"""simple docstring"""



import math
class 	__UpperCAmelCase						:







   '''simple docstring'''





   def __init__( self      ,			snake_case_      ,			snake_case_      ,			snake_case_      ,			snake_case_       ):







          '''simple docstring'''


          A__					:    str														= x
          A__					:    List[Any]														= y
          A__					:    Dict														= step_size
          A__					:    int														= function_to_optimize





   def 		lowerCamelCase				( self       ):







          '''simple docstring'''


          return self.function(self.x      ,			self.y       )





   def 		lowerCamelCase				( self       ):







          '''simple docstring'''


          A__					:    Any														= self.step_size
          return [
              SearchProblem(snake_case_      ,			snake_case_      ,			snake_case_      ,			self.function       )
              for x, y in (
                  (self.x - step_size, self.y - step_size),
                  (self.x - step_size, self.y),
                  (self.x - step_size, self.y + step_size),
                  (self.x, self.y - step_size),
                  (self.x, self.y + step_size),
                  (self.x + step_size, self.y - step_size),
                  (self.x + step_size, self.y),
                  (self.x + step_size, self.y + step_size),
              )
          ]





   def __hash__( self       ):







          '''simple docstring'''


          return hash(str(self       )       )





   def __eq__( self      ,			snake_case_       ):







          '''simple docstring'''


          if isinstance(snake_case_      ,			snake_case_       ):
                 return hash(str(self       )       ) == hash(str(snake_case_       )       )
          return False





   def __str__( self       ):







          '''simple docstring'''


          return F'''x: {self.x} y: {self.y}'''





def    _A(		lowerCAmelCase ,     lowerCAmelCase = True ,     lowerCAmelCase = math.inf ,     lowerCAmelCase = -math.inf ,     lowerCAmelCase = math.inf ,     lowerCAmelCase = -math.inf ,     lowerCAmelCase = False ,     lowerCAmelCase = 1_0000 ,     ):
       A__					:    Dict														= search_prob
       A__					:    int														= []  # list to store the current score at each iteration
       A__					:    Optional[int]														= 0
       A__					:    Any														= False
       A__					:    Optional[int]														= set()
       while not solution_found and iterations < max_iter:
              visited.add(lowerCAmelCase       )
              iterations += 1
              A__					:    List[Any]														= current_state.score()
              scores.append(lowerCAmelCase       )
              A__					:    Any														= current_state.get_neighbors()
              A__					:    Union[str, Any]														= -math.inf
              A__					:    Tuple														= math.inf
              A__					:    List[str]														= None  # to hold the next best neighbor
              for neighbor in neighbors:
                     if neighbor in visited:
                            continue  # do not want to visit the same state again
                     if (
                         neighbor.x > max_x
                         or neighbor.x < min_x
                         or neighbor.y > max_y
                         or neighbor.y < min_y
                     ):
                            continue  # neighbor outside our bounds
                     A__					:    List[Any]														= neighbor.score() - current_score
                     if find_max:  # finding max
                            # going to direction with greatest ascent
                            if change > max_change and change > 0:
                                   A__					:    Any														= change
                                   A__					:    List[Any]														= neighbor
                     else:  # finding min
                            # to direction with greatest descent
                            if change < min_change and change < 0:
                                   A__					:    Dict														= change
                                   A__					:    Tuple														= neighbor
              if next_state is not None:
                     # we found at least one neighbor which improved the current state
                     A__					:    Dict														= next_state
              else:
                     # since we have no neighbor that improves the solution we stop the search
                     A__					:    List[Any]														= True

       if visualization:
              from matplotlib import pyplot as plt

              plt.plot(range(lowerCAmelCase       ) ,     lowerCAmelCase       )
              plt.xlabel("""Iterations"""       )
              plt.ylabel("""Function values"""       )
              plt.show()

       return current_state


if __name__ == "__main__":
    import doctest

    doctest.testmod()

    def    _A(		lowerCAmelCase ,     lowerCAmelCase       ):
           return (x**2) + (y**2)

    # starting the problem with initial coordinates (3, 4)
    _UpperCamelCase         =		SearchProblem(x=3, y=4, step_size=1, function_to_optimize=test_fa)
    _UpperCamelCase         =		hill_climbing(prob, find_max=False)
    print(
        "The minimum score for f(x, y) = x^2 + y^2 found via hill climbing: "
        F'{local_min.score()}'
    )

    # starting the problem with initial coordinates (12, 47)
    _UpperCamelCase         =		SearchProblem(x=12, y=47, step_size=1, function_to_optimize=test_fa)
    _UpperCamelCase         =		hill_climbing(
        prob, find_max=False, max_x=1_00, min_x=5, max_y=50, min_y=-5, visualization=True
    )
    print(
        "The minimum score for f(x, y) = x^2 + y^2 with the domain 100 > x > 5 "
        F'and 50 > y > - 5 found via hill climbing: {local_min.score()}'
    )

    def    _A(		lowerCAmelCase ,     lowerCAmelCase       ):
           return (3 * x**2) - (6 * y)

    _UpperCamelCase         =		SearchProblem(x=3, y=4, step_size=1, function_to_optimize=test_fa)
    _UpperCamelCase         =		hill_climbing(prob, find_max=True)



    print(
        "The maximum score for f(x, y) = x^2 + y^2 found via hill climbing: "
        F'{local_min.score()}'
    )






"""simple docstring"""



def    _A(		lowerCAmelCase       ):
							A__					:    str														= len(lowerCAmelCase       )
							A__					:    List[Any]														= [0] * length
							A__					:    Union[str, Any]														= [[False for i in range(lowerCAmelCase       )] for j in range(lowerCAmelCase       )]
							for i, c in enumerate(lowerCAmelCase       ):
														A__					:    Dict														= i
														for j in range(i + 1       ):
																					if c == string[j] and (i - j < 2 or is_palindromic[j + 1][i - 1]):
																												A__					:    List[str]														= True
																												A__					:    Optional[Any]														= min(lowerCAmelCase ,     0 if j == 0 else (cut[j - 1] + 1)       )
														A__					:    Optional[int]														= mincut
							return cut[length - 1]


if __name__ == "__main__":
				_UpperCamelCase         =		input("Enter the string: ").strip()
				_UpperCamelCase         =		find_minimum_partitions(s)
				print(F'Minimum number of partitions required for the \'{s}\' is {ans}')





