



"""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		(					_SCREAMING_SNAKE_CASE      :  str ):






				'''simple docstring'''



				_UpperCAmelCase							=			[]
				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		(					_SCREAMING_SNAKE_CASE      :  List[str]    ,   _SCREAMING_SNAKE_CASE      :  Optional[Any] ):






				'''simple docstring'''



				_UpperCAmelCase							=			[]
				for d in reversed(_UpperCAmelCase ):
								idx.append(flat_idx % d )
								_UpperCAmelCase							=			flat_idx // d

				return tuple(reversed(_UpperCAmelCase ) )







@torch.jit.ignore
def        lowercase		(					_SCREAMING_SNAKE_CASE      :  Union[str, Any]    ,   _SCREAMING_SNAKE_CASE      :  int    ,   _SCREAMING_SNAKE_CASE      :  Optional[Any]    ,   _SCREAMING_SNAKE_CASE      :  str = None    ,   _SCREAMING_SNAKE_CASE      :  Optional[Any] = None    ,   ):






				'''simple docstring'''



				def reduce_edge_list(_SCREAMING_SNAKE_CASE      :  Any ) -> None:
								_UpperCAmelCase							=			True
								for i in range(len(_UpperCAmelCase ) ):
												_UpperCAmelCase							=			-1 * (i + 1)
												l[reversed_idx] &= tally
												_UpperCAmelCase							=			l[reversed_idx]

				if start_edges is None:
								_UpperCAmelCase							=			[s == 0 for s in start]
								reduce_edge_list(_UpperCAmelCase )
				if end_edges is None:
								_UpperCAmelCase							=			[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 ),)]

				_UpperCAmelCase							=			[]
				_UpperCAmelCase							=			[]

				# 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

				_UpperCAmelCase							=			tuple(_UpperCAmelCase )
				_UpperCAmelCase							=			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

								_UpperCAmelCase							=			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

								_UpperCAmelCase							=			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() )
								_UpperCAmelCase							=			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		(					_SCREAMING_SNAKE_CASE      :  Optional[Any]    ,   _SCREAMING_SNAKE_CASE      :  int    ,   _SCREAMING_SNAKE_CASE      :  Union[str, Any]    ,   _SCREAMING_SNAKE_CASE      :  Union[str, Any] ):






				'''simple docstring'''



				_UpperCAmelCase							=			t.shape[:no_batch_dims]
				_UpperCAmelCase							=			list(_flat_idx_to_idx(_UpperCAmelCase    ,   _UpperCAmelCase ) )
				# _get_minimal_slice_set is inclusive
				_UpperCAmelCase							=			list(_flat_idx_to_idx(flat_end - 1    ,   _UpperCAmelCase ) )

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

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

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







def        lowercase		(					_SCREAMING_SNAKE_CASE      :  str    ,   _SCREAMING_SNAKE_CASE      :  List[str]    ,   _SCREAMING_SNAKE_CASE      :  int    ,   _SCREAMING_SNAKE_CASE      :  str    ,   _SCREAMING_SNAKE_CASE      :  Dict = False    ,   _SCREAMING_SNAKE_CASE      :  Optional[int] = None    ,   _SCREAMING_SNAKE_CASE      :  Dict = False    ,   ):






				'''simple docstring'''



				if not (len(_UpperCAmelCase ) > 0):
								raise ValueError('''Must provide at least one input''' )

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

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

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

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

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

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

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

								_UpperCAmelCase							=			tensor_tree_map(_UpperCAmelCase    ,   _UpperCAmelCase )

