCamelCase						)
 if end_edges is None:
  __magic_name__     =      [e == (d - 1) for e, d in zip(__UpperCamelCase      ,   __UpperCamelCase						)]
  reduce_edge_list(__UpperCamelCase						)

 # Base cases. Either start/end are empty and we're done, or the final,
 # one-dimensional tensor can be simply sliced
 if len(__UpperCamelCase						) == 0:
  return [()]
 elif len(__UpperCamelCase						) == 1:
  return [(slice(start[0]      ,   end[0] + 1						),)]

 __magic_name__     =      []
 __magic_name__     =      []

 # Dimensions common to start and end can be selected directly
 for s, e in zip(__UpperCamelCase      ,   __UpperCamelCase						):
  if s == e:
   path_list.append(slice(__UpperCamelCase      ,   s + 1						)						)
  else:
   break

 __magic_name__     =      tuple(__UpperCamelCase						)
 __magic_name__     =      len(__UpperCamelCase						)

 # start == end, and we're done
 if divergence_idx == len(__UpperCamelCase						):
  return [path]

 def upper() -> Tuple[Tuple[slice, ...], ...]:
  assert start_edges is not None
  assert end_edges is not None

  __magic_name__     =      start[divergence_idx]
  return tuple(
      path + (slice(__UpperCamelCase      ,   sdi + 1						),) + s
      for s in _get_minimal_slice_set(
          start[divergence_idx + 1 :]      ,   [d - 1 for d in dims[divergence_idx + 1 :]]      ,   dims[divergence_idx + 1 :]      ,   start_edges=start_edges[divergence_idx + 1 :]      ,   end_edges=[True for _ in end_edges[divergence_idx + 1 :]]      ,   )						)

 def lower() -> Tuple[Tuple[slice, ...], ...]:
  assert start_edges is not None
  assert end_edges is not None

  __magic_name__     =      end[divergence_idx]
  return tuple(
      path + (slice(__UpperCamelCase      ,   edi + 1						),) + s
      for s in _get_minimal_slice_set(
          [0 for _ in start[divergence_idx + 1 :]]      ,   end[divergence_idx + 1 :]      ,   dims[divergence_idx + 1 :]      ,   start_edges=[True for _ in start_edges[divergence_idx + 1 :]]      ,   end_edges=end_edges[divergence_idx + 1 :]      ,   )						)

 # If both start and end are at the edges of the subtree rooted at
 # divergence_idx, we can just select the whole subtree at once
 if start_edges[divergence_idx] and end_edges[divergence_idx]:
  slices.append(path + (slice(start[divergence_idx]      ,   end[divergence_idx] + 1						),)						)
 # If just start is at the edge, we can grab almost all of the subtree,
 # treating only the ragged bottom edge as an edge case
 elif start_edges[divergence_idx]:
  slices.append(path + (slice(start[divergence_idx]      ,   end[divergence_idx]						),)						)
  slices.extend(lower()						)
 # Analogous to the previous case, but the top is ragged this time
 elif end_edges[divergence_idx]:
  slices.extend(upper()						)
  slices.append(path + (slice(start[divergence_idx] + 1      ,   end[divergence_idx] + 1						),)						)
 # If both sides of the range are ragged, we need to handle both sides
 # separately. If there's contiguous meat in between them, we can index it
 # in one big chunk
 else:
  slices.extend(upper()						)
  __magic_name__     =      end[divergence_idx] - start[divergence_idx]
  if middle_ground > 1:
   slices.append(path + (slice(start[divergence_idx] + 1      ,   end[divergence_idx]						),)						)
  slices.extend(lower()						)

 return slices





@torch.jit.ignore
def 	lowercase      (   __UpperCamelCase      ,   __UpperCamelCase      ,   __UpperCamelCase      ,   __UpperCamelCase						) ->      torch.Tensor:
 __magic_name__     =      t.shape[:no_batch_dims]
 __magic_name__     =      list(_flat_idx_to_idx(__UpperCamelCase      ,   __UpperCamelCase						)						)
 # _get_minimal_slice_set is inclusive
 __magic_name__     =      list(_flat_idx_to_idx(flat_end - 1      ,   __UpperCamelCase						)						)

 # Get an ordered list of slices to perform
 __magic_name__     =      _get_minimal_slice_set(
     __UpperCamelCase      ,   __UpperCamelCase      ,   __UpperCamelCase      ,   )

 __magic_name__     =      [t[s] for s in slices]

 return torch.cat([s.view((-1,) + t.shape[no_batch_dims:]						) for s in sliced_tensors]						)





def 	lowercase      (   __UpperCamelCase      ,   __UpperCamelCase      ,   __UpperCamelCase      ,   __UpperCamelCase      ,   __UpperCamelCase = False      ,   __UpperCamelCase = None      ,   __UpperCamelCase = False      ,   ) ->      Any:
 if not (len(__UpperCamelCase						) > 0):
  raise ValueError('''Must provide at least one input'''						)

