"""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 SCREAMING_SNAKE_CASE__			(   __UpperCAmelCase )  ->  List[Tuple[int, ...]]:
   lowercase__:   List[Any]					=      []
   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 SCREAMING_SNAKE_CASE__			(   __UpperCAmelCase       ,    __UpperCAmelCase )  ->  Tuple[int, ...]:
   lowercase__:   Any					=      []
   for d in reversed(__UpperCAmelCase ):
      idx.append(flat_idx % d )
      lowercase__:   List[Any]					=      flat_idx // d

   return tuple(reversed(__UpperCAmelCase ) )



@torch.jit.ignore
def SCREAMING_SNAKE_CASE__			(   __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:
      lowercase__:   str					=      True
      for i in range(len(__UpperCAmelCase ) ):
         lowercase__:   Optional[int]					=      -1 * (i + 1)
         l[reversed_idx] &= tally
         lowercase__:   List[Any]					=      l[reversed_idx]

   if start_edges is None:
      lowercase__:   Any					=      [s == 0 for s in start]
      reduce_edge_list(__UpperCAmelCase )
   if end_edges is None:
      lowercase__:   List[str]					=      [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 ),)]

   lowercase__:   List[Tuple[slice, ...]]					=      []
   lowercase__:   List[slice]					=      []

   # 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

   lowercase__:   Tuple[slice, ...]					=      tuple(__UpperCAmelCase )
   lowercase__:   Optional[Any]					=      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

      lowercase__:   Dict					=      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

      lowercase__:   Optional[int]					=      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() )
      lowercase__:   str					=      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 SCREAMING_SNAKE_CASE__			(   __UpperCAmelCase       ,    __UpperCAmelCase       ,    __UpperCAmelCase       ,    __UpperCAmelCase )  ->  torch.Tensor:
   lowercase__:   Dict					=      t.shape[:no_batch_dims]
   lowercase__:   Dict					=      list(_flat_idx_to_idx(__UpperCAmelCase       ,    __UpperCAmelCase ) )
   # _get_minimal_slice_set is inclusive
   lowercase__:   Union[str, Any]					=      list(_flat_idx_to_idx(flat_end - 1       ,    __UpperCAmelCase ) )

   # Get an ordered list of slices to perform
   lowercase__:   Optional[Any]					=      _get_minimal_slice_set(
       __UpperCAmelCase       ,    __UpperCAmelCase       ,    __UpperCAmelCase       ,    )

   lowercase__:   Tuple					=      [t[s] for s in slices]

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



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

   lowercase__:   Union[str, Any]					=      [shape[:no_batch_dims] for shape in _fetch_dims(__UpperCAmelCase )]
   lowercase__:   List[str]					=      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:
            lowercase__:   Optional[Any]					=      t.expand(orig_batch_dims + t.shape[no_batch_dims:] )
         lowercase__:   Any					=      t.reshape(-1       ,    *t.shape[no_batch_dims:] )
      else:
         lowercase__:   Union[str, Any]					=      t.expand(orig_batch_dims + t.shape[no_batch_dims:] )
      return t

   lowercase__:   Dict[str, Any]					=      tensor_tree_map(_prep_inputs       ,    __UpperCAmelCase )
   lowercase__:   List[Any]					=      None
   if _out is not None:
      lowercase__:   List[str]					=      tensor_tree_map(lambda __UpperCAmelCase : t.view([-1] + list(t.shape[no_batch_dims:] ) )       ,    _out )

   lowercase__:   List[Any]					=      1
   for d in orig_batch_dims:
      flat_batch_dim *= d

   lowercase__:   str					=      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

   lowercase__:   int					=      0
   lowercase__:   Tuple					=      prepped_outputs
   for _ in range(__UpperCAmelCase ):
      # Chunk the input
      if not low_mem:
         lowercase__:   int					=      _select_chunk
      else:
         lowercase__:   List[str]					=      partial(
             _chunk_slice       ,    flat_start=__UpperCAmelCase       ,    flat_end=min(__UpperCAmelCase       ,    i + chunk_size )       ,    no_batch_dims=len(__UpperCAmelCase )       ,    )

      lowercase__:   Dict[str, Any]					=      tensor_tree_map(__UpperCAmelCase       ,    __UpperCAmelCase )

