





'''simple docstring'''

import math
import random
from typing import Any

from .hill_climbing import SearchProblem





def lowerCamelCase						(     __lowerCamelCase :    Dict					,       __lowerCamelCase :    bool = True					,       __lowerCamelCase :    float = math.inf					,       __lowerCamelCase :    float = -math.inf					,       __lowerCamelCase :    float = math.inf					,       __lowerCamelCase :    float = -math.inf					,       __lowerCamelCase :    bool = False					,       __lowerCamelCase :    float = 100					,       __lowerCamelCase :    float = 0.01					,       __lowerCamelCase :    float = 1					,       )						->Any:
    _SCREAMING_SNAKE_CASE									=			False
    _SCREAMING_SNAKE_CASE									=			search_prob
    _SCREAMING_SNAKE_CASE									=			start_temperate
    _SCREAMING_SNAKE_CASE									=			[]
    _SCREAMING_SNAKE_CASE									=			0
    _SCREAMING_SNAKE_CASE									=			None

    while not search_end:
        _SCREAMING_SNAKE_CASE									=			current_state.score()
        if best_state is None or current_score > best_state.score():
            _SCREAMING_SNAKE_CASE									=			current_state
        scores.append(__lowerCamelCase    )
        iterations += 1
        _SCREAMING_SNAKE_CASE									=			None
        _SCREAMING_SNAKE_CASE									=			current_state.get_neighbors()
        while (
            next_state is None and neighbors
        ):  # till we do not find a neighbor that we can move to
            _SCREAMING_SNAKE_CASE									=			random.randint(0					,       len(__lowerCamelCase    ) - 1    )  # picking a random neighbor
            _SCREAMING_SNAKE_CASE									=			neighbors.pop(__lowerCamelCase    )
            _SCREAMING_SNAKE_CASE									=			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:
                _SCREAMING_SNAKE_CASE									=			change * -1  # in case we are finding minimum
            if change > 0:  # improves the solution
                _SCREAMING_SNAKE_CASE									=			picked_neighbor
            else:
                _SCREAMING_SNAKE_CASE									=			(math.e) ** (
                    change / current_temp
                )  # probability generation function
                if random.random() < probability:  # random number within probability
                    _SCREAMING_SNAKE_CASE									=			picked_neighbor
        _SCREAMING_SNAKE_CASE									=			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
            _SCREAMING_SNAKE_CASE									=			True
        else:
            _SCREAMING_SNAKE_CASE									=			next_state

    if visualization:
        from matplotlib import pyplot as plt

        plt.plot(range(__lowerCamelCase    )					,       __lowerCamelCase    )
        plt.xlabel("""Iterations"""    )
        plt.ylabel("""Function values"""    )
        plt.show()
    return best_state


if __name__ == "__main__":





      def lowerCamelCase						(     __lowerCamelCase :    Optional[Any]					,       __lowerCamelCase :    List[str]    )						->Optional[Any]:
          return (x**2) + (y**2)

      # starting the problem with initial coordinates (12, 47)
      lowercase_					= SearchProblem(x=12, y=47, step_size=1, function_to_optimize=test_fa)
      lowercase_					= simulated_annealing(
          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()}"""
      )

      # starting the problem with initial coordinates (12, 47)
      lowercase_					= SearchProblem(x=12, y=47, step_size=1, function_to_optimize=test_fa)
      lowercase_					= simulated_annealing(
          prob, find_max=True, max_x=100, min_x=5, max_y=50, 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 lowerCamelCase						(     __lowerCamelCase :    Optional[Any]					,       __lowerCamelCase :    int    )						->int:
          return (3 * x**2) - (6 * y)

      lowercase_					= SearchProblem(x=3, y=4, step_size=1, function_to_optimize=test_fa)
      lowercase_					= 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()}"""
      )

      lowercase_					= SearchProblem(x=3, y=4, step_size=1, function_to_optimize=test_fa)
      lowercase_					= 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()}"""
      )






def    __UpperCAmelCase (	__a      :			int		,__a      :			list[int]		,__a      :			int	)			->     int:

					"""simple docstring"""

					def count_of_possible_combinations(__a      :			int	) -> int:
										if target < 0:
															return 0
										if target == 0:
															return 1
										return sum(count_of_possible_combinations(target - item	) for item in array	)

					return count_of_possible_combinations(__a	)



def    __UpperCAmelCase (	__a      :			int		,__a      :			list[int]		,__a      :			int	)			->     int:

					"""simple docstring"""

					def count_of_possible_combinations_with_dp_array(
					    __a      :			int		,__a      :			list[int]	) -> int:
										if target < 0:
															return 0
										if target == 0:
															return 1
										if dp_array[target] != -1:
															return dp_array[target]
										_a	:    Union[str, Any]         =		sum(
										    count_of_possible_combinations_with_dp_array(target - item		,__a	)
										    for item in array	)
										_a	:    Optional[int]         =		answer
										return answer

					_a	:    int         =		[-1] * (target + 1)
					return count_of_possible_combinations_with_dp_array(__a		,__a	)



def    __UpperCAmelCase (	__a      :			int		,__a      :			list[int]		,__a      :			int	)			->     int:

					"""simple docstring"""

					_a	:    str         =		[0] * (target + 1)
					_a	:    Optional[Any]         =		1

					for i in range(1		,target + 1	):
										for j in range(__a	):
															if i - array[j] >= 0:
																				dp_array[i] += dp_array[i - array[j]]

					return dp_array[target]


if __name__ == "__main__":
			import doctest

			doctest.testmod()
			a__				=		3
			a__				=		5
			a__				=		[1, 2, 5]
			print(combination_sum_iv(n, array, target))