 __magic_name__     =      [shape[:no_batch_dims] for shape in _fetch_dims(__UpperCamelCase						)]
 __magic_name__     =      tuple([max(__UpperCamelCase						) for s in zip(*__UpperCamelCase						)]						)

 def _prep_inputs(__UpperCamelCase						) -> torch.Tensor:
  if not low_mem:
   if not sum(t.shape[:no_batch_dims]						) == no_batch_dims:
    __magic_name__     =      t.expand(orig_batch_dims + t.shape[no_batch_dims:]						)
   __magic_name__     =      t.reshape(-1      ,   *t.shape[no_batch_dims:]						)
  else:
   __magic_name__     =      t.expand(orig_batch_dims + t.shape[no_batch_dims:]						)
  return t

 __magic_name__     =      tensor_tree_map(_prep_inputs      ,   __UpperCamelCase						)
 __magic_name__     =      None
 if _out is not None:
  __magic_name__     =      tensor_tree_map(lambda __UpperCamelCase						: t.view([-1] + list(t.shape[no_batch_dims:]						)						)      ,   _out						)

 __magic_name__     =      1
 for d in orig_batch_dims:
  flat_batch_dim *= d

 __magic_name__     =      flat_batch_dim // chunk_size + (flat_batch_dim % chunk_size != 0)

 def _select_chunk(__UpperCamelCase						) -> torch.Tensor:
  return t[i : i + chunk_size] if t.shape[0] != 1 else t

 __magic_name__     =      0
 __magic_name__     =      prepped_outputs
 for _ in range(__UpperCamelCase						):
  # Chunk the input
  if not low_mem:
   __magic_name__     =      _select_chunk
  else:
   __magic_name__     =      partial(
       _chunk_slice      ,   flat_start=__UpperCamelCase      ,   flat_end=min(__UpperCamelCase      ,   i + chunk_size						)      ,   no_batch_dims=len(__UpperCamelCase						)      ,   )

  __magic_name__     =      tensor_tree_map(__UpperCamelCase      ,   __UpperCamelCase						)

  # Run the layer on the chunk
  __magic_name__     =      layer(**__UpperCamelCase						)

  # Allocate space for the output
  if out is None:
   __magic_name__     =      tensor_tree_map(lambda __UpperCamelCase						: t.new_zeros((flat_batch_dim,) + t.shape[1:]						)      ,   __UpperCamelCase						)

  # Put the chunk in its pre-allocated space
  if isinstance(__UpperCamelCase      ,   __UpperCamelCase						):

   def assign(__UpperCamelCase      ,   __UpperCamelCase						) -> None:
    for k, v in da.items():
     if isinstance(__UpperCamelCase      ,   __UpperCamelCase						):
      assign(__UpperCamelCase      ,   da[k]						)
     else:
      if _add_into_out:
       v[i : i + chunk_size] += da[k]
      else:
       __magic_name__     =      da[k]

   assign(__UpperCamelCase      ,   __UpperCamelCase						)
  elif isinstance(__UpperCamelCase      ,   __UpperCamelCase						):
   for xa, xa in zip(__UpperCamelCase      ,   __UpperCamelCase						):
    if _add_into_out:
     xa[i : i + chunk_size] += xa
    else:
     __magic_name__     =      xa
  elif isinstance(__UpperCamelCase      ,   torch.Tensor						):
   if _add_into_out:
    out[i : i + chunk_size] += output_chunk
   else:
    __magic_name__     =      output_chunk
  else:
   raise ValueError('''Not supported'''						)

  i += chunk_size

 __magic_name__     =      tensor_tree_map(lambda __UpperCamelCase						: t.view(orig_batch_dims + t.shape[1:]						)      ,   __UpperCamelCase						)

 return out
class        _lowercase					:







     def __init__(      self ,						UpperCamelCase_ = 512 ,						):
      __magic_name__     =      max_chunk_size
      __magic_name__     =      None
      __magic_name__     =      None







     def 	lowerCAmelCase__    (      self ,						UpperCamelCase_ ,						UpperCamelCase_ ,						UpperCamelCase_       ):
      logging.info('''Tuning chunk size...'''       )

      if min_chunk_size >= self.max_chunk_size:
       return min_chunk_size

      __magic_name__     =      [2**l for l in range(int(math.log(self.max_chunk_size ,						2       )       ) + 1       )]
      __magic_name__     =      [c for c in candidates if c > min_chunk_size]
      __magic_name__     =      [min_chunk_size] + candidates
      candidates[-1] += 4

      def test_chunk_size(UpperCamelCase_       ) -> bool:
       try:
        with torch.no_grad():
         fn(*UpperCamelCase_ ,						chunk_size=UpperCamelCase_       )
        return True
       except RuntimeError:
        return False

