




'''simple docstring'''



from collections.abc import Callable




def   lowercase__(			__UpperCamelCase:					Callable[[float], float]      ,__UpperCamelCase:					float      ,__UpperCamelCase:					float    ):

      """simple docstring"""






      SCREAMING_SNAKE_CASE   :      float    					=						a
      SCREAMING_SNAKE_CASE   :      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:
            SCREAMING_SNAKE_CASE   :      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:
                        SCREAMING_SNAKE_CASE   :      Dict    					=						mid
                  else:
                        SCREAMING_SNAKE_CASE   :      List[Any]    					=						mid
                  SCREAMING_SNAKE_CASE   :      Dict    					=						start + (end - start) / 2.0
            return mid




def   lowercase__(			__UpperCamelCase:					float    ):

      """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

def 						A							(  snake_case__     ):




			'''simple docstring'''


			for i in range(1		,					len(matrix[0]     )     ):
						matrix[0][i] += matrix[0][i - 1]

			# preprocessing the first column
			for i in range(1		,					len(snake_case__     )     ):
						matrix[i][0] += matrix[i - 1][0]

			# updating the path cost for current position
			for i in range(1		,					len(snake_case__     )     ):
						for j in range(1		,					len(matrix[0]     )     ):
									matrix[i][j] += min(matrix[i - 1][j]		,					matrix[i][j - 1]     )

			return matrix[-1][-1]


if __name__ == "__main__":
						import doctest

						doctest.testmod()


