





'''simple docstring'''



import math
import warnings
from dataclasses import dataclass
from typing import List, Optional, Tuple, Union

import numpy as np
import torch
from scipy import integrate

from ..configuration_utils import ConfigMixin, register_to_config
from ..utils import BaseOutput
from .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin






@dataclass
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->LMSDiscrete
class 							__lowercase				(					lowerCAmelCase__  ):







	'''simple docstring'''

	a			: torch.FloatTensor
	a			: Optional[torch.FloatTensor]      =				None





def       _lowerCAmelCase  ( lowerCamelCase_	:     str						,				lowerCamelCase_	:     Dict=0.9_99						,				lowerCamelCase_	:     List[str]="cosine"						,				):
			if alpha_transform_type == "cosine":

						def alpha_bar_fn(lowerCamelCase_	:     List[Any] ):
									return math.cos((t + 0.0_08) / 1.0_08 * math.pi / 2 ) ** 2

			elif alpha_transform_type == "exp":

						def alpha_bar_fn(lowerCamelCase_	:     List[Any] ):
									return math.exp(t * -12.0 )

			else:
						raise ValueError(f"Unsupported alpha_tranform_type: {alpha_transform_type}" )

			__lowercase   =							[]
			for i in range(lowerCamelCase_ ):
						__lowercase   =							i / num_diffusion_timesteps
						__lowercase   =							(i + 1) / num_diffusion_timesteps
						betas.append(min(1 - alpha_bar_fn(lowerCamelCase_ ) / alpha_bar_fn(lowerCamelCase_ )						,				lowerCamelCase_ ) )
			return torch.tensor(lowerCamelCase_						,				dtype=torch.floataa )






class 							__lowercase				(					lowerCAmelCase__       ,					lowerCAmelCase__  ):







	'''simple docstring'''

	a			: Dict      =				[e.name for e in KarrasDiffusionSchedulers]
	a			: Dict      =				1


	@register_to_config
	def __init__(self   ,_lowerCamelCase = 1000   ,_lowerCamelCase = 0.0_0_0_1   ,_lowerCamelCase = 0.0_2   ,_lowerCamelCase = "linear"   ,_lowerCamelCase = None   ,_lowerCamelCase = False   ,_lowerCamelCase = "epsilon"   ,_lowerCamelCase = "linspace"   ,_lowerCamelCase = 0   ,)							->							Union[str, Any]:







				'''simple docstring'''





				if trained_betas is not None:
							__lowercase   =							torch.tensor(_lowerCamelCase   ,dtype=torch.floataa       )
				elif beta_schedule == "linear":
							__lowercase   =							torch.linspace(_lowerCamelCase   ,_lowerCamelCase   ,_lowerCamelCase   ,dtype=torch.floataa       )
				elif beta_schedule == "scaled_linear":
							# this schedule is very specific to the latent diffusion model.
							__lowercase   =							(
							    torch.linspace(beta_start**0.5   ,beta_end**0.5   ,_lowerCamelCase   ,dtype=torch.floataa       ) ** 2
							)
				elif beta_schedule == "squaredcos_cap_v2":
							# Glide cosine schedule
							__lowercase   =							betas_for_alpha_bar(_lowerCamelCase       )
				else:
							raise NotImplementedError(f"{beta_schedule} does is not implemented for {self.__class__}"       )

				__lowercase   =							1.0 - self.betas
				__lowercase   =							torch.cumprod(self.alphas   ,dim=0       )

				__lowercase   =							np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5       )
				__lowercase   =							np.concatenate([sigmas[::-1], [0.0]]       ).astype(np.floataa       )
				__lowercase   =							torch.from_numpy(_lowerCamelCase       )

				# setable values
				__lowercase   =							None
				__lowercase   =							use_karras_sigmas
				self.set_timesteps(_lowerCamelCase   ,_lowerCamelCase       )
				__lowercase   =							[]
				__lowercase   =							False


	@property
	def   _UpperCAmelCase   (self       )							->							Union[str, Any]:







