



"""simple docstring"""





class      _lowercase :


      def __init__(    self				:	Union[str, Any]							,   a				:	str = ""							,   a				:	bool = False						):





            """simple docstring"""







            __snake_case      :    dict[str, RadixNode]  			={}

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

            __snake_case      :    List[str]  			=prefix


      def _UpperCamelCase						(    self				:	Dict							,   a				:	str						):





            """simple docstring"""







            __snake_case      :    Optional[Any]  			=0
            for q, w in zip(self.prefix							,   a						):
                  if q != w:
                        break

                  x += 1

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


      def _UpperCamelCase						(    self				:	Tuple							,   a				:	list[str]						):





            """simple docstring"""







            for word in words:
                  self.insert(a						)


      def _UpperCamelCase						(    self				:	Optional[int]							,   a				:	str						):





            """simple docstring"""







            if self.prefix == word:
                  __snake_case      :    Optional[Any]  			=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:
                  __snake_case      :    List[str]  			=RadixNode(prefix=a							,   is_leaf=a						)

            else:
                  __snake_case      :    int  			=self.nodes[word[0]]
                  __snake_case      :    Any  			=incoming_node.match(
                      a						)

                  # 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(a						)

                  # 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:
                        __snake_case      :    Union[str, Any]  			=remaining_prefix

                        __snake_case      :    Optional[int]  			=self.nodes[matching_string[0]]
                        __snake_case      :    Tuple  			=RadixNode(a							,   a						)
                        __snake_case      :    Dict  			=aux_node

                        if remaining_word == "":
                              __snake_case      :    List[str]  			=True
                        else:
                              self.nodes[matching_string[0]].insert(a						)


      def _UpperCamelCase						(    self				:	Optional[int]							,   a				:	str						):





            """simple docstring"""







            __snake_case      :    Any  			=self.nodes.get(word[0]							,   a						)
            if not incoming_node:
                  return False
            else:
                  __snake_case      :    Union[str, Any]  			=incoming_node.match(
                      a						)
                  # 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(a						)


      def _UpperCamelCase						(    self				:	Union[str, Any]							,   a				:	str						):





            """simple docstring"""







            __snake_case      :    List[str]  			=self.nodes.get(word[0]							,   a						)
            if not incoming_node:
                  return False
            else:
                  __snake_case      :    List[str]  			=incoming_node.match(
                      a						)
                  # 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(a						)
                  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:
                                          __snake_case      :    Optional[Any]  			=list(self.nodes.values()						)[0]
                                          __snake_case      :    List[str]  			=merging_node.is_leaf
                                          self.prefix += merging_node.prefix
                                          __snake_case      :    str  			=merging_node.nodes
                    # If there is more than 1 edge, we just mark it as non-leaf
                              elif len(incoming_node.nodes						) > 1:
                                    __snake_case      :    Any  			=False
                              # If there is 1 edge, we merge it with its child
                              else:
                                    __snake_case      :    List[Any]  			=list(incoming_node.nodes.values()						)[0]
                                    __snake_case      :    str  			=merging_node.is_leaf
                                    incoming_node.prefix += merging_node.prefix
                                    __snake_case      :    Any  			=merging_node.nodes

                              return True







      def _UpperCamelCase						(    self				:	int							,   a				:	int = 0						):





            """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     __lowercase					(    )					->					bool:
      __snake_case      :    Optional[Any]  			='''banana bananas bandana band apple all beast'''.split()
      __snake_case      :    List[Any]  			=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     __lowercase					(    )					->					None:
      assert test_trie()



def     __lowercase					(    )					->					None:
      __snake_case      :    Optional[Any]  			=RadixNode()
      __snake_case      :    Optional[int]  			='''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()










"""simple docstring"""





from __future__ import annotations

import math
from collections import Counter
from string import ascii_lowercase



def     __lowercase					(    a :				str )					->					None:
      __snake_case			,				__snake_case      :    List[Any]  			=analyze_text(a )
      __snake_case      :    Union[str, Any]  			=list(''' ''' + ascii_lowercase )
      # what is our total sum of probabilities.
      __snake_case      :    List[Any]  			=sum(single_char_strings.values() )

      # one length string
      __snake_case      :    str  			=0
      # for each alpha we go in our dict and if it is in it we calculate entropy
      for ch in my_alphas:
            if ch in single_char_strings:
                  __snake_case      :    Union[str, Any]  			=single_char_strings[ch]
                  __snake_case      :    Any  			=my_str / all_sum
                  my_fir_sum += prob * math.loga(a )  # entropy formula.

    # print entropy
      print(f'''{round(-1 * my_fir_sum ):.1f}''' )

      # two len string
      __snake_case      :    Optional[Any]  			=sum(two_char_strings.values() )
      __snake_case      :    Dict  			=0
      # for each alpha (two in size) calculate entropy.
      for cha in my_alphas:
            for cha in my_alphas:
                  __snake_case      :    Tuple  			=cha + cha
                  if sequence in two_char_strings:
                        __snake_case      :    List[Any]  			=two_char_strings[sequence]
                        __snake_case      :    Tuple  			=int(a ) / all_sum
                        my_sec_sum += prob * math.loga(a )

    # print second entropy
      print(f'''{round(-1 * my_sec_sum ):.1f}''' )

      # print the difference between them
      print(f'''{round((-1 * my_sec_sum) - (-1 * my_fir_sum) ):.1f}''' )



def     __lowercase					(    a :				str )					->					tuple[dict, dict]:
      __snake_case      :    List[str]  			=Counter()  # type: ignore
      __snake_case      :    Union[str, Any]  			=Counter()  # type: ignore
      single_char_strings[text[-1]] += 1

      # first case when we have space at start.
      two_char_strings[" " + text[0]] += 1
      for i in range(0       ,		len(a ) - 1 ):
            single_char_strings[text[i]] += 1
            two_char_strings[text[i : i + 2]] += 1
      return single_char_strings, two_char_strings



def     __lowercase					(    )					->					int:
      import doctest

      doctest.testmod()
      # text = (
      #     "Had repulsive dashwoods suspicion sincerity but advantage now him. Remark "
      #     "easily garret nor nay. Civil those mrs enjoy shy fat merry. You greatest "
      #     "jointure saw horrible. He private he on be imagine suppose. Fertile "
      #     "beloved evident through no service elderly is. Blind there if every no so "
      #     "at. Own neglected you preferred way sincerity delivered his attempted. To "
      #     "of message cottage windows do besides against uncivil.  Delightful "
      #     "unreserved impossible few estimating men favourable see entreaties. She "
      #     "propriety immediate was improving. He or entrance humoured likewise "
      #     "moderate. Much nor game son say feel. Fat make met can must form into "
      #     "gate. Me we offending prevailed discovery. "
      # )

      # calculate_prob(text)


if __name__ == "__main__":
    main()


