class 	__snake_case	:





      '''simple docstring'''






      def __init__(					self     :				Optional[int]    ,  _UpperCamelCase     :				str = ""    ,  _UpperCamelCase     :				bool = False)				->None:


          """simple docstring"""


          _lowerCamelCase     :		dict[str, RadixNode] 						=						{}

          # A node will be a leaf if the tree contains its word
          _lowerCamelCase     :		str 						=						is_leaf

          _lowerCamelCase     :		str 						=						prefix



      def 	_SCREAMING_SNAKE_CASE    (					self     :				List[str]    ,  _UpperCamelCase     :				str)				->tuple[str, str, str]:


          """simple docstring"""


          _lowerCamelCase     :		List[Any] 						=						0
          for q, w in zip(self.prefix    ,  _UpperCamelCase):
              if q != w:
                  break

              x += 1

          return self.prefix[:x], self.prefix[x:], word[x:]



      def 	_SCREAMING_SNAKE_CASE    (					self     :				int    ,  _UpperCamelCase     :				list[str])				->None:


          """simple docstring"""


          for word in words:
              self.insert(_UpperCamelCase)



      def 	_SCREAMING_SNAKE_CASE    (					self     :				Tuple    ,  _UpperCamelCase     :				str)				->None:


          """simple docstring"""


          if self.prefix == word:
              _lowerCamelCase     :		List[str] 						=						True

          # Case 2: The node has no edges that have a prefix to the word
          # Solution: We create an edge from the current node to a new one
          # containing the word
          elif word[0] not in self.nodes:
              _lowerCamelCase     :		Optional[Any] 						=						RadixNode(prefix=_UpperCamelCase    ,  is_leaf=_UpperCamelCase)

          else:
              _lowerCamelCase     :		Dict 						=						self.nodes[word[0]]
              _lowerCamelCase						,							_lowerCamelCase						,							_lowerCamelCase     :		Any 						=						incoming_node.match(
                  _UpperCamelCase)

              # Case 3: The node prefix is equal to the matching
              # Solution: We insert remaining word on the next node
              if remaining_prefix == "":
                  self.nodes[matching_string[0]].insert(_UpperCamelCase)

              # Case 4: The word is greater equal to the matching
              # Solution: Create a node in between both nodes, change
              # prefixes and add the new node for the remaining word
              else:
                  _lowerCamelCase     :		Optional[Any] 						=						remaining_prefix

                  _lowerCamelCase     :		str 						=						self.nodes[matching_string[0]]
                  _lowerCamelCase     :		List[str] 						=						RadixNode(_UpperCamelCase    ,  _UpperCamelCase)
                  _lowerCamelCase     :		List[str] 						=						aux_node

                  if remaining_word == "":
                      _lowerCamelCase     :		Union[str, Any] 						=						True
                  else:
                      self.nodes[matching_string[0]].insert(_UpperCamelCase)



      def 	_SCREAMING_SNAKE_CASE    (					self     :				Optional[Any]    ,  _UpperCamelCase     :				str)				->bool:


          """simple docstring"""


          _lowerCamelCase     :		Tuple 						=						self.nodes.get(word[0]    ,  _UpperCamelCase)
          if not incoming_node:
              return False
          else:
              _lowerCamelCase						,							_lowerCamelCase						,							_lowerCamelCase     :		int 						=						incoming_node.match(
                  _UpperCamelCase)
              # If there is remaining prefix, the word can't be on the tree
              if remaining_prefix != "":
                  return False
              # This applies when the word and the prefix are equal
              elif remaining_word == "":
                  return incoming_node.is_leaf
              # We have word remaining so we check the next node
              else:
                  return incoming_node.find(_UpperCamelCase)



      def 	_SCREAMING_SNAKE_CASE    (					self     :				Optional[Any]    ,  _UpperCamelCase     :				str)				->bool:


          """simple docstring"""


          _lowerCamelCase     :		List[str] 						=						self.nodes.get(word[0]    ,  _UpperCamelCase)
          if not incoming_node:
              return False
          else:
              _lowerCamelCase						,							_lowerCamelCase						,							_lowerCamelCase     :		Any 						=						incoming_node.match(
                  _UpperCamelCase)
              # If there is remaining prefix, the word can't be on the tree
              if remaining_prefix != "":
                  return False
              # We have word remaining so we check the next node
              elif remaining_word != "":
                  return incoming_node.delete(_UpperCamelCase)
              else:
                  # If it is not a leaf, we don't have to delete
                  if not incoming_node.is_leaf:
                      return False
                  else:
                      # We delete the nodes if no edges go from it
                      if len(incoming_node.nodes) == 0:
                          del self.nodes[word[0]]
                          # We merge the current node with its only child
                          if len(self.nodes) == 1 and not self.is_leaf:
                              _lowerCamelCase     :		List[str] 						=						list(self.nodes.values())[0]
                              _lowerCamelCase     :		Any 						=						merging_node.is_leaf
                              self.prefix += merging_node.prefix
                              _lowerCamelCase     :		List[Any] 						=						merging_node.nodes
                    # If there is more than 1 edge, we just mark it as non-leaf
                      elif len(incoming_node.nodes) > 1:
                          _lowerCamelCase     :		Dict 						=						False
                      # If there is 1 edge, we merge it with its child
                      else:
                          _lowerCamelCase     :		Dict 						=						list(incoming_node.nodes.values())[0]
                          _lowerCamelCase     :		str 						=						merging_node.is_leaf
                          incoming_node.prefix += merging_node.prefix
                          _lowerCamelCase     :		Any 						=						merging_node.nodes

