
"""simple docstring"""




from collections.abc import Callable




def 			_lowerCAmelCase		(		_UpperCamelCase			,					_UpperCamelCase			,					_UpperCamelCase    ):






  """simple docstring"""



  _lowercase:      float   			=  a
  _lowercase:      float   			=  b
  if function(_UpperCamelCase    ) == 0:  # one of the a or b is a root for the function
    return a
  elif function(_UpperCamelCase    ) == 0:
    return b
  elif (
      function(_UpperCamelCase    ) * function(_UpperCamelCase    ) > 0
  ):  # if none of these are root and they are both positive or negative,
    # then this algorithm can't find the root
    raise ValueError('''could not find root in given interval.'''    )
  else:
    _lowercase:      float   			=  start + (end - start) / 2.0
    while abs(start - mid    ) > 10**-7:  # until precisely equals to 10^-7
      if function(_UpperCamelCase    ) == 0:
        return mid
      elif function(_UpperCamelCase    ) * function(_UpperCamelCase    ) < 0:
        _lowercase:      Union[str, Any]   			=  mid
      else:
        _lowercase:      Any   			=  mid
      _lowercase:      List[Any]   			=  start + (end - start) / 2.0
    return mid




def 			_lowerCAmelCase		(		_UpperCamelCase    ):






  """simple docstring"""



  return x**3 - 2 * x - 5


if __name__ == "__main__":
  print(bisection(f, 1, 1_0_0_0))

  import doctest

  doctest.testmod()


"""simple docstring"""




from __future__ import annotations

import typing
from collections import Counter




def 			_lowerCAmelCase		(		_UpperCamelCase    ):






  """simple docstring"""



  _lowercase:      typing.Counter[int]   			=  Counter()
  for base in range(1			,					max_perimeter + 1    ):
    for perpendicular in range(_UpperCamelCase			,					max_perimeter + 1    ):
      _lowercase:      str   			=  (base * base + perpendicular * perpendicular) ** 0.5
      if hypotenuse == int(_UpperCamelCase    ):
        _lowercase:      str   			=  int(base + perpendicular + hypotenuse    )
        if perimeter > max_perimeter:
          continue
        triplets[perimeter] += 1
  return triplets




def 			_lowerCAmelCase		(		_UpperCamelCase = 1_000    ):






  """simple docstring"""



  _lowercase:      int   			=  pythagorean_triple(_UpperCamelCase    )
  return triplets.most_common(1    )[0][0]


if __name__ == "__main__":
  print(f"""Perimeter {solution()} has maximum solutions""")
