





'''simple docstring'''




class 					SCREAMING_SNAKE_CASE       :


     def __init__(		self):

          '''simple docstring'''






          __A		:					dict[str, TrieNode]						=			{}  # Mapping from char to TrieNode
          __A		:					Optional[Any]						=			False


     def 				SCREAMING_SNAKE_CASE    (		self		,      _UpperCAmelCase):

          '''simple docstring'''






          for word in words:
               self.insert(_UpperCAmelCase)


     def 				SCREAMING_SNAKE_CASE    (		self		,      _UpperCAmelCase):

          '''simple docstring'''






          __A		:					Dict						=			self
          for char in word:
               if char not in curr.nodes:
                    __A		:					Optional[Any]						=			TrieNode()
               __A		:					Any						=			curr.nodes[char]
          __A		:					str						=			True


     def 				SCREAMING_SNAKE_CASE    (		self		,      _UpperCAmelCase):

          '''simple docstring'''






          __A		:					Union[str, Any]						=			self
          for char in word:
               if char not in curr.nodes:
                    return False
               __A		:					Optional[int]						=			curr.nodes[char]
          return curr.is_leaf


     def 				SCREAMING_SNAKE_CASE    (		self		,      _UpperCAmelCase):

          '''simple docstring'''






          def _delete(_UpperCAmelCase		,      _UpperCAmelCase		,      _UpperCAmelCase) -> bool:
               if index == len(_UpperCAmelCase):
                    # If word does not exist
                    if not curr.is_leaf:
                         return False
                    __A		:					Any						=			False
                    return len(curr.nodes) == 0
               __A		:					Dict						=			word[index]
               __A		:					Optional[Any]						=			curr.nodes.get(_UpperCAmelCase)
               # If char not in current trie node
               if not char_node:
                    return False
               # Flag to check if node can be deleted
               __A		:					int						=			_delete(_UpperCAmelCase		,      _UpperCAmelCase		,      index + 1)
               if delete_curr:
                    del curr.nodes[char]
                    return len(curr.nodes) == 0
               return delete_curr

          _delete(self		,      _UpperCAmelCase		,      0)






def 			_lowerCAmelCase     (    __snake_case    :					TrieNode					,				__snake_case    :					str     )	->	None:
     if node.is_leaf:
          print(__snake_case					,				end=' '     )

     for key, value in node.nodes.items():
          print_words(__snake_case					,				word + key     )






def 			_lowerCAmelCase     (    )	->	bool:
     __A		:					Tuple						=			'banana bananas bandana band apple all beast'.split()
     __A		:					Optional[Any]						=			TrieNode()
     root.insert_many(__snake_case     )
     # print_words(root, "")
     assert all(root.find(__snake_case     ) for word in words     )
     assert root.find('banana'     )
     assert not root.find('bandanas'     )
     assert not root.find('apps'     )
     assert root.find('apple'     )
     assert root.find('all'     )
     root.delete('all'     )
     assert not root.find('all'     )
     root.delete('banana'     )
     assert not root.find('banana'     )
     assert root.find('bananas'     )
     return True






def 			_lowerCAmelCase     (    __snake_case    :					str					,				__snake_case    :					bool     )	->	None:
     print(str(__snake_case     )					,				'works!' if passes else 'doesn\'t work :('     )






def 			_lowerCAmelCase     (    )	->	None:
     assert test_trie()






def 			_lowerCAmelCase     (    )	->	None:
     print_results('Testing trie functionality'					,				test_trie()     )


if __name__ == "__main__":
  main()




'''simple docstring'''





from __future__ import annotations

import math




def 							lowerCamelCase	(					_snake_case	:    float  ,_snake_case	:    int							):





    '''simple docstring'''


    lowercase__									=    u
    for i in range(1  ,_snake_case							):
        lowercase__									=    temp * (u - i)
    return temp




def 							lowerCamelCase	(					):





    '''simple docstring'''


    lowercase__									=    int(input("enter the numbers of values: "							)							)
    lowercase__									=    []
    for _ in range(_snake_case							):
        y.append([]							)
    for i in range(_snake_case							):
        for j in range(_snake_case							):
            y[i].append(_snake_case							)
            lowercase__									=    0

    print("enter the values of parameters in a list: "							)
    lowercase__									=    list(map(_snake_case  ,input().split()							)							)

    print("enter the values of corresponding parameters: "							)
    for i in range(_snake_case							):
        lowercase__									=    float(input()							)

    lowercase__									=    int(input("enter the value to interpolate: "							)							)
    lowercase__									=    (value - x[0]) / (x[1] - x[0])

    # for calculating forward difference table

    for i in range(1  ,_snake_case							):
        for j in range(n - i							):
            lowercase__									=    y[j + 1][i - 1] - y[j][i - 1]

    lowercase__									=    y[0][0]
    for i in range(1  ,_snake_case							):
        summ += (ucal(_snake_case  ,_snake_case							) * y[0][i]) / math.factorial(_snake_case							)

    print(f'''the value at {value} is {summ}'''							)


if __name__ == "__main__":
 main()