      __magic_name__     =      0
      __magic_name__     =      len(UpperCamelCase_       ) - 1
      while i > min_viable_chunk_size_index:
       __magic_name__     =      test_chunk_size(candidates[i]       )
       if not viable:
        __magic_name__     =      (min_viable_chunk_size_index + i) // 2
       else:
        __magic_name__     =      i
        __magic_name__     =      (i + len(UpperCamelCase_       ) - 1) // 2

      return candidates[min_viable_chunk_size_index]







     def 	lowerCAmelCase__    (      self ,						UpperCamelCase_ ,						UpperCamelCase_       ):
      __magic_name__     =      True
      for aa, aa in zip(UpperCamelCase_ ,						UpperCamelCase_       ):
       assert type(UpperCamelCase_       ) == type(UpperCamelCase_       )
       if isinstance(UpperCamelCase_ ,						(list, tuple)       ):
        consistent &= self._compare_arg_caches(UpperCamelCase_ ,						UpperCamelCase_       )
       elif isinstance(UpperCamelCase_ ,						UpperCamelCase_       ):
        __magic_name__     =      [v for _, v in sorted(aa.items() ,						key=lambda UpperCamelCase_       : x[0]       )]
        __magic_name__     =      [v for _, v in sorted(aa.items() ,						key=lambda UpperCamelCase_       : x[0]       )]
        consistent &= self._compare_arg_caches(UpperCamelCase_ ,						UpperCamelCase_       )
       else:
        consistent &= aa == aa

      return consistent







     def 	lowerCAmelCase__    (      self ,						UpperCamelCase_ ,						UpperCamelCase_ ,						UpperCamelCase_ ,						):
      __magic_name__     =      True
      __magic_name__     =      tree_map(lambda UpperCamelCase_       : a.shape if isinstance(UpperCamelCase_ ,						torch.Tensor       ) else a ,						UpperCamelCase_ ,						UpperCamelCase_       )
      if self.cached_arg_data is not None:
       # If args have changed shape/value, we need to re-tune
       assert len(self.cached_arg_data       ) == len(UpperCamelCase_       )
       __magic_name__     =      self._compare_arg_caches(self.cached_arg_data ,						UpperCamelCase_       )
      else:
       # Otherwise, we can reuse the precomputed value
       __magic_name__     =      False

      if not consistent:
       __magic_name__     =      self._determine_favorable_chunk_size(
           UpperCamelCase_ ,						UpperCamelCase_ ,						UpperCamelCase_ ,						)
       __magic_name__     =      arg_data

      assert self.cached_chunk_size is not None

      return self.cached_chunk_size




"""simple docstring"""






from __future__ import annotations

from sys import maxsize
from typing import Generic, TypeVar

__lowerCamelCase										=		TypeVar("T")





def 	lowercase      (   __UpperCamelCase						) ->      int:
 return (position - 1) // 2





def 	lowercase      (   __UpperCamelCase						) ->      int:
 return (2 * position) + 1





def 	lowercase      (   __UpperCamelCase						) ->      int:
 return (2 * position) + 2
class        _lowercase					(     Generic[T]     ):







     def __init__(      self       ):
      __magic_name__     =      []
      __magic_name__     =      {}
      __magic_name__     =      0







     def __len__(      self       ):
      return self.elements







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







     def 	lowerCAmelCase__    (      self       ):
      # Check if the priority queue is empty
      return self.elements == 0







     def 	lowerCAmelCase__    (      self ,						UpperCamelCase_ ,						UpperCamelCase_       ):
      # Add an element with given priority to the queue
      self.heap.append((elem, weight)       )
      __magic_name__     =      self.elements
      self.elements += 1
      self._bubble_up(UpperCamelCase_       )







     def 	lowerCAmelCase__    (      self       ):
      # Remove and return the element with lowest weight (highest priority)
      if self.elements > 1:
       self._swap_nodes(0 ,						self.elements - 1       )
      __magic_name__   ,						__magic_name__     =      self.heap.pop()
      del self.position_map[elem]
      self.elements -= 1
      if self.elements > 0:
       __magic_name__   ,						__magic_name__     =      self.heap[0]
       self._bubble_down(UpperCamelCase_       )
      return elem







