




"""simple docstring"""







from __future__ import annotations





def 							lowercase					(snake_case__   : dict      ,       snake_case__   : str )     ->  set[str]:


				'''simple docstring'''






				lowerCAmelCase ,						lowerCAmelCase  =				set(snake_case__ ), [start]

				while stack:
								lowerCAmelCase  =				stack.pop()
								explored.add(snake_case__ )
								# Differences from BFS:
								# 1) pop last element instead of first one
								# 2) add adjacent elements to stack without exploring them
								for adj in reversed(graph[v] ):
												if adj not in explored:
																stack.append(snake_case__ )
				return explored


a      =							{
    'A': ['B', 'C', 'D'],
    'B': ['A', 'D', 'E'],
    'C': ['A', 'F'],
    'D': ['B', 'D'],
    'E': ['B', 'F'],
    'F': ['C', 'E', 'G'],
    'G': ['F'],
}

if __name__ == "__main__":
		import doctest

		doctest.testmod()
		print(depth_first_search(G, 'A'))











"""simple docstring"""







from queue import PriorityQueue
from typing import Any

import numpy as np





def 							lowercase					(snake_case__   : dict      ,       snake_case__   : str      ,       snake_case__   : set      ,       snake_case__   : set      ,       snake_case__   : dict      ,       snake_case__   : dict      ,       snake_case__   : PriorityQueue      ,       snake_case__   : dict      ,       snake_case__   : float | int      ,       )     ->  float | int:


				'''simple docstring'''






				for nxt, d in graph[v]:
								if nxt in visited_forward:
												continue
								lowerCAmelCase  =				cst_fwd.get(snake_case__      ,       np.inf )
								lowerCAmelCase  =				cst_fwd[v] + d
								if new_cost_f < old_cost_f:
												queue.put((new_cost_f, nxt) )
												lowerCAmelCase  =				new_cost_f
												lowerCAmelCase  =				v
								if nxt in visited_backward:
												if cst_fwd[v] + d + cst_bwd[nxt] < shortest_distance:
																lowerCAmelCase  =				cst_fwd[v] + d + cst_bwd[nxt]
				return shortest_distance





def 							lowercase					(snake_case__   : str      ,       snake_case__   : str      ,       snake_case__   : dict      ,       snake_case__   : dict )     ->  int:


				'''simple docstring'''






				lowerCAmelCase  =				-1

				lowerCAmelCase  =				set()
				lowerCAmelCase  =				set()
				lowerCAmelCase  =				{source: 0}
				lowerCAmelCase  =				{destination: 0}
				lowerCAmelCase  =				{source: None}
				lowerCAmelCase  =				{destination: None}
				lowerCAmelCase  =				PriorityQueue()
				lowerCAmelCase  =				PriorityQueue()

				lowerCAmelCase  =				np.inf

				queue_forward.put((0, source) )
				queue_backward.put((0, destination) )

				if source == destination:
								return 0

				while not queue_forward.empty() and not queue_backward.empty():
								lowerCAmelCase ,						lowerCAmelCase  =				queue_forward.get()
								visited_forward.add(snake_case__ )

								lowerCAmelCase ,						lowerCAmelCase  =				queue_backward.get()
								visited_backward.add(snake_case__ )

								lowerCAmelCase  =				pass_and_relaxation(
								    snake_case__      ,       snake_case__      ,       snake_case__      ,       snake_case__      ,       snake_case__      ,       snake_case__      ,       snake_case__      ,       snake_case__      ,       snake_case__      ,       )

								lowerCAmelCase  =				pass_and_relaxation(
								    snake_case__      ,       snake_case__      ,       snake_case__      ,       snake_case__      ,       snake_case__      ,       snake_case__      ,       snake_case__      ,       snake_case__      ,       snake_case__      ,       )

								if cst_fwd[v_fwd] + cst_bwd[v_bwd] >= shortest_distance:
												break

				if shortest_distance != np.inf:
								lowerCAmelCase  =				shortest_distance
				return shortest_path_distance


a      =							{
    'B': [['C', 1]],
    'C': [['D', 1]],
    'D': [['F', 1]],
    'E': [['B', 1], ['G', 2]],
    'F': [],
    'G': [['F', 1]],
}
a      =							{
    'B': [['E', 1]],
    'C': [['B', 1]],
    'D': [['C', 1]],
    'F': [['D', 1], ['G', 1]],
    'E': [[None, np.inf]],
    'G': [['E', 2]],
}

if __name__ == "__main__":
		import doctest

		doctest.testmod()





