






def      snake_case		(							UpperCAmelCase	:       Optional[int],						UpperCAmelCase	:       int   ):
    A	 =      0
    A	 =      len(snake_case_   ) - 1

    while left <= right:
        # avoid divided by 0 during interpolation
        if sorted_collection[left] == sorted_collection[right]:
            if sorted_collection[left] == item:
                return left
            else:
                return None

        A	 =      left + ((item - sorted_collection[left]) * (right - left)) // (
            sorted_collection[right] - sorted_collection[left]
        )

        # out of range check
        if point < 0 or point >= len(snake_case_   ):
            return None

        A	 =      sorted_collection[point]
        if current_item == item:
            return point
        else:
            if point < left:
                A	 =      left
                A	 =      point
            elif point > right:
                A	 =      right
                A	 =      point
            else:
                if item < current_item:
                    A	 =      point - 1
                else:
                    A	 =      point + 1
    return None







def      snake_case		(							UpperCAmelCase	:       int,						UpperCAmelCase	:       Union[str, Any],						UpperCAmelCase	:       List[str],						UpperCAmelCase	:       List[str]   ):

    # avoid divided by 0 during interpolation
    if sorted_collection[left] == sorted_collection[right]:
        if sorted_collection[left] == item:
            return left
        else:
            return None

    A	 =      left + ((item - sorted_collection[left]) * (right - left)) // (
        sorted_collection[right] - sorted_collection[left]
    )

    # out of range check
    if point < 0 or point >= len(snake_case_   ):
        return None

    if sorted_collection[point] == item:
        return point
    elif point < left:
        return interpolation_search_by_recursion(snake_case_,						snake_case_,						snake_case_,						snake_case_   )
    elif point > right:
        return interpolation_search_by_recursion(snake_case_,						snake_case_,						snake_case_,						snake_case_   )
    else:
        if sorted_collection[point] > item:
            return interpolation_search_by_recursion(
                snake_case_,						snake_case_,						snake_case_,						point - 1   )
        else:
            return interpolation_search_by_recursion(
                snake_case_,						snake_case_,						point + 1,						snake_case_   )







def      snake_case		(							UpperCAmelCase	:       str   ):
    if collection != sorted(snake_case_   ):
        raise ValueError('Collection must be ascending sorted'   )
    return True


if __name__ == "__main__":
     import sys
     lowerCAmelCase_           = 0
     if debug == 1:
          lowerCAmelCase_           = [10, 30, 40, 45, 50, 66, 77, 93]
          try:
               __assert_sorted(collection)
          except ValueError:
               sys.exit('Sequence must be ascending sorted to apply interpolation search')
          lowerCAmelCase_           = 67

     lowerCAmelCase_           = interpolation_search(collection, target)
     if result is not None:
          print(f'''{target} found at positions: {result}''')
     else:
          print('Not found')













import copy
import re
class      UpperCamelCase :







		"""simple docstring"""



		snake_case    =   "hp"
		snake_case    =   {}
		snake_case    =   None
		@classmethod
		def       A(  cls		:       Union[str, Any]						,_SCREAMING_SNAKE_CASE		:       int						,_SCREAMING_SNAKE_CASE		:       List[Any]		)    ->   int:


						'''simple docstring'''
						A	 =      prefix
						A	 =      defaults
						cls.build_naming_info()
		@staticmethod
		def       A(  _SCREAMING_SNAKE_CASE		:       List[str]						,_SCREAMING_SNAKE_CASE		:       List[Any]		)    ->   Optional[Any]:


						'''simple docstring'''
						if len(_SCREAMING_SNAKE_CASE		) == 0:
										return ""
						A	 =      None
						if any(char.isdigit() for char in word		):
										raise Exception(f'Parameters should not contain numbers: \'{word}\' contains a number'		)
						if word in info["short_word"]:
										return info["short_word"][word]
						for prefix_len in range(1						,len(_SCREAMING_SNAKE_CASE		) + 1		):
										A	 =      word[:prefix_len]
										if prefix in info["reverse_short_word"]:
														continue
										else:
														A	 =      prefix
														break

						if short_word is None:
										# Paranoid fallback
										def int_to_alphabetic(_SCREAMING_SNAKE_CASE		:       Optional[int]		):
														A	 =      ''
														while integer != 0:
																		A	 =      chr(ord('A'		) + integer % 1_0		) + s
																		integer //= 1_0
														return s

