

import math
class     SCREAMING_SNAKE_CASE__     :





       '''simple docstring'''




       def __init__(						self       :						Any    ,		lowerCAmelCase__       :						int    ,		lowerCAmelCase__       :						int    ,		lowerCAmelCase__       :						int    ,		lowerCAmelCase__       :						Any							)			->    Union[str, Any]:
             snake_case__					=   x
             snake_case__					=   y
             snake_case__					=   step_size
             snake_case__					=   function_to_optimize

       def UpperCAmelCase_						(						self       :						Optional[int]							)			->    int:
             return self.function(self.x    ,		self.y							)

       def UpperCAmelCase_						(						self       :						List[Any]							)			->    Union[str, Any]:
             snake_case__					=   self.step_size
             return [
                 SearchProblem(lowerCAmelCase__    ,		lowerCAmelCase__    ,		lowerCAmelCase__    ,		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       :						Dict							)			->    int:
             return hash(str(self							)							)

       def __eq__(						self       :						Tuple    ,		lowerCAmelCase__       :						Optional[int]							)			->    List[str]:
             if isinstance(lowerCAmelCase__    ,		lowerCAmelCase__							):
                   return hash(str(self							)							) == hash(str(lowerCAmelCase__							)							)
             return False

       def __str__(						self       :						str							)			->    List[str]:
             return f'''x: {self.x} y: {self.y}'''





def 			_lowercase    (      __UpperCamelCase     :		List[str]   ,       __UpperCamelCase     :		bool = True   ,       __UpperCamelCase     :		float = math.inf   ,       __UpperCamelCase     :		float = -math.inf   ,       __UpperCamelCase     :		float = math.inf   ,       __UpperCamelCase     :		float = -math.inf   ,       __UpperCamelCase     :		bool = False   ,       __UpperCamelCase     :		int = 1_0000   ,       ):
      snake_case__					=   search_prob
      snake_case__					=   []  # list to store the current score at each iteration
      snake_case__					=   0
      snake_case__					=   False
      snake_case__					=   set()
      while not solution_found and iterations < max_iter:
            visited.add(__UpperCamelCase )
            iterations += 1
            snake_case__					=   current_state.score()
            scores.append(__UpperCamelCase )
            snake_case__					=   current_state.get_neighbors()
            snake_case__					=   -math.inf
            snake_case__					=   math.inf
            snake_case__					=   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
                  snake_case__					=   neighbor.score() - current_score
                  if find_max:  # finding max
                        # going to direction with greatest ascent
                        if change > max_change and change > 0:
                              snake_case__					=   change
                              snake_case__					=   neighbor
                  else:  # finding min
                        # to direction with greatest descent
                        if change < min_change and change < 0:
                              snake_case__					=   change
                              snake_case__					=   neighbor
            if next_state is not None:
                  # we found at least one neighbor which improved the current state
                  snake_case__					=   next_state
            else:
                  # since we have no neighbor that improves the solution we stop the search
                  snake_case__					=   True

      if visualization:
            from matplotlib import pyplot as plt

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

      return current_state


if __name__ == "__main__":
       import doctest

       doctest.testmod()





       def 			_lowercase    (      __UpperCamelCase     :		Optional[Any]   ,       __UpperCamelCase     :		Optional[Any] ):
             return (x**2) + (y**2)

       # starting the problem with initial coordinates (3, 4)
       lowerCAmelCase						:   Union[str, Any]										=    SearchProblem(x=3, y=4, step_size=1, function_to_optimize=test_fa)
       lowerCAmelCase						:   Any										=    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)
       lowerCAmelCase						:   Union[str, Any]										=    SearchProblem(x=12, y=47, step_size=1, function_to_optimize=test_fa)
       lowerCAmelCase						:   str										=    hill_climbing(
           prob, find_max=False, max_x=100, 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 			_lowercase    (      __UpperCamelCase     :		Optional[Any]   ,       __UpperCamelCase     :		Dict ):
             return (3 * x**2) - (6 * y)

       lowerCAmelCase						:   List[Any]										=    SearchProblem(x=3, y=4, step_size=1, function_to_optimize=test_fa)
       lowerCAmelCase						:   Optional[Any]										=    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()}"""
       )








import sys





def 			_lowercase    (      __UpperCamelCase     :		int   ,       __UpperCamelCase     :		list[int] ):
      if not numbers:
            return 0
      if target == 0 and target in numbers:
            return 0
      if not isinstance(__UpperCamelCase   ,       (list, tuple) ) or not all(
          isinstance(__UpperCamelCase   ,       __UpperCamelCase ) for number in numbers ):
            raise ValueError("""numbers must be an iterable of integers""" )

      snake_case__					=   snake_case__					=   snake_case__					=   0
      snake_case__					=   sys.maxsize

      while right < len(__UpperCamelCase ):
            curr_sum += numbers[right]
            while curr_sum >= target and left <= right:
                  snake_case__					=   min(__UpperCamelCase   ,       right - left + 1 )
                  curr_sum -= numbers[left]
                  left += 1
            right += 1

      return 0 if min_len == sys.maxsize else min_len






