"""simple docstring"""


def 					__a   (		A      ):






     '''simple docstring'''



     lowercase__				 =							len(A      )
     for i in range(1    ,				A      ):
          lowercase__				 =							collection[i]
          lowercase__				 =							0
          lowercase__				 =							i - 1

          while low <= high:
               lowercase__				 =							(low + high) // 2
               if val < collection[mid]:
                    lowercase__				 =							mid - 1
               else:
                    lowercase__				 =							mid + 1
          for j in range(A    ,				A    ,				-1      ):
               lowercase__				 =							collection[j - 1]
          lowercase__				 =							val
     return collection


if __name__ == "__main__":
      lowerCAmelCase_:					str     =					input("Enter numbers separated by a comma:\n").strip()
      lowerCAmelCase_:					str     =					[int(item) for item in user_input.split(",")]
      print(binary_insertion_sort(unsorted))





"""simple docstring"""


from sympy import diff, lambdify, symbols
from sympy.functions import *  # noqa: F403







def 					__a   (		A    ,				A    ,				A = "x"    ,				A = 10**-10    ,				A = 1    ,				):






     '''simple docstring'''



     lowercase__				 =							symbols(A      )
     lowercase__				 =							lambdify(A    ,				A      )
     lowercase__				 =							lambdify(A    ,				diff(A    ,				A      )      )

     lowercase__				 =							starting_point

     while True:
          if diff_function(A      ) != 0:
               lowercase__				 =							prev_guess - multiplicity * func(A      ) / diff_function(
                   A      )
          else:
               raise ZeroDivisionError("Could not find root"      ) from None

          # Precision is checked by comparing the difference of consecutive guesses
          if abs(next_guess - prev_guess      ) < precision:
               return next_guess

          lowercase__				 =							next_guess


# Let's Execute
if __name__ == "__main__":
 # Find root of trigonometric function
 # Find value of pi
 print(F'The root of sin(x) = 0 is {newton_raphson("sin(x)", 2)}')

 # Find root of polynomial
 # Find fourth Root of 5
 print(F'The root of x**4 - 5 = 0 is {newton_raphson("x**4 -5", 0.4 +5j)}')

 # Find value of e
 print(
     "The root of log(y) - 1 = 0 is ",
     F'{newton_raphson("log(y) - 1", 2, variable="y")}',
 )

 # Exponential Roots
 print(
     "The root of exp(x) - 1 = 0 is",
     F'{newton_raphson("exp(x) - 1", 1_0, precision=0.005)}',
 )

 # Find root of cos(x)
 print(F'The root of cos(x) = 0 is {newton_raphson("cos(x)", 0)}')




