

def 					__lowercase      (     _A						,    _A			)     ->						Optional[Any]:
      SCREAMING_SNAKE_CASE :      Any       =   0
      SCREAMING_SNAKE_CASE :      List[Any]       =   len(_A			) - 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

            SCREAMING_SNAKE_CASE :      List[str]       =   left + ((item - sorted_collection[left]) * (right - left)) // (
                sorted_collection[right] - sorted_collection[left]
            )

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

            SCREAMING_SNAKE_CASE :      Dict       =   sorted_collection[point]
            if current_item == item:
                  return point
            else:
                  if point < left:
                        SCREAMING_SNAKE_CASE :      Any       =   left
                        SCREAMING_SNAKE_CASE :      Optional[Any]       =   point
                  elif point > right:
                        SCREAMING_SNAKE_CASE :      Optional[int]       =   right
                        SCREAMING_SNAKE_CASE :      Tuple       =   point
                  else:
                        if item < current_item:
                              SCREAMING_SNAKE_CASE :      int       =   point - 1
                        else:
                              SCREAMING_SNAKE_CASE :      List[str]       =   point + 1
      return None






def 					__lowercase      (     _A						,    _A						,    _A						,    _A			)     ->						str:

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

      SCREAMING_SNAKE_CASE :      int       =   left + ((item - sorted_collection[left]) * (right - left)) // (
          sorted_collection[right] - sorted_collection[left]
      )

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

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






def 					__lowercase      (     _A			)     ->						List[str]:
      if collection != sorted(_A			):
            raise ValueError("""Collection must be ascending sorted"""			)
      return True


if __name__ == "__main__":
  import sys
  UpperCAmelCase__ :     Optional[Any]				    =    0
  if debug == 1:
    UpperCAmelCase__ :     Optional[int]				    =    [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""")
    UpperCAmelCase__ :     int				    =    67

  UpperCAmelCase__ :     Optional[Any]				    =    interpolation_search(collection, target)
  if result is not None:
    print(F"""{target} found at positions: {result}""")
  else:
    print("""Not found""")







from __future__ import annotations

import numpy as np






def 					__lowercase      (     _A			)     ->						tuple[np.ndarray, np.ndarray]:
      SCREAMING_SNAKE_CASE     ,	SCREAMING_SNAKE_CASE :      Dict       =   np.shape(_A			)
      if rows != columns:
            SCREAMING_SNAKE_CASE :      int       =   (
                """'table' has to be of square shaped array but got a """
                F"{rows}x{columns} array:\n{table}"
            )
            raise ValueError(_A			)

      SCREAMING_SNAKE_CASE :      Union[str, Any]       =   np.zeros((rows, columns)			)
      SCREAMING_SNAKE_CASE :      Optional[Any]       =   np.zeros((rows, columns)			)
      for i in range(_A			):
            for j in range(_A			):
                  SCREAMING_SNAKE_CASE :      Tuple       =   sum(lower[i][k] * upper[k][j] for k in range(_A			)			)
                  if upper[j][j] == 0:
                        raise ArithmeticError("""No LU decomposition exists"""			)
                  SCREAMING_SNAKE_CASE :      Union[str, Any]       =   (table[i][j] - total) / upper[j][j]
            SCREAMING_SNAKE_CASE :      Optional[Any]       =   1
            for j in range(_A						,    _A			):
                  SCREAMING_SNAKE_CASE :      List[str]       =   sum(lower[i][k] * upper[k][j] for k in range(_A			)			)
                  SCREAMING_SNAKE_CASE :      Optional[Any]       =   table[i][j] - total
      return lower, upper


if __name__ == "__main__":
  import doctest

  doctest.testmod()