     def 	lowerCAmelCase__    (      self ,						UpperCamelCase_ ,						UpperCamelCase_       ):
      # Update the weight of the given key
      __magic_name__     =      self.position_map[elem]
      __magic_name__     =      (elem, weight)
      if position > 0:
       __magic_name__     =      get_parent_position(UpperCamelCase_       )
       __magic_name__   ,						__magic_name__     =      self.heap[parent_position]
       if parent_weight > weight:
        self._bubble_up(UpperCamelCase_       )
       else:
        self._bubble_down(UpperCamelCase_       )
      else:
       self._bubble_down(UpperCamelCase_       )







     def 	lowerCAmelCase__    (      self ,						UpperCamelCase_       ):
      # Place a node at the proper position (upward movement) [to be used internally
      # only]
      __magic_name__     =      self.position_map[elem]
      if curr_pos == 0:
       return None
      __magic_name__     =      get_parent_position(UpperCamelCase_       )
      __magic_name__   ,						__magic_name__     =      self.heap[curr_pos]
      __magic_name__   ,						__magic_name__     =      self.heap[parent_position]
      if parent_weight > weight:
       self._swap_nodes(UpperCamelCase_ ,						UpperCamelCase_       )
       return self._bubble_up(UpperCamelCase_       )
      return None







     def 	lowerCAmelCase__    (      self ,						UpperCamelCase_       ):
      # Place a node at the proper position (downward movement) [to be used
      # internally only]
      __magic_name__     =      self.position_map[elem]
      __magic_name__   ,						__magic_name__     =      self.heap[curr_pos]
      __magic_name__     =      get_child_left_position(UpperCamelCase_       )
      __magic_name__     =      get_child_right_position(UpperCamelCase_       )
      if child_left_position < self.elements and child_right_position < self.elements:
       __magic_name__   ,						__magic_name__     =      self.heap[child_left_position]
       __magic_name__   ,						__magic_name__     =      self.heap[child_right_position]
       if child_right_weight < child_left_weight and child_right_weight < weight:
        self._swap_nodes(UpperCamelCase_ ,						UpperCamelCase_       )
        return self._bubble_down(UpperCamelCase_       )
      if child_left_position < self.elements:
       __magic_name__   ,						__magic_name__     =      self.heap[child_left_position]
       if child_left_weight < weight:
        self._swap_nodes(UpperCamelCase_ ,						UpperCamelCase_       )
        return self._bubble_down(UpperCamelCase_       )
      else:
       return None
      if child_right_position < self.elements:
       __magic_name__   ,						__magic_name__     =      self.heap[child_right_position]
       if child_right_weight < weight:
        self._swap_nodes(UpperCamelCase_ ,						UpperCamelCase_       )
        return self._bubble_down(UpperCamelCase_       )
      return None







     def 	lowerCAmelCase__    (      self ,						UpperCamelCase_ ,						UpperCamelCase_       ):
      # Swap the nodes at the given positions
      __magic_name__     =      self.heap[nodea_pos][0]
      __magic_name__     =      self.heap[nodea_pos][0]
      __magic_name__   ,						__magic_name__     =      (
          self.heap[nodea_pos],
          self.heap[nodea_pos],
      )
      __magic_name__     =      nodea_pos
      __magic_name__     =      nodea_pos


class        _lowercase					(     Generic[T]     ):







     def __init__(      self       ):
      __magic_name__     =      {}
      __magic_name__     =      0







     def __repr__(      self       ):
      return str(self.connections       )







     def __len__(      self       ):
      return self.nodes







     def 	lowerCAmelCase__    (      self ,						UpperCamelCase_       ):
      # Add a node in the graph if it is not in the graph
      if node not in self.connections:
       __magic_name__     =      {}
       self.nodes += 1







     def 	lowerCAmelCase__    (      self ,						UpperCamelCase_ ,						UpperCamelCase_ ,						UpperCamelCase_       ):
      # Add an edge between 2 nodes in the graph
      self.add_node(UpperCamelCase_       )
      self.add_node(UpperCamelCase_       )
      __magic_name__     =      weight
      __magic_name__     =      weight





def 	lowercase      (   __UpperCamelCase      ,   ) ->      tuple[dict[T, int], dict[T, T | None]]:
 __magic_name__     =      {node: maxsize for node in graph.connections}
 __magic_name__     =      {node: None for node in graph.connections}

 __magic_name__     =      MinPriorityQueue()
 for node, weight in dist.items():
  priority_queue.push(__UpperCamelCase      ,   __UpperCamelCase						)

 if priority_queue.is_empty():
  return dist, parent

 # initialization
 __magic_name__     =      priority_queue.extract_min()
 __magic_name__     =      0
 for neighbour in graph.connections[node]:
  if dist[neighbour] > dist[node] + graph.connections[node][neighbour]:
   __magic_name__     =      dist[node] + graph.connections[node][neighbour]
   priority_queue.update_key(__UpperCamelCase      ,   dist[neighbour]						)
   __magic_name__     =      node

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