				'''simple docstring'''





				if self.config.timestep_spacing in ["linspace", "trailing"]:
							return self.sigmas.max()

				return (self.sigmas.max() ** 2 + 1) ** 0.5


	def   _UpperCAmelCase   (self   ,_lowerCamelCase   ,_lowerCamelCase       )							->							torch.FloatTensor:







				'''simple docstring'''





				if isinstance(_lowerCamelCase   ,torch.Tensor       ):
							__lowercase   =							timestep.to(self.timesteps.device       )
				__lowercase   =							(self.timesteps == timestep).nonzero().item()
				__lowercase   =							self.sigmas[step_index]
				__lowercase   =							sample / ((sigma**2 + 1) ** 0.5)
				__lowercase   =							True
				return sample


	def   _UpperCAmelCase   (self   ,_lowerCamelCase   ,_lowerCamelCase   ,_lowerCamelCase       )							->							Tuple:







				'''simple docstring'''





				def lms_derivative(_lowerCamelCase       ):
							__lowercase   =							1.0
							for k in range(_lowerCamelCase       ):
										if current_order == k:
													continue
										prod *= (tau - self.sigmas[t - k]) / (self.sigmas[t - current_order] - self.sigmas[t - k])
							return prod

				__lowercase   =							integrate.quad(_lowerCamelCase   ,self.sigmas[t]   ,self.sigmas[t + 1]   ,epsrel=1E-4       )[0]

				return integrated_coeff


	def   _UpperCAmelCase   (self   ,_lowerCamelCase   ,_lowerCamelCase = None       )							->							List[str]:







				'''simple docstring'''





				__lowercase   =							num_inference_steps

				# "linspace", "leading", "trailing" corresponds to annotation of Table 2. of https://arxiv.org/abs/2305.08891
				if self.config.timestep_spacing == "linspace":
							__lowercase   =							np.linspace(0   ,self.config.num_train_timesteps - 1   ,_lowerCamelCase   ,dtype=_lowerCamelCase       )[
							    ::-1
							].copy()
				elif self.config.timestep_spacing == "leading":
							__lowercase   =							self.config.num_train_timesteps // self.num_inference_steps
							# creates integer timesteps by multiplying by ratio
							# casting to int to avoid issues when num_inference_step is power of 3
							__lowercase   =							(np.arange(0   ,_lowerCamelCase       ) * step_ratio).round()[::-1].copy().astype(_lowerCamelCase       )
							timesteps += self.config.steps_offset
				elif self.config.timestep_spacing == "trailing":
							__lowercase   =							self.config.num_train_timesteps / self.num_inference_steps
							# creates integer timesteps by multiplying by ratio
							# casting to int to avoid issues when num_inference_step is power of 3
							__lowercase   =							(np.arange(self.config.num_train_timesteps   ,0   ,-step_ratio       )).round().copy().astype(_lowerCamelCase       )
							timesteps -= 1
				else:
							raise ValueError(
							    f"{self.config.timestep_spacing} is not supported. Please make sure to choose one of 'linspace', 'leading' or 'trailing'."       )

				__lowercase   =							np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5       )
				__lowercase   =							np.log(_lowerCamelCase       )
				__lowercase   =							np.interp(_lowerCamelCase   ,np.arange(0   ,len(_lowerCamelCase       )       )   ,_lowerCamelCase       )

				if self.use_karras_sigmas:
							__lowercase   =							self._convert_to_karras(in_sigmas=_lowerCamelCase       )
							__lowercase   =							np.array([self._sigma_to_t(_lowerCamelCase   ,_lowerCamelCase       ) for sigma in sigmas]       )

				__lowercase   =							np.concatenate([sigmas, [0.0]]       ).astype(np.floataa       )

				__lowercase   =							torch.from_numpy(_lowerCamelCase       ).to(device=_lowerCamelCase       )
				if str(_lowerCamelCase       ).startswith('''mps'''       ):
							# mps does not support float64
							__lowercase   =							torch.from_numpy(_lowerCamelCase       ).to(_lowerCamelCase   ,dtype=torch.floataa       )
				else:
							__lowercase   =							torch.from_numpy(_lowerCamelCase       ).to(device=_lowerCamelCase       )

				__lowercase   =							[]


	def   _UpperCAmelCase   (self   ,_lowerCamelCase   ,_lowerCamelCase       )							->							Any:







