


"""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     (      lowerCamelCase_  :      Union[dict, list, tuple, torch.Tensor]  ):
				SCREAMING_SNAKE_CASE__     							=				[]
				if isinstance(lowerCamelCase_						,					lowerCamelCase_  ):
								for v in tree.values():
												shapes.extend(_fetch_dims(lowerCamelCase_  )  )
				elif isinstance(lowerCamelCase_						,					(list, tuple)  ):
								for t in tree:
												shapes.extend(_fetch_dims(lowerCamelCase_  )  )
				elif isinstance(lowerCamelCase_						,					torch.Tensor  ):
								shapes.append(tree.shape  )
				else:
								raise ValueError("Not supported"  )

				return shapes


@torch.jit.ignore
def __lowercase     (      lowerCamelCase_  :      int						,					lowerCamelCase_  :      Tuple[int, ...]  ):
				SCREAMING_SNAKE_CASE__     							=				[]
				for d in reversed(lowerCamelCase_  ):
								idx.append(flat_idx % d  )
								SCREAMING_SNAKE_CASE__     							=				flat_idx // d

				return tuple(reversed(lowerCamelCase_  )  )


@torch.jit.ignore
def __lowercase     (      lowerCamelCase_  :      Sequence[int]						,					lowerCamelCase_  :      Sequence[int]						,					lowerCamelCase_  :      Sequence[int]						,					lowerCamelCase_  :      Optional[Sequence[bool]] = None						,					lowerCamelCase_  :      Optional[Sequence[bool]] = None						,					):

				# 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(lowerCamelCase_  :      List[bool]  ) -> None:
								SCREAMING_SNAKE_CASE__     							=				True
								for i in range(len(lowerCamelCase_  )  ):
												SCREAMING_SNAKE_CASE__     							=				-1 * (i + 1)
												l[reversed_idx] &= tally
												SCREAMING_SNAKE_CASE__     							=				l[reversed_idx]

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

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

				SCREAMING_SNAKE_CASE__     							=				[]
				SCREAMING_SNAKE_CASE__     							=				[]

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

				SCREAMING_SNAKE_CASE__     							=				tuple(lowerCamelCase_  )
				SCREAMING_SNAKE_CASE__     							=				len(lowerCamelCase_  )

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

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

								SCREAMING_SNAKE_CASE__     							=				start[divergence_idx]
								return tuple(
								    path + (slice(lowerCamelCase_						,					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

								SCREAMING_SNAKE_CASE__     							=				end[divergence_idx]
								return tuple(
								    path + (slice(lowerCamelCase_						,					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()  )
								SCREAMING_SNAKE_CASE__     							=				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     (      lowerCamelCase_  :      torch.Tensor						,					lowerCamelCase_  :      int						,					lowerCamelCase_  :      int						,					lowerCamelCase_  :      int  ):
				SCREAMING_SNAKE_CASE__     							=				t.shape[:no_batch_dims]
				SCREAMING_SNAKE_CASE__     							=				list(_flat_idx_to_idx(lowerCamelCase_						,					lowerCamelCase_  )  )
				# _get_minimal_slice_set is inclusive
				SCREAMING_SNAKE_CASE__     							=				list(_flat_idx_to_idx(flat_end - 1						,					lowerCamelCase_  )  )

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

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

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


def __lowercase     (      lowerCamelCase_  :      Callable						,					lowerCamelCase_  :      Dict[str, Any]						,					lowerCamelCase_  :      int						,					lowerCamelCase_  :      int						,					lowerCamelCase_  :      bool = False						,					lowerCamelCase_  :      Any = None						,					lowerCamelCase_  :      bool = False						,					):
				if not (len(lowerCamelCase_  ) > 0):
								raise ValueError("Must provide at least one input"  )

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

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

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

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

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

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

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

								SCREAMING_SNAKE_CASE__     							=				tensor_tree_map(lowerCamelCase_						,					lowerCamelCase_  )

								# Run the layer on the chunk
								SCREAMING_SNAKE_CASE__     							=				layer(**lowerCamelCase_  )

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

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

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

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

								i += chunk_size

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

				return out


class 			lowerCamelCase_		:





