






'''simple docstring'''






import math
import random
from typing import Any

from .hill_climbing import SearchProblem




def        _SCREAMING_SNAKE_CASE  (				A  :       Optional[int]  ,		A  :       bool = True  ,		A  :       float = math.inf  ,		A  :       float = -math.inf  ,		A  :       float = math.inf  ,		A  :       float = -math.inf  ,		A  :       bool = False  ,		A  :       float = 1_00  ,		A  :       float = 0.01  ,		A  :       float = 1  ,		)    -> Any:







   """simple docstring"""
   __snake_case				:      List[str]     							= False
   __snake_case				:      List[str]     							= search_prob
   __snake_case				:      Any     							= start_temperate
   __snake_case				:      Any     							= []
   __snake_case				:      Union[str, Any]     							= 0
   __snake_case				:      Optional[int]     							= None

   while not search_end:
      __snake_case				:      Dict     							= current_state.score()
      if best_state is None or current_score > best_state.score():
         __snake_case				:      List[Any]     							= current_state
      scores.append(A  )
      iterations += 1
      __snake_case				:      Tuple     							= None
      __snake_case				:      Optional[int]     							= current_state.get_neighbors()
      while (
          next_state is None and neighbors
      ):  # till we do not find a neighbor that we can move to
         __snake_case				:      Optional[Any]     							= random.randint(0  ,		len(A  ) - 1  )  # picking a random neighbor
         __snake_case				:      Union[str, Any]     							= neighbors.pop(A  )
         __snake_case				:      Dict     							= picked_neighbor.score() - current_score

         if (
             picked_neighbor.x > max_x
             or picked_neighbor.x < min_x
             or picked_neighbor.y > max_y
             or picked_neighbor.y < min_y
         ):
            continue  # neighbor outside our bounds

         if not find_max:
            __snake_case				:      Optional[Any]     							= change * -1  # in case we are finding minimum
         if change > 0:  # improves the solution
            __snake_case				:      List[str]     							= picked_neighbor
         else:
            __snake_case				:      Any     							= (math.e) ** (
                change / current_temp
            )  # probability generation function
            if random.random() < probability:  # random number within probability
               __snake_case				:      Union[str, Any]     							= picked_neighbor
      __snake_case				:      int     							= current_temp - (current_temp * rate_of_decrease)

      if current_temp < threshold_temp or next_state is None:
         # temperature below threshold, or could not find a suitable neighbor
         __snake_case				:      str     							= True
      else:
         __snake_case				:      Optional[int]     							= next_state

   if visualization:
      from matplotlib import pyplot as plt

      plt.plot(range(A  )  ,		A  )
      plt.xlabel('Iterations'  )
      plt.ylabel('Function values'  )
      plt.show()
   return best_state


if __name__ == "__main__":




      def        _SCREAMING_SNAKE_CASE  (				A  :       Dict  ,		A  :       List[str]  )    -> Dict:







         """simple docstring"""
         return (x**2) + (y**2)

      # starting the problem with initial coordinates (12, 47)
      __A    	=   SearchProblem(x=1_2, y=4_7, step_size=1, function_to_optimize=test_fa)
      __A    	=   simulated_annealing(
          prob, find_max=False, max_x=1_0_0, min_x=5, max_y=5_0, 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()}'''
      )

      # starting the problem with initial coordinates (12, 47)
      __A    	=   SearchProblem(x=1_2, y=4_7, step_size=1, function_to_optimize=test_fa)
      __A    	=   simulated_annealing(
          prob, find_max=True, max_x=1_0_0, min_x=5, max_y=5_0, min_y=-5, visualization=True
      )
      print(
          '''The maximum 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        _SCREAMING_SNAKE_CASE  (				A  :       str  ,		A  :       List[Any]  )    -> Any:







         """simple docstring"""
         return (3 * x**2) - (6 * y)

      __A    	=   SearchProblem(x=3, y=4, step_size=1, function_to_optimize=test_fa)
      __A    	=   simulated_annealing(prob, find_max=False, visualization=True)
      print(
          '''The minimum score for f(x, y) = 3*x^2 - 6*y found via hill climbing: '''
          f'''{local_min.score()}'''
      )

      __A    	=   SearchProblem(x=3, y=4, step_size=1, function_to_optimize=test_fa)
      __A    	=   simulated_annealing(prob, find_max=True, visualization=True)





      print(
          '''The maximum score for f(x, y) = 3*x^2 - 6*y found via hill climbing: '''
          f'''{local_min.score()}'''
      )







'''simple docstring'''






from __future__ import annotations

import math
import random
from collections.abc import Collection
from typing import overload




class a_    :







   def __init__(self					,   __a = None)			->      None:
      """simple docstring"""






      if components is None:
         __snake_case				:      List[str]     							= []
      __snake_case				:      Optional[int]     							= list(__a)







   def __len__(self)			->      int:
      """simple docstring"""






      return len(self.__components)







   def __str__(self)			->      str:
      """simple docstring"""






      return "(" + ",".join(map(__a					,   self.__components)) + ")"







   def __add__(self					,   __a)			->      Vector:
      """simple docstring"""