				'''simple docstring'''





				__lowercase   =							np.log(_lowerCamelCase       )

				# get distribution
				__lowercase   =							log_sigma - log_sigmas[:, np.newaxis]

				# get sigmas range
				__lowercase   =							np.cumsum((dists >= 0)   ,axis=0       ).argmax(axis=0       ).clip(max=log_sigmas.shape[0] - 2       )
				__lowercase   =							low_idx + 1

				__lowercase   =							log_sigmas[low_idx]
				__lowercase   =							log_sigmas[high_idx]

				# interpolate sigmas
				__lowercase   =							(low - log_sigma) / (low - high)
				__lowercase   =							np.clip(_lowerCamelCase   ,0   ,1       )

				# transform interpolation to time range
				__lowercase   =							(1 - w) * low_idx + w * high_idx
				__lowercase   =							t.reshape(sigma.shape       )
				return t


	def   _UpperCAmelCase   (self   ,_lowerCamelCase       )							->							torch.FloatTensor:







				'''simple docstring'''





				__lowercase   =							in_sigmas[-1].item()
				__lowercase   =							in_sigmas[0].item()

				__lowercase   =							7.0  # 7.0 is the value used in the paper
				__lowercase   =							np.linspace(0   ,1   ,self.num_inference_steps       )
				__lowercase   =							sigma_min ** (1 / rho)
				__lowercase   =							sigma_max ** (1 / rho)
				__lowercase   =							(max_inv_rho + ramp * (min_inv_rho - max_inv_rho)) ** rho
				return sigmas


	def   _UpperCAmelCase   (self   ,_lowerCamelCase   ,_lowerCamelCase   ,_lowerCamelCase   ,_lowerCamelCase = 4   ,_lowerCamelCase = True   ,)							->							Union[LMSDiscreteSchedulerOutput, Tuple]:







				'''simple docstring'''





				if not self.is_scale_input_called:
							warnings.warn(
							    '''The `scale_model_input` function should be called before `step` to ensure correct denoising. '''
							    '''See `StableDiffusionPipeline` for a usage example.'''       )

				if isinstance(_lowerCamelCase   ,torch.Tensor       ):
							__lowercase   =							timestep.to(self.timesteps.device       )
				__lowercase   =							(self.timesteps == timestep).nonzero().item()
				__lowercase   =							self.sigmas[step_index]

				# 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
				if self.config.prediction_type == "epsilon":
							__lowercase   =							sample - sigma * model_output
				elif self.config.prediction_type == "v_prediction":
							# * c_out + input * c_skip
							__lowercase   =							model_output * (-sigma / (sigma**2 + 1) ** 0.5) + (sample / (sigma**2 + 1))
				elif self.config.prediction_type == "sample":
							__lowercase   =							model_output
				else:
							raise ValueError(
							    f"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, or `v_prediction`"       )

				# 2. Convert to an ODE derivative
				__lowercase   =							(sample - pred_original_sample) / sigma
				self.derivatives.append(_lowerCamelCase       )
				if len(self.derivatives       ) > order:
							self.derivatives.pop(0       )

				# 3. Compute linear multistep coefficients
				__lowercase   =							min(step_index + 1   ,_lowerCamelCase       )
				__lowercase   =							[self.get_lms_coefficient(_lowerCamelCase   ,_lowerCamelCase   ,_lowerCamelCase       ) for curr_order in range(_lowerCamelCase       )]

				# 4. Compute previous sample based on the derivatives path
				__lowercase   =							sample + sum(
				    coeff * derivative for coeff, derivative in zip(_lowerCamelCase   ,reversed(self.derivatives       )       )       )

				if not return_dict:
							return (prev_sample,)

				return LMSDiscreteSchedulerOutput(prev_sample=_lowerCamelCase   ,pred_original_sample=_lowerCamelCase       )


	def   _UpperCAmelCase   (self   ,_lowerCamelCase   ,_lowerCamelCase   ,_lowerCamelCase   ,)							->							torch.FloatTensor:







				'''simple docstring'''