				"""simple docstring"""







				def __init__(						self       ,		UpperCAmelCase__ = 512       ,		):
								SCREAMING_SNAKE_CASE__     							=				max_chunk_size
								SCREAMING_SNAKE_CASE__     							=				None
								SCREAMING_SNAKE_CASE__     							=				None



				def   lowerCAmelCase__		(						self       ,		UpperCAmelCase__       ,		UpperCAmelCase__       ,		UpperCAmelCase__     ):
								logging.info("Tuning chunk size..."     )

								if min_chunk_size >= self.max_chunk_size:
												return min_chunk_size

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

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

								return candidates[min_viable_chunk_size_index]



				def   lowerCAmelCase__		(						self       ,		UpperCAmelCase__       ,		UpperCAmelCase__     ):
								SCREAMING_SNAKE_CASE__     							=				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__     ):
																SCREAMING_SNAKE_CASE__     							=				[v for _, v in sorted(aa.items()       ,		key=lambda UpperCAmelCase__     : x[0]     )]
																SCREAMING_SNAKE_CASE__     							=				[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__       ,		):
								SCREAMING_SNAKE_CASE__     							=				True
								SCREAMING_SNAKE_CASE__     							=				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__     )
												SCREAMING_SNAKE_CASE__     							=				self._compare_arg_caches(self.cached_arg_data       ,		UpperCAmelCase__     )
								else:
												# Otherwise, we can reuse the precomputed value
												SCREAMING_SNAKE_CASE__     							=				False

								if not consistent:
												SCREAMING_SNAKE_CASE__     							=				self._determine_favorable_chunk_size(
												    UpperCAmelCase__       ,		UpperCAmelCase__       ,		UpperCAmelCase__       ,		)
												SCREAMING_SNAKE_CASE__     							=				arg_data

								assert self.cached_chunk_size is not None

								return self.cached_chunk_size




"""simple docstring"""






from __future__ import annotations

from collections.abc import Sequence
from typing import Literal


def __lowercase     (      lowerCamelCase_  :      str						,					lowerCamelCase_  :      str  ):
				SCREAMING_SNAKE_CASE__     							=				list(lowerCamelCase_  )
				SCREAMING_SNAKE_CASE__     							=				list(lowerCamelCase_  )
				SCREAMING_SNAKE_CASE__     							=				0
				for i in range(len(lowerCamelCase_  )  ):
								if lista[i] != lista[i]:
												count += 1
												SCREAMING_SNAKE_CASE__     							=				"_"
				if count > 1:
								return False
				else:
								return "".join(lowerCamelCase_  )


def __lowercase     (      lowerCamelCase_  :      list[str]  ):
				SCREAMING_SNAKE_CASE__     							=				[]
				while True:
								SCREAMING_SNAKE_CASE__     							=				["$"] * len(lowerCamelCase_  )
								SCREAMING_SNAKE_CASE__     							=				[]
								for i in range(len(lowerCamelCase_  )  ):
												for j in range(i + 1						,					len(lowerCamelCase_  )  ):
																SCREAMING_SNAKE_CASE__     							=				compare_string(binary[i]						,					binary[j]  )
																if k is False:
																				SCREAMING_SNAKE_CASE__     							=				"*"
																				SCREAMING_SNAKE_CASE__     							=				"*"
																				temp.append("X"  )
								for i in range(len(lowerCamelCase_  )  ):
												if checka[i] == "$":
																pi.append(binary[i]  )
								if len(lowerCamelCase_  ) == 0:
												return pi
								SCREAMING_SNAKE_CASE__     							=				list(set(lowerCamelCase_  )  )


def __lowercase     (      lowerCamelCase_  :      int						,					lowerCamelCase_  :      Sequence[float]  ):
				SCREAMING_SNAKE_CASE__     							=				[]
				for minterm in minterms:
								SCREAMING_SNAKE_CASE__     							=				""
								for _ in range(lowerCamelCase_  ):
												SCREAMING_SNAKE_CASE__     							=				str(minterm % 2  ) + string
												minterm //= 2
								temp.append(lowerCamelCase_  )
				return temp


