

import math
import random
from typing import Any

from .hill_climbing import SearchProblem



def       __lowerCAmelCase      (						A       ,     A = True       ,     A = math.inf       ,     A = -math.inf       ,     A = math.inf       ,     A = -math.inf       ,     A = False       ,     A = 100       ,     A = 0.01       ,     A = 1       ,     ):
	UpperCAmelCase_       				=			False
	UpperCAmelCase_       				=			search_prob
	UpperCAmelCase_       				=			start_temperate
	UpperCAmelCase_       				=			[]
	UpperCAmelCase_       				=			0
	UpperCAmelCase_       				=			None

	while not search_end:
		UpperCAmelCase_       				=			current_state.score()
		if best_state is None or current_score > best_state.score():
			UpperCAmelCase_       				=			current_state
		scores.append(A    )
		iterations += 1
		UpperCAmelCase_       				=			None
		UpperCAmelCase_       				=			current_state.get_neighbors()
		while (
		    next_state is None and neighbors
		):  # till we do not find a neighbor that we can move to
			UpperCAmelCase_       				=			random.randint(0       ,     len(A    ) - 1    )  # picking a random neighbor
			UpperCAmelCase_       				=			neighbors.pop(A    )
			UpperCAmelCase_       				=			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:
				UpperCAmelCase_       				=			change * -1  # in case we are finding minimum
			if change > 0:  # improves the solution
				UpperCAmelCase_       				=			picked_neighbor
			else:
				UpperCAmelCase_       				=			(math.e) ** (
				    change / current_temp
				)  # probability generation function
				if random.random() < probability:  # random number within probability
					UpperCAmelCase_       				=			picked_neighbor
		UpperCAmelCase_       				=			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
			UpperCAmelCase_       				=			True
		else:
			UpperCAmelCase_       				=			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       __lowerCAmelCase      (						A       ,     A    ):
					return (x**2) + (y**2)

				# starting the problem with initial coordinates (12, 47)
				_a:    List[str] 							=			SearchProblem(x=12, y=47, step_size=1, function_to_optimize=test_fa)
				_a:    Dict 							=			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)
				_a:    List[Any] 							=			SearchProblem(x=12, y=47, step_size=1, function_to_optimize=test_fa)
				_a:    Optional[int] 							=			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      (						A       ,     A    ):
					return (3 * x**2) - (6 * y)

				_a:    Any 							=			SearchProblem(x=3, y=4, step_size=1, function_to_optimize=test_fa)
				_a:    Any 							=			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:    Union[str, Any] 							=			SearchProblem(x=3, y=4, step_size=1, function_to_optimize=test_fa)
				_a:    Tuple 							=			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()}'
				)


from __future__ import annotations



def       __lowerCAmelCase      (						A       ,     A    ):
	print(F"Vertex\tShortest Distance from vertex {src}"    )
	for i, d in enumerate(A    ):
		print(F"{i}\t\t{d}"    )



def       __lowerCAmelCase      (						A       ,     A       ,     A    ):
	for j in range(A    ):
		UpperCAmelCase_				,   UpperCAmelCase_				,   UpperCAmelCase_       				=			(graph[j][k] for k in ["src", "dst", "weight"])
		if distance[u] != float("inf"    ) and distance[u] + w < distance[v]:
			return True
	return False



def       __lowerCAmelCase      (						A       ,     A       ,     A       ,     A    ):
	UpperCAmelCase_       				=			[float("inf"    )] * vertex_count
	UpperCAmelCase_       				=			0.0

	for _ in range(vertex_count - 1    ):
		for j in range(A    ):
			UpperCAmelCase_				,   UpperCAmelCase_				,   UpperCAmelCase_       				=			(graph[j][k] for k in ["src", "dst", "weight"])

			if distance[u] != float("inf"    ) and distance[u] + w < distance[v]:
				UpperCAmelCase_       				=			distance[u] + w

	UpperCAmelCase_       				=			check_negative_cycle(A       ,     A       ,     A    )
	if negative_cycle_exists:
		raise Exception("Negative cycle found"    )

	return distance


if __name__ == "__main__":
				import doctest

				doctest.testmod()

				_a:    List[str] 							=			int(input("""Enter number of vertices: """).strip())
				_a:    str 							=			int(input("""Enter number of edges: """).strip())

				_a:    list[dict[str, int]] 							=			[{} for _ in range(E)]

				for i in range(E):
								print("""Edge """, i + 1)
								_a							,			_a							,			_a:    Any 							=			(
								    int(x)
								    for x in input("""Enter source, destination, weight: """).strip().split(""" """)
								)
								_a:    str 							=			{"""src""": src, """dst""": dest, """weight""": weight}

				_a:    List[Any] 							=			int(input("""\nEnter shortest path source:""").strip())
				_a:    Optional[int] 							=			bellman_ford(graph, V, E, source)
				print_distance(shortest_distance, 0)