code: 
  
  
  
  
  
  
  from typing import Dict, Optional, Tuple
  
  import torch
  def        UpperCAmelCase      (   _lowercase      ):
  
  
      '''simple docstring'''
  
  
  
      _lowercase     =	boundaries[1] - boundaries[0]
      _lowercase     =	boundaries + step / 2
      _lowercase     =	torch.cat([bin_centers, (bin_centers[-1] + step).unsqueeze(-1      )],      dim=0      )
      return bin_centers
  def        UpperCAmelCase      (   _lowercase,      _lowercase,      ):
  
  
      '''simple docstring'''
  
  
  
      _lowercase     =	_calculate_bin_centers(_lowercase      )
      return (
          torch.sum(aligned_distance_error_probs * bin_centers,      dim=-1      ),
          bin_centers[-1],
      )
  def        UpperCAmelCase      (   _lowercase,      _lowercase = 31,      _lowercase = 64,      **_lowercase,      ):
  
  
      '''simple docstring'''
  
  
  
      _lowercase     =	torch.linspace(0,      _lowercase,      steps=(no_bins - 1),      device=logits.device      )
  
      _lowercase     =	torch.nn.functional.softmax(_lowercase,      dim=-1      )
      _lowercase ,    _lowercase     =	_calculate_expected_aligned_error(
          alignment_confidence_breaks=_lowercase,      aligned_distance_error_probs=_lowercase,      )
  
      return {
          "aligned_confidence_probs": aligned_confidence_probs,
          "predicted_aligned_error": predicted_aligned_error,
          "max_predicted_aligned_error": max_predicted_aligned_error,
      }
  def        UpperCAmelCase      (   _lowercase,      _lowercase = None,      _lowercase = 31,      _lowercase = 64,      _lowercase = 1e-8,      **_lowercase,      ):
  
  
      '''simple docstring'''
  
  
  
      if residue_weights is None:
          _lowercase     =	logits.new_ones(logits.shape[-2]      )
  
      _lowercase     =	torch.linspace(0,      _lowercase,      steps=(no_bins - 1),      device=logits.device      )
  
      _lowercase     =	_calculate_bin_centers(_lowercase      )
      torch.sum(_lowercase      )
      _lowercase     =	logits.shape[-2]
      _lowercase     =	max(_lowercase,      19      )
  
      _lowercase     =	1.24 * (clipped_n - 15) ** (1.0 / 3) - 1.8
  
      _lowercase     =	torch.nn.functional.softmax(_lowercase,      dim=-1      )
  
      _lowercase     =	1.0 / (1 + (bin_centers**2) / (da**2))
      _lowercase     =	torch.sum(probs * tm_per_bin,      dim=-1      )
  
      _lowercase     =	residue_weights / (eps + residue_weights.sum())
      _lowercase     =	torch.sum(predicted_tm_term * normed_residue_mask,      dim=-1      )
  
      _lowercase     =	per_alignment * residue_weights
  
      _lowercase     =	(weighted == torch.max(_lowercase      )).nonzero()[0]
      return per_alignment[tuple(_lowercase      )]
  
style_context: 
  
  
  
  
  
  
  from __future__ import annotations
  
  import sys
  
  class 					snake_case_							:
  
  
  
  
  
  
  
     """simple docstring"""
  
  
  
     def __init__(    self:	Any   ,       snake_case__:	str   ,       snake_case__:	int	)  ->		Optional[Any]:
  
  
         """simple docstring"""
  
  
  
         _lowercase     =	letter
         _lowercase     =	freq
         _lowercase     =	{}
  
     def __repr__(    self:	Optional[int]	)  ->		str:
  
  
         """simple docstring"""
  
  
  
         return f'''{self.letter}:{self.freq}'''
  
  
  
  
  
  
  class 					snake_case_							:
  
  
  
  
  
  
  
     """simple docstring"""
  
  
  
     def __init__(    self:	Optional[int]   ,       snake_case__:	int   ,       snake_case__:	Letter | TreeNode   ,       snake_case__:	Letter | TreeNode	)  ->		List[Any]:
  
  
         """simple docstring"""
  
  
  
         _lowercase     =	freq
         _lowercase     =	left
         _lowercase     =	right
  
  
  
  
  
  
  def        UpperCAmelCase      (   _lowercase      ):
  
  
      '''simple docstring'''
  
  
  
      _lowercase     =	{}
      with open(_lowercase      ) as f:
          while True:
              _lowercase     =	f.read(1      )
              if not c:
                  break
              _lowercase     =	chars[c] + 1 if c in chars else 1
      return sorted((Letter(_lowercase,      _lowercase      ) for c, f in chars.items()),      key=lambda _lowercase      : x.freq      )
  def        UpperCAmelCase      (   _lowercase      ):
  
  
      '''simple docstring'''
  
  
  
      _lowercase     =	letters  # type: ignore
      while len(_lowercase      ) > 1:
          _lowercase     =	response.pop(0      )
          _lowercase     =	response.pop(0      )
          _lowercase     =	left.freq + right.freq
          _lowercase     =	TreeNode(_lowercase,      _lowercase,      _lowercase      )
          response.append(_lowercase      )
          response.sort(key=lambda _lowercase      : x.freq      )
      return response[0]
  def        UpperCAmelCase      (   _lowercase,      _lowercase      ):
  
  
      '''simple docstring'''
  
  
  
      if isinstance(_lowercase,      _lowercase      ):
          _lowercase     =	bitstring
          return [root]
      _lowercase     =	root  # type: ignore
      _lowercase     =	[]
      letters += traverse_tree(treenode.left,      bitstring + '0'      )
      letters += traverse_tree(treenode.right,      bitstring + '1'      )
      return letters
  def        UpperCAmelCase      (   _lowercase      ):
  
  
      '''simple docstring'''
  
  
  
      _lowercase     =	parse_file(_lowercase      )
      _lowercase     =	build_tree(_lowercase      )
      _lowercase     =	{
          k: v for letter in traverse_tree(_lowercase,      ''      ) for k, v in letter.bitstring.items()
      }
      print(f'''Huffman Coding  of {file_path}: '''      )
      with open(_lowercase      ) as f:
          while True:
              _lowercase     =	f.read(1      )
              if not c:
                  break
              print(letters[c],      end=' '      )
      print()
  
  
  if __name__ == "__main__":
     # pass the file path to the huffman function
     huffman(sys.argv[1])
  