def __lowercase     (      lowerCamelCase_  :      str						,					lowerCamelCase_  :      str						,					lowerCamelCase_  :      int  ):
				SCREAMING_SNAKE_CASE__     							=				list(lowerCamelCase_  )
				SCREAMING_SNAKE_CASE__     							=				list(lowerCamelCase_  )
				SCREAMING_SNAKE_CASE__     							=				0
				for i in range(len(lowerCamelCase_  )  ):
								if lista[i] != lista[i]:
												count_n += 1
				return count_n == count


def __lowercase     (      lowerCamelCase_  :      list[list[int]]						,					lowerCamelCase_  :      list[str]  ):
				SCREAMING_SNAKE_CASE__     							=				[]
				SCREAMING_SNAKE_CASE__     							=				[0] * len(lowerCamelCase_  )
				for i in range(len(chart[0]  )  ):
								SCREAMING_SNAKE_CASE__     							=				0
								SCREAMING_SNAKE_CASE__     							=				-1
								for j in range(len(lowerCamelCase_  )  ):
												if chart[j][i] == 1:
																count += 1
																SCREAMING_SNAKE_CASE__     							=				j
								if count == 1:
												SCREAMING_SNAKE_CASE__     							=				1
				for i in range(len(lowerCamelCase_  )  ):
								if select[i] == 1:
												for j in range(len(chart[0]  )  ):
																if chart[i][j] == 1:
																				for k in range(len(lowerCamelCase_  )  ):
																								SCREAMING_SNAKE_CASE__     							=				0
												temp.append(prime_implicants[i]  )
				while True:
								SCREAMING_SNAKE_CASE__     							=				0
								SCREAMING_SNAKE_CASE__     							=				-1
								SCREAMING_SNAKE_CASE__     							=				0
								for i in range(len(lowerCamelCase_  )  ):
												SCREAMING_SNAKE_CASE__     							=				chart[i].count(1  )
												if count_n > max_n:
																SCREAMING_SNAKE_CASE__     							=				count_n
																SCREAMING_SNAKE_CASE__     							=				i

								if max_n == 0:
												return temp

								temp.append(prime_implicants[rem]  )

								for i in range(len(chart[0]  )  ):
												if chart[rem][i] == 1:
																for j in range(len(lowerCamelCase_  )  ):
																				SCREAMING_SNAKE_CASE__     							=				0


def __lowercase     (      lowerCamelCase_  :      list[str]						,					lowerCamelCase_  :      list[str]  ):
				SCREAMING_SNAKE_CASE__     							=				[[0 for x in range(len(lowerCamelCase_  )  )] for x in range(len(lowerCamelCase_  )  )]
				for i in range(len(lowerCamelCase_  )  ):
								SCREAMING_SNAKE_CASE__     							=				prime_implicants[i].count("_"  )
								for j in range(len(lowerCamelCase_  )  ):
												if is_for_table(prime_implicants[i]						,					binary[j]						,					lowerCamelCase_  ):
																SCREAMING_SNAKE_CASE__     							=				1

				return chart


def __lowercase     (      ):
				SCREAMING_SNAKE_CASE__     							=				int(input("Enter the no. of variables\n"  )  )
				SCREAMING_SNAKE_CASE__     							=				[
				    float(lowerCamelCase_  )
				    for x in input(
				        "Enter the decimal representation of Minterms 'Spaces Separated'\n"  ).split()
				]
				SCREAMING_SNAKE_CASE__     							=				decimal_to_binary(lowerCamelCase_						,					lowerCamelCase_  )

				SCREAMING_SNAKE_CASE__     							=				check(lowerCamelCase_  )
				print("Prime Implicants are:"  )
				print(lowerCamelCase_  )
				SCREAMING_SNAKE_CASE__     							=				prime_implicant_chart(lowerCamelCase_						,					lowerCamelCase_  )

				SCREAMING_SNAKE_CASE__     							=				selection(lowerCamelCase_						,					lowerCamelCase_  )
				print("Essential Prime Implicants are:"  )
				print(lowerCamelCase_  )


if __name__ == "__main__":
	import doctest

	doctest.testmod()
	main()