      # Run the layer on the chunk
      lowercase__:   Optional[int]					=      layer(**__UpperCAmelCase )

      # Allocate space for the output
      if out is None:
         lowercase__:   List[Any]					=      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:
                     lowercase__:   int					=      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:
               lowercase__:   Union[str, Any]					=      xa
      elif isinstance(__UpperCAmelCase       ,    torch.Tensor ):
         if _add_into_out:
            out[i : i + chunk_size] += output_chunk
         else:
            lowercase__:   Union[str, Any]					=      output_chunk
      else:
         raise ValueError('''Not supported''' )

      i += chunk_size

   lowercase__:   Dict					=      tensor_tree_map(lambda __UpperCAmelCase : t.view(orig_batch_dims + t.shape[1:] )       ,    __UpperCAmelCase )

   return out




class     UpperCAmelCase						:



    """simple docstring"""

    def __init__(   self    ,			_UpperCAmelCase = 512    ,			):
       lowercase__:   int					=      max_chunk_size
       lowercase__:   Optional[int]					=      None
       lowercase__:   Optional[tuple]					=      None






    def _snake_case			(   self    ,			_UpperCAmelCase    ,			_UpperCAmelCase    ,			_UpperCAmelCase							):
       logging.info('''Tuning chunk size...'''							)

       if min_chunk_size >= self.max_chunk_size:
          return min_chunk_size

       lowercase__:   List[int]					=      [2**l for l in range(int(math.log(self.max_chunk_size    ,			2							)							) + 1							)]
       lowercase__:   Dict					=      [c for c in candidates if c > min_chunk_size]
       lowercase__:   int					=      [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

       lowercase__:   Any					=      0
       lowercase__:   Optional[Any]					=      len(_UpperCAmelCase							) - 1
       while i > min_viable_chunk_size_index:
          lowercase__:   List[Any]					=      test_chunk_size(candidates[i]							)
          if not viable:
             lowercase__:   List[str]					=      (min_viable_chunk_size_index + i) // 2
          else:
             lowercase__:   int					=      i
             lowercase__:   List[str]					=      (i + len(_UpperCAmelCase							) - 1) // 2

       return candidates[min_viable_chunk_size_index]






    def _snake_case			(   self    ,			_UpperCAmelCase    ,			_UpperCAmelCase							):
       lowercase__:   Dict					=      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							):
             lowercase__:   Any					=      [v for _, v in sorted(aa.items()    ,			key=lambda _UpperCAmelCase							: x[0]							)]
             lowercase__:   Dict					=      [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 _snake_case			(   self    ,			_UpperCAmelCase    ,			_UpperCAmelCase    ,			_UpperCAmelCase    ,			):
       lowercase__:   Dict					=      True
       lowercase__:   tuple					=      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							)
          lowercase__:   int					=      self._compare_arg_caches(self.cached_arg_data    ,			_UpperCAmelCase							)
       else:
          # Otherwise, we can reuse the precomputed value
          lowercase__:   Union[str, Any]					=      False

       if not consistent:
          lowercase__:   List[Any]					=      self._determine_favorable_chunk_size(
              _UpperCAmelCase    ,			_UpperCAmelCase    ,			_UpperCAmelCase    ,			)
          lowercase__:   Union[str, Any]					=      arg_data

       assert self.cached_chunk_size is not None

       return self.cached_chunk_size

"""simple docstring"""






def SCREAMING_SNAKE_CASE__			(   __UpperCAmelCase )  ->  int:

   if not grid or not grid[0]:
      raise TypeError('''The grid does not contain the appropriate information''' )

   for cell_n in range(1       ,    len(grid[0] ) ):
      grid[0][cell_n] += grid[0][cell_n - 1]
   lowercase__:   Tuple					=      grid[0]

   for row_n in range(1       ,    len(__UpperCAmelCase ) ):
      lowercase__:   Tuple					=      grid[row_n]
      lowercase__:   Dict					=      fill_row(__UpperCAmelCase       ,    __UpperCAmelCase )
      lowercase__:   Union[str, Any]					=      grid[row_n]

   return grid[-1][-1]



def SCREAMING_SNAKE_CASE__			(   __UpperCAmelCase       ,    __UpperCAmelCase )  ->  list:
   current_row[0] += row_above[0]
   for cell_n in range(1       ,    len(__UpperCAmelCase ) ):
      current_row[cell_n] += min(current_row[cell_n - 1]       ,    row_above[cell_n] )

   return current_row


if __name__ == "__main__":
       import doctest

       doctest.testmod()