								# Run the layer on the chunk
								_UpperCAmelCase							=			layer(**_UpperCAmelCase )

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

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

												def assign(_SCREAMING_SNAKE_CASE      :  Any    ,   _SCREAMING_SNAKE_CASE      :  Optional[Any] ) -> 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:
																												_UpperCAmelCase							=			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:
																				_UpperCAmelCase							=			xa
								elif isinstance(_UpperCAmelCase    ,   torch.Tensor ):
												if _add_into_out:
																out[i : i + chunk_size] += output_chunk
												else:
																_UpperCAmelCase							=			output_chunk
								else:
												raise ValueError('''Not supported''' )

								i += chunk_size

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

				return out
class 	_a       :
			"""simple docstring"""



			def __init__(						self   :			List[str] ,      __UpperCamelCase   :			int = 5_1_2 ,      )->Optional[Any]:
							_UpperCAmelCase							=			max_chunk_size
							_UpperCAmelCase							=			None
							_UpperCAmelCase							=			None



			def        lowercase__  (						self   :			Tuple ,      __UpperCamelCase   :			Callable ,      __UpperCamelCase   :			tuple ,      __UpperCamelCase   :			int      )->Dict:
							logging.info('''Tuning chunk size...'''      )

							if min_chunk_size >= self.max_chunk_size:
											return min_chunk_size

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

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

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

							return candidates[min_viable_chunk_size_index]



			def        lowercase__  (						self   :			Union[str, Any] ,      __UpperCamelCase   :			Iterable ,      __UpperCamelCase   :			Iterable      )->int:
							_UpperCAmelCase							=			True
							for aa, aa in zip(__SCREAMING_SNAKE_CASE ,      __SCREAMING_SNAKE_CASE      ):
											assert type(__SCREAMING_SNAKE_CASE      ) == type(__SCREAMING_SNAKE_CASE      )
											if isinstance(__SCREAMING_SNAKE_CASE ,      (list, tuple)      ):
															consistent &= self._compare_arg_caches(__SCREAMING_SNAKE_CASE ,      __SCREAMING_SNAKE_CASE      )
											elif isinstance(__SCREAMING_SNAKE_CASE ,      __SCREAMING_SNAKE_CASE      ):
															_UpperCAmelCase							=			[v for _, v in sorted(aa.items() ,      key=lambda __UpperCamelCase      : x[0]      )]
															_UpperCAmelCase							=			[v for _, v in sorted(aa.items() ,      key=lambda __UpperCamelCase      : x[0]      )]
															consistent &= self._compare_arg_caches(__SCREAMING_SNAKE_CASE ,      __SCREAMING_SNAKE_CASE      )
											else:
															consistent &= aa == aa

							return consistent



			def        lowercase__  (						self   :			List[Any] ,      __UpperCamelCase   :			Callable ,      __UpperCamelCase   :			tuple ,      __UpperCamelCase   :			int ,      )->List[Any]:
							_UpperCAmelCase							=			True
							_UpperCAmelCase							=			tree_map(lambda __UpperCamelCase      : a.shape if isinstance(__SCREAMING_SNAKE_CASE ,      torch.Tensor      ) else a ,      __SCREAMING_SNAKE_CASE ,      __SCREAMING_SNAKE_CASE      )
							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(__SCREAMING_SNAKE_CASE      )
											_UpperCAmelCase							=			self._compare_arg_caches(self.cached_arg_data ,      __SCREAMING_SNAKE_CASE      )
							else:
											# Otherwise, we can reuse the precomputed value
											_UpperCAmelCase							=			False

							if not consistent:
											_UpperCAmelCase							=			self._determine_favorable_chunk_size(
											    __SCREAMING_SNAKE_CASE ,      __SCREAMING_SNAKE_CASE ,      __SCREAMING_SNAKE_CASE ,      )
											_UpperCAmelCase							=			arg_data

							assert self.cached_chunk_size is not None

							return self.cached_chunk_size








from collections import defaultdict

from graphs.minimum_spanning_tree_prims import prisms_algorithm as mst





def      __snake_case	(			):
    __a       ,   __a						       =				9, 14  # noqa: F841
    __a						       =				[
        [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],
    ]

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

    __a						       =				mst(_UpperCAmelCase				)

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





