



from __future__ import annotations

snake_case__					:     Any    		=   {
    """A""": ["""B""", """C""", """E"""],
    """B""": ["""A""", """D""", """E"""],
    """C""": ["""A""", """F""", """G"""],
    """D""": ["""B"""],
    """E""": ["""A""", """B""", """D"""],
    """F""": ["""C"""],
    """G""": ["""C"""],
}

class   _A   :


						'''simple docstring'''





						def __init__(	self	:							List[Any]							,      lowerCamelCase	:							dict[str, list[str]]							,      lowerCamelCase	:							str	):






							'''simple docstring'''



							__lowercase		       =			graph
							# mapping node to its parent in resulting breadth first tree
							__lowercase		       =			{}
							__lowercase		       =			source_vertex



						def     _snake_case	(	self	:							Tuple	):






							'''simple docstring'''



							__lowercase		       =			{self.source_vertex}
							__lowercase		       =			None
							__lowercase		       =			[self.source_vertex]  # first in first out queue

							while queue:
								__lowercase		       =			queue.pop(0	)
								for adjacent_vertex in self.graph[vertex]:
									if adjacent_vertex not in visited:
										visited.add(_snake_case	)
										__lowercase		       =			vertex
										queue.append(_snake_case	)



						def     _snake_case	(	self	:							str							,      lowerCamelCase	:							str	):






							'''simple docstring'''



							if target_vertex == self.source_vertex:
								return self.source_vertex

							__lowercase		       =			self.parent.get(_snake_case	)
							if target_vertex_parent is None:
								__lowercase		       =			(
								    f"""No path from vertex: {self.source_vertex} to vertex: {target_vertex}"""
								)
								raise ValueError(_snake_case	)

							return self.shortest_path(_snake_case	) + f"""->{target_vertex}"""


if __name__ == "__main__":
	snake_case__					:     List[Any]    		=   Graph(graph, """G""")
	g.breath_first_search()
	print(g.shortest_path("""D"""))
	print(g.shortest_path("""G"""))
	print(g.shortest_path("""Foo"""))








from __future__ import annotations

from collections import namedtuple
from dataclasses import dataclass

@dataclass
class   _A   :


						'''simple docstring'''





						_snake_case			:     int
						_snake_case			:     TreeNode | None      							=      None
						_snake_case			:     TreeNode | None      							=      None

snake_case__					:     Dict    		=   namedtuple("""CoinsDistribResult""", """moves excess""")



def    snake_case_				(    _SCREAMING_SNAKE_CASE   ):

	if root is None:
		return 0

	# Validation
	def count_nodes(_SCREAMING_SNAKE_CASE   ) -> int:
		if node is None:
			return 0

		return count_nodes(node.left   ) + count_nodes(node.right   ) + 1

	def count_coins(_SCREAMING_SNAKE_CASE   ) -> int:
		if node is None:
			return 0

		return count_coins(node.left   ) + count_coins(node.right   ) + node.data

	if count_nodes(_SCREAMING_SNAKE_CASE   ) != count_coins(_SCREAMING_SNAKE_CASE   ):
		raise ValueError("The nodes number should be same as the number of coins"   )

	# Main calculation
	def get_distrib(_SCREAMING_SNAKE_CASE   ) -> CoinsDistribResult:

		if node is None:
			return CoinsDistribResult(0  ,	1   )

		__lowercase       ,    __lowercase		       =			get_distrib(node.left   )
		__lowercase       ,    __lowercase		       =			get_distrib(node.right   )

		__lowercase		       =			1 - left_distrib_excess
		__lowercase		       =			1 - right_distrib_excess

		__lowercase		       =			(
		    left_distrib_moves
		    + right_distrib_moves
		    + abs(_SCREAMING_SNAKE_CASE   )
		    + abs(_SCREAMING_SNAKE_CASE   )
		)
		__lowercase		       =			node.data - coins_to_left - coins_to_right

		return CoinsDistribResult(_SCREAMING_SNAKE_CASE  ,	_SCREAMING_SNAKE_CASE   )

	return get_distrib(_SCREAMING_SNAKE_CASE   )[0]


if __name__ == "__main__":
	import doctest

	doctest.testmod()