                      return True




      def 	_SCREAMING_SNAKE_CASE    (					self     :				Dict    ,  _UpperCamelCase     :				int = 0)				->None:


          """simple docstring"""


          if self.prefix != "":
              print("""-""" * height    ,  self.prefix    ,  """  (leaf)""" if self.is_leaf else """""")

          for value in self.nodes.values():
              value.print_tree(height + 1)







def 						A__  (					):







    '''simple docstring'''
    _lowerCamelCase     :		Dict 						=						"""banana bananas bandana band apple all beast""".split()
    _lowerCamelCase     :		int 						=						RadixNode()
    root.insert_many(__A	)

    assert all(root.find(__A	) for word in words	)
    assert not root.find("""bandanas"""	)
    assert not root.find("""apps"""	)
    root.delete("""all"""	)
    assert not root.find("""all"""	)
    root.delete("""banana"""	)
    assert not root.find("""banana"""	)
    assert root.find("""bananas"""	)

    return True







def 						A__  (					):







    '''simple docstring'''
    assert test_trie()







def 						A__  (					):







    '''simple docstring'''
    _lowerCamelCase     :		List[Any] 						=						RadixNode()
    _lowerCamelCase     :		Dict 						=						"""banana bananas bandanas bandana band apple all beast""".split()
    root.insert_many(__A	)

    print("""Words:"""   , __A	)
    print("""Tree:"""	)
    root.print_tree()


if __name__ == "__main__":
    main()





from __future__ import annotations

from math import pi
from typing import Protocol

import matplotlib.pyplot as plt
import numpy as np




class 	__snake_case	( __lowerCAmelCase		):





      '''simple docstring'''






      def 	_SCREAMING_SNAKE_CASE    (					self     :				Optional[Any]    ,  _UpperCamelCase     :				float)				->float:


          """simple docstring"""


          return 0.0







def 						A__  (					__A   , __A	):







    '''simple docstring'''
    _lowerCamelCase     :		int 						=						min([-20, np.min(fft_results[1 : samplerate // 2 - 1]	)]	)
    _lowerCamelCase     :		Tuple 						=						max([20, np.max(fft_results[1 : samplerate // 2 - 1]	)]	)
    return lowest, highest







def 						A__  (					__A   , __A	):







    '''simple docstring'''
    _lowerCamelCase     :		Tuple 						=						512
    _lowerCamelCase     :		Tuple 						=						[1] + [0] * (size - 1)
    _lowerCamelCase     :		Optional[Any] 						=						[filter_type.process(__A	) for item in inputs]

    _lowerCamelCase     :		Optional[Any] 						=						[0] * (samplerate - size)  # zero-padding
    outputs += filler
    _lowerCamelCase     :		Tuple 						=						np.abs(np.fft.fft(__A	)	)
    _lowerCamelCase     :		List[Any] 						=						20 * np.logaa(__A	)

    # Frequencies on log scale from 24 to nyquist frequency
    plt.xlim(24   , samplerate / 2 - 1	)
    plt.xlabel("""Frequency (Hz)"""	)
    plt.xscale("""log"""	)

    # Display within reasonable bounds
    _lowerCamelCase     :		Any 						=						get_bounds(__A   , __A	)
    plt.ylim(max([-80, bounds[0]]	)   , min([80, bounds[1]]	)	)
    plt.ylabel("""Gain (dB)"""	)

    plt.plot(__A	)
    plt.show()







def 						A__  (					__A   , __A	):







    '''simple docstring'''
    _lowerCamelCase     :		Tuple 						=						512
    _lowerCamelCase     :		Union[str, Any] 						=						[1] + [0] * (size - 1)
    _lowerCamelCase     :		int 						=						[filter_type.process(__A	) for item in inputs]

    _lowerCamelCase     :		Optional[Any] 						=						[0] * (samplerate - size)  # zero-padding
    outputs += filler
    _lowerCamelCase     :		Any 						=						np.angle(np.fft.fft(__A	)	)

    # Frequencies on log scale from 24 to nyquist frequency
    plt.xlim(24   , samplerate / 2 - 1	)
    plt.xlabel("""Frequency (Hz)"""	)
    plt.xscale("""log"""	)

    plt.ylim(-2 * pi   , 2 * pi	)
    plt.ylabel("""Phase shift (Radians)"""	)
    plt.plot(np.unwrap(__A   , -2 * pi	)	)
    plt.show()