				__lowercase   =							self.sigmas.to(device=original_samples.device   ,dtype=original_samples.dtype       )
				if original_samples.device.type == "mps" and torch.is_floating_point(_lowerCamelCase       ):
							# mps does not support float64
							__lowercase   =							self.timesteps.to(original_samples.device   ,dtype=torch.floataa       )
							__lowercase   =							timesteps.to(original_samples.device   ,dtype=torch.floataa       )
				else:
							__lowercase   =							self.timesteps.to(original_samples.device       )
							__lowercase   =							timesteps.to(original_samples.device       )

				__lowercase   =							[(schedule_timesteps == t).nonzero().item() for t in timesteps]

				__lowercase   =							sigmas[step_indices].flatten()
				while len(sigma.shape       ) < len(original_samples.shape       ):
							__lowercase   =							sigma.unsqueeze(-1       )

				__lowercase   =							original_samples + noise * sigma
				return noisy_samples


	def __len__(self       )							->							Optional[Any]:







				'''simple docstring'''





				return self.config.num_train_timesteps











from __future__ import annotations

import sys






class 	A	:
     """simple docstring"""

     def __init__(			self     :      str		,     A__     :      str		,     A__     :      int	) ->				str:
           lowerCamelCase__					     = letter
           lowerCamelCase__					     = freq
           lowerCamelCase__					     = {}




     def __repr__(			self     :      Any	) ->				str:
           return F"""{self.letter}:{self.freq}"""






class 	A	:
     """simple docstring"""

     def __init__(			self     :      Optional[Any]		,     A__     :      int		,     A__     :      Letter | TreeNode		,     A__     :      Letter | TreeNode	) ->				Any:
           lowerCamelCase__					     = freq
           lowerCamelCase__					     = left
           lowerCamelCase__					     = right

def 	lowerCAmelCase_	(     lowerCamelCase:				str  )    ->	list[Letter]:


      '''simple docstring'''




      lowerCamelCase__					     = {}
      with open(lowerCamelCase  ) as f:
            while True:
                  lowerCamelCase__					     = f.read(1  )
                  if not c:
                        break
                  lowerCamelCase__					     = chars[c] + 1 if c in chars else 1
      return sorted((Letter(lowerCamelCase   , lowerCamelCase  ) for c, f in chars.items())   , key=lambda lowerCamelCase  : x.freq  )

def 	lowerCAmelCase_	(     lowerCamelCase:				list[Letter]  )    ->	Letter | TreeNode:


      '''simple docstring'''




      lowerCamelCase__					     = letters  # type: ignore
      while len(lowerCamelCase  ) > 1:
            lowerCamelCase__					     = response.pop(0  )
            lowerCamelCase__					     = response.pop(0  )
            lowerCamelCase__					     = left.freq + right.freq
            lowerCamelCase__					     = TreeNode(lowerCamelCase   , lowerCamelCase   , lowerCamelCase  )
            response.append(lowerCamelCase  )
            response.sort(key=lambda lowerCamelCase  : x.freq  )
      return response[0]

def 	lowerCAmelCase_	(     lowerCamelCase:				Letter | TreeNode   , lowerCamelCase:				str  )    ->	list[Letter]:


      '''simple docstring'''




      if isinstance(lowerCamelCase   , lowerCamelCase  ):
            lowerCamelCase__					     = bitstring
            return [root]
      lowerCamelCase__					     = root  # type: ignore
      lowerCamelCase__					     = []
      letters += traverse_tree(treenode.left   , bitstring + '0'  )
      letters += traverse_tree(treenode.right   , bitstring + '1'  )
      return letters

def 	lowerCAmelCase_	(     lowerCamelCase:				str  )    ->	None:


      '''simple docstring'''




      lowerCamelCase__					     = parse_file(lowerCamelCase  )
      lowerCamelCase__					     = build_tree(lowerCamelCase  )
      lowerCamelCase__					     = {
          k: v for letter in traverse_tree(lowerCamelCase   , ''  ) for k, v in letter.bitstring.items()
      }
      print(f"""Huffman Coding  of {file_path}: """  )
      with open(lowerCamelCase  ) as f:
            while True:
                  lowerCamelCase__					     = 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])