      __snake_case				:      Optional[Any]     							= len(self)
      if size == len(__a):
         __snake_case				:      Optional[int]     							= [self.__components[i] + other.component(__a) for i in range(__a)]
         return Vector(__a)
      else:
         raise Exception('must have the same size')







   def __sub__(self					,   __a)			->      Vector:
      """simple docstring"""






      __snake_case				:      Optional[Any]     							= len(self)
      if size == len(__a):
         __snake_case				:      Optional[int]     							= [self.__components[i] - other.component(__a) for i in range(__a)]
         return Vector(__a)
      else:  # error case
         raise Exception('must have the same size')







   @overload
   def __mul__(self					,   __a)			->      Vector:
      """simple docstring"""






      ...







   @overload
   def __mul__(self					,   __a)			->      float:
      """simple docstring"""






      ...







   def __mul__(self					,   __a)			->      float | Vector:
      """simple docstring"""






      if isinstance(__a					,   (float, int)):
         __snake_case				:      str     							= [c * other for c in self.__components]
         return Vector(__a)
      elif isinstance(__a					,   __a) and len(self) == len(__a):
         __snake_case				:      List[Any]     							= len(self)
         __snake_case				:      Dict     							= [self.__components[i] * other.component(__a) for i in range(__a)]
         return sum(__a)
      else:  # error case
         raise Exception('invalid operand!')







   def     SCREAMING_SNAKE_CASE__					(self)			->      Vector:
      """simple docstring"""






      return Vector(self.__components)







   def     SCREAMING_SNAKE_CASE__					(self					,   __a)			->      float:
      """simple docstring"""






      if isinstance(__a					,   __a) and -len(self.__components) <= i < len(self.__components):
         return self.__components[i]
      else:
         raise Exception('index out of range')







   def     SCREAMING_SNAKE_CASE__					(self					,   __a					,   __a)			->      None:
      """simple docstring"""






      assert -len(self.__components) <= pos < len(self.__components)
      __snake_case				:      int     							= value







   def     SCREAMING_SNAKE_CASE__					(self)			->      float:
      """simple docstring"""






      if len(self.__components) == 0:
         raise Exception('Vector is empty')
      __snake_case				:      Tuple     							= [c**2 for c in self.__components]
      return math.sqrt(sum(__a))







   def     SCREAMING_SNAKE_CASE__					(self					,   __a					,   __a = False)			->      float:
      """simple docstring"""






      __snake_case				:      Tuple     							= self * other
      __snake_case				:      Optional[int]     							= self.euclidean_length() * other.euclidean_length()
      if deg:
         return math.degrees(math.acos(num / den))
      else:
         return math.acos(num / den)




def        _SCREAMING_SNAKE_CASE  (				A  :       int  )    -> Vector:







   """simple docstring"""
   assert isinstance(A  ,		A  )
   return Vector([0] * dimension  )




def        _SCREAMING_SNAKE_CASE  (				A  :       int  ,		A  :       int  )    -> Vector:







   """simple docstring"""
   assert isinstance(A  ,		A  ) and (isinstance(A  ,		A  ))
   __snake_case				:      Any     							= [0] * dimension
   __snake_case				:      int     							= 1
   return Vector(A  )




def        _SCREAMING_SNAKE_CASE  (				A  :       float  ,		A  :       Vector  ,		A  :       Vector  )    -> Vector:







   """simple docstring"""
   assert (
       isinstance(A  ,		A  )
       and isinstance(A  ,		A  )
       and (isinstance(A  ,		(int, float)  ))
   )
   return x * scalar + y




def        _SCREAMING_SNAKE_CASE  (				A  :       int  ,		A  :       int  ,		A  :       int  )    -> Vector:







   """simple docstring"""
   random.seed(A  )
   __snake_case				:      List[Any]     							= [random.randint(A  ,		A  ) for _ in range(A  )]
   return Vector(A  )




class a_    :







   def __init__(self					,   __a					,   __a					,   __a)			->      None:
      """simple docstring"""






      __snake_case				:      Union[str, Any]     							= matrix
      __snake_case				:      int     							= w
      __snake_case				:      str     							= h







   def __str__(self)			->      str:
      """simple docstring"""






      __snake_case				:      Dict     							= ''
      for i in range(self.__height):
         ans += "|"
         for j in range(self.__width):
            if j < self.__width - 1:
               ans += str(self.__matrix[i][j]) + ","
            else:
               ans += str(self.__matrix[i][j]) + "|\n"
      return ans







   def __add__(self					,   __a)			->      Matrix:
      """simple docstring"""






      if self.__width == other.width() and self.__height == other.height():
         __snake_case				:      Tuple     							= []
         for i in range(self.__height):
            __snake_case				:      List[Any]     							= [
                self.__matrix[i][j] + other.component(__a					,   __a)
                for j in range(self.__width)
            ]
            matrix.append(__a)
         return Matrix(__a					,   self.__width					,   self.__height)
      else:
         raise Exception('matrix must have the same dimension!')







