




'''simple docstring'''







import heapq



def 					lowerCamