





import math as m




def        lowerCAmelCase_       (							UpperCamelCase_    ,						UpperCamelCase_    ,						UpperCamelCase_=0.0_01     )   ->						Optional[int]:
       return (f(a + h     ) - f(a - h     )) / (2 * h)




def        lowerCAmelCase_       (							UpperCamelCase_    ,						UpperCamelCase_=0    ,						UpperCamelCase_=100    ,						UpperCamelCase_=0.00_01    ,						UpperCamelCase_=1e-6    ,						UpperCamelCase_=False     )   ->						Optional[int]:
       UpperCamelCase_      				=     xa  # set the initial guess
       UpperCamelCase_      				=     [a]
       UpperCamelCase_      				=     abs(f(UpperCamelCase_     )     )
       UpperCamelCase_      				=     lambda UpperCamelCase_     : calc_derivative(UpperCamelCase_    ,						UpperCamelCase_    ,						h=UpperCamelCase_     )  # noqa: E731  Derivative of f(x)
       for _ in range(UpperCamelCase_     ):
              if fa(UpperCamelCase_     ) == 0:
                     raise ValueError("No converging solution found"     )
              UpperCamelCase_      				=     a - f(UpperCamelCase_     ) / fa(UpperCamelCase_     )  # Calculate the next estimate
              if logsteps:
                     steps.append(UpperCamelCase_     )
              if error < maxerror:
                     break
       else:
              raise ValueError("Iteration limit reached, no converging solution found"     )
       if logsteps:
              # If logstep is true, then log intermediate steps
              return a, error, steps
       return a, error


if __name__ == "__main__":
     from matplotlib import pyplot as plt

     _UpperCAmelCase				       = lambda x: m.tanh(x) ** 2 - m.exp(3 * x)  # noqa: E731
     _UpperCAmelCase       ,  _UpperCAmelCase       ,  _UpperCAmelCase				       = newton_raphson(
         f, xa=1_0, maxiter=1_0_0_0, step=1e-6, logsteps=True
     )
     plt.plot([abs(f(x)) for x in steps])
     plt.xlabel('step')
     plt.ylabel('error')
     plt.show()
     print(f'''solution = {{{solution:f}}}, error = {{{error:f}}}''')








def        lowerCAmelCase_       (							UpperCamelCase_    ,						UpperCamelCase_     )   ->						list:
       UpperCamelCase_      				=     sorted(UpperCamelCase_    ,						key=lambda UpperCamelCase_     : value[2]    ,						reverse=UpperCamelCase_     )

       # Create a list of size equal to the maximum deadline
       # and initialize it with -1
       UpperCamelCase_      				=     max(UpperCamelCase_    ,						key=lambda UpperCamelCase_     : value[1]     )[1]
       UpperCamelCase_      				=     [-1] * max_deadline

       # Finding the maximum profit and the count of jobs
       UpperCamelCase_      				=     0
       UpperCamelCase_      				=     0
       for job in jobs:
              # Find a free time slot for this job
              # (Note that we start from the last possible slot)
              for i in range(job[1] - 1    ,						-1    ,						-1     ):
                     if time_slots[i] == -1:
                            UpperCamelCase_      				=     job[0]
                            count += 1
                            max_profit += job[2]
                            break
       return [count, max_profit]


if __name__ == "__main__":
     import doctest

     doctest.testmod()