   def __sub__(self					,   __a)			->      Matrix:
      """simple docstring"""






      if self.__width == other.width() and self.__height == other.height():
         __snake_case				:      str     							= []
         for i in range(self.__height):
            __snake_case				:      List[str]     							= [
                self.__matrix[i][j] - other.component(__a					,   __a)
                for j in range(self.__width)
            ]
            matrix.append(__a)
         return Matrix(__a					,   self.__width					,   self.__height)
      else:
         raise Exception('matrices must have the same dimension!')







   @overload
   def __mul__(self					,   __a)			->      Matrix:
      """simple docstring"""






      ...







   @overload
   def __mul__(self					,   __a)			->      Vector:
      """simple docstring"""






      ...







   def __mul__(self					,   __a)			->      Vector | Matrix:
      """simple docstring"""






      if isinstance(__a					,   __a):  # matrix-vector
         if len(__a) == self.__width:
            __snake_case				:      Tuple     							= zero_vector(self.__height)
            for i in range(self.__height):
               __snake_case				:      Union[str, Any]     							= [
                   self.__matrix[i][j] * other.component(__a)
                   for j in range(self.__width)
               ]
               ans.change_component(__a					,   sum(__a))
            return ans
         else:
            raise Exception(
                'vector must have the same size as the '
                'number of columns of the matrix!')
      elif isinstance(__a					,   (int, float)):  # matrix-scalar
         __snake_case				:      str     							= [
             [self.__matrix[i][j] * other for j in range(self.__width)]
             for i in range(self.__height)
         ]
         return Matrix(__a					,   self.__width					,   self.__height)
      return None







   def     SCREAMING_SNAKE_CASE__					(self)			->      int:
      """simple docstring"""






      return self.__height







   def     SCREAMING_SNAKE_CASE__					(self)			->      int:
      """simple docstring"""






      return self.__width







   def     SCREAMING_SNAKE_CASE__					(self					,   __a					,   __a)			->      float:
      """simple docstring"""






      if 0 <= x < self.__height and 0 <= y < self.__width:
         return self.__matrix[x][y]
      else:
         raise Exception('change_component: indices out of bounds')







   def     SCREAMING_SNAKE_CASE__					(self					,   __a					,   __a					,   __a)			->      None:
      """simple docstring"""






      if 0 <= x < self.__height and 0 <= y < self.__width:
         __snake_case				:      List[Any]     							= value
      else:
         raise Exception('change_component: indices out of bounds')







   def     SCREAMING_SNAKE_CASE__					(self					,   __a					,   __a)			->      float:
      """simple docstring"""






      if self.__height != self.__width:
         raise Exception('Matrix is not square')
      __snake_case				:      List[Any]     							= self.__matrix[:x] + self.__matrix[x + 1 :]
      for i in range(len(__a)):
         __snake_case				:      Tuple     							= minor[i][:y] + minor[i][y + 1 :]
      return Matrix(__a					,   self.__width - 1					,   self.__height - 1).determinant()







   def     SCREAMING_SNAKE_CASE__					(self					,   __a					,   __a)			->      float:
      """simple docstring"""






      if self.__height != self.__width:
         raise Exception('Matrix is not square')
      if 0 <= x < self.__height and 0 <= y < self.__width:
         return (-1) ** (x + y) * self.minor(__a					,   __a)
      else:
         raise Exception('Indices out of bounds')







   def     SCREAMING_SNAKE_CASE__					(self)			->      float:
      """simple docstring"""






      if self.__height != self.__width:
         raise Exception('Matrix is not square')
      if self.__height < 1:
         raise Exception('Matrix has no element')
      elif self.__height == 1:
         return self.__matrix[0][0]
      elif self.__height == 2:
         return (
             self.__matrix[0][0] * self.__matrix[1][1]
             - self.__matrix[0][1] * self.__matrix[1][0]
         )
      else:
         __snake_case				:      Any     							= [
             self.__matrix[0][y] * self.cofactor(0					,   __a) for y in range(self.__width)
         ]
         return sum(__a)




def        _SCREAMING_SNAKE_CASE  (				A  :       int  )    -> Matrix:







   """simple docstring"""
   __snake_case				:      list[list[float]]     							= [[0] * n for _ in range(A  )]
   return Matrix(A  ,		A  ,		A  )





def        _SCREAMING_SNAKE_CASE  (				A  :       int  ,		A  :       int  ,		A  :       int  ,		A  :       int  )    -> Matrix:







   """simple docstring"""
   random.seed(A  )
   __snake_case				:      list[list[float]]     							= [
       [random.randint(A  ,		A  ) for _ in range(A  )] for _ in range(A  )
   ]
   return Matrix(A  ,		A  ,		A  )