										A	 =      0
										while True:
														A	 =      word + '#' + int_to_alphabetic(_SCREAMING_SNAKE_CASE		)
														if sword in info["reverse_short_word"]:
																		continue
														else:
																		A	 =      sword
																		break

						A	 =      short_word
						A	 =      word
						return short_word
		@staticmethod
		def       A(  _SCREAMING_SNAKE_CASE		:       Optional[int]						,_SCREAMING_SNAKE_CASE		:       Optional[int]		)    ->   int:


						'''simple docstring'''
						A	 =      param_name.split('_'		)

						A	 =      [TrialShortNamer.shortname_for_word(_SCREAMING_SNAKE_CASE						,_SCREAMING_SNAKE_CASE		) for word in words]

						# We try to create a separatorless short name, but if there is a collision we have to fallback
						# to a separated short name
						A	 =      ['', '_']

						for separator in separators:
										A	 =      separator.join(_SCREAMING_SNAKE_CASE		)
										if shortname not in info["reverse_short_param"]:
														A	 =      shortname
														A	 =      param_name
														return shortname

						return param_name
		@staticmethod
		def       A(  _SCREAMING_SNAKE_CASE		:       Optional[Any]						,_SCREAMING_SNAKE_CASE		:       Optional[int]		)    ->   List[str]:


						'''simple docstring'''
						A	 =      TrialShortNamer.shortname_for_key(_SCREAMING_SNAKE_CASE						,_SCREAMING_SNAKE_CASE		)
						A	 =      short_name
						A	 =      param_name
		@classmethod
		def       A(  cls		:       Optional[int]		)    ->   str:


						'''simple docstring'''
						if cls.NAMING_INFO is not None:
										return

						A	 =      {
						    'short_word': {},
						    'reverse_short_word': {},
						    'short_param': {},
						    'reverse_short_param': {},
						}

						A	 =      list(cls.DEFAULTS.keys()		)

						for k in field_keys:
										cls.add_new_param_name(_SCREAMING_SNAKE_CASE						,_SCREAMING_SNAKE_CASE		)

						A	 =      info
		@classmethod
		def       A(  cls		:       List[str]						,_SCREAMING_SNAKE_CASE		:       str		)    ->   List[Any]:


						'''simple docstring'''
						cls.build_naming_info()
						assert cls.PREFIX is not None
						A	 =      [copy.copy(cls.PREFIX		)]

						for k, v in params.items():
										if k not in cls.DEFAULTS:
														raise Exception(f'You should provide a default value for the param name {k} with value {v}'		)
										if v == cls.DEFAULTS[k]:
														# The default value is not added to the name
														continue

										A	 =      cls.NAMING_INFO['short_param'][k]

										if isinstance(_SCREAMING_SNAKE_CASE						,_SCREAMING_SNAKE_CASE		):
														A	 =      1 if v else 0

										A	 =      '' if isinstance(_SCREAMING_SNAKE_CASE						,(int, float)		) else '-'
										A	 =      f'{key}{sep}{v}'
										name.append(_SCREAMING_SNAKE_CASE		)

						return "_".join(_SCREAMING_SNAKE_CASE		)







		@classmethod
		def       A(  cls		:       int						,_SCREAMING_SNAKE_CASE		:       Optional[int]		)    ->   str:


						'''simple docstring'''
						A	 =      repr[len(cls.PREFIX		) + 1 :]
						if repr == "":
										A	 =      []
						else:
										A	 =      repr.split('_'		)

						A	 =      {}

						for value in values:
										if "-" in value:
														A ,		A	 =      value.split('-'		)
										else:
														A	 =      re.sub('[0-9.]'						,''						,_SCREAMING_SNAKE_CASE		)
														A	 =      float(re.sub('[^0-9.]'						,''						,_SCREAMING_SNAKE_CASE		)		)

										A	 =      cls.NAMING_INFO['reverse_short_param'][p_k]

										A	 =      p_v

						for k in cls.DEFAULTS:
										if k not in parameters:
														A	 =      cls.DEFAULTS[k]

						return parameters





