
import math
import random
from typing import Any

from .hill_climbing import SearchProblem
def    lowerCAmelCase_	(				SCREAMING_SNAKE_CASE_    ,      SCREAMING_SNAKE_CASE_ = True    ,      SCREAMING_SNAKE_CASE_ = math.inf    ,      SCREAMING_SNAKE_CASE_ = -math.inf    ,      SCREAMING_SNAKE_CASE_ = math.inf    ,      SCREAMING_SNAKE_CASE_ = -math.inf    ,      SCREAMING_SNAKE_CASE_ = False    ,      SCREAMING_SNAKE_CASE_ = 1_00    ,      SCREAMING_SNAKE_CASE_ = 0.01    ,      SCREAMING_SNAKE_CASE_ = 1    ,      )     ->     Any:




   """simple docstring"""
   _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(SCREAMING_SNAKE_CASE_						)
      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(SCREAMING_SNAKE_CASE_						) - 1						)  # picking a random neighbor
         _SCREAMING_SNAKE_CASE      =				neighbors.pop(SCREAMING_SNAKE_CASE_						)
         _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(SCREAMING_SNAKE_CASE_						)    ,      SCREAMING_SNAKE_CASE_						)
      plt.xlabel("""Iterations"""						)
      plt.ylabel("""Function values"""						)
      plt.show()
   return best_state


if __name__ == "__main__":
     def    lowerCAmelCase_	(				SCREAMING_SNAKE_CASE_    ,      SCREAMING_SNAKE_CASE_						)     ->     str:




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

     # starting the problem with initial coordinates (12, 47)
     UpperCamelCase__      :		int       							=  SearchProblem(x=12, y=47, step_size=1, function_to_optimize=test_fa)
     UpperCamelCase__      :		List[str]       							=  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)
     UpperCamelCase__      :		int       							=  SearchProblem(x=12, y=47, step_size=1, function_to_optimize=test_fa)
     UpperCamelCase__      :		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_	(				SCREAMING_SNAKE_CASE_    ,      SCREAMING_SNAKE_CASE_						)     ->     Optional[Any]:




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

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

     UpperCamelCase__      :		Union[str, Any]       							=  SearchProblem(x=3, y=4, step_size=1, function_to_optimize=test_fa)
     UpperCamelCase__      :		Dict       							=  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
def    lowerCAmelCase_	(				SCREAMING_SNAKE_CASE_    ,      SCREAMING_SNAKE_CASE_						)     ->     Tuple:




   """simple docstring"""
   print(F"Vertex\tShortest Distance from vertex {src}"						)
   for i, d in enumerate(SCREAMING_SNAKE_CASE_						):
      print(F"{i}\t\t{d}"						)
def    lowerCAmelCase_	(				SCREAMING_SNAKE_CASE_    ,      SCREAMING_SNAKE_CASE_    ,      SCREAMING_SNAKE_CASE_						)     ->     List[Any]:




   """simple docstring"""
   for j in range(SCREAMING_SNAKE_CASE_						):
      _SCREAMING_SNAKE_CASE ,							_SCREAMING_SNAKE_CASE ,							_SCREAMING_SNAKE_CASE      =				(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_	(				SCREAMING_SNAKE_CASE_    ,      SCREAMING_SNAKE_CASE_    ,      SCREAMING_SNAKE_CASE_    ,      SCREAMING_SNAKE_CASE_						)     ->     list[float]:




   """simple docstring"""
   _SCREAMING_SNAKE_CASE      =				[float("""inf"""						)] * vertex_count
   _SCREAMING_SNAKE_CASE      =				0.0

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

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

   _SCREAMING_SNAKE_CASE      =				check_negative_cycle(SCREAMING_SNAKE_CASE_    ,      SCREAMING_SNAKE_CASE_    ,      SCREAMING_SNAKE_CASE_						)
   if negative_cycle_exists:
      raise Exception("""Negative cycle found"""						)

   return distance


if __name__ == "__main__":
     import doctest

     doctest.testmod()

     UpperCamelCase__      :		int       							=  int(input("Enter number of vertices: ").strip())
     UpperCamelCase__      :		int       							=  int(input("Enter number of edges: ").strip())

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

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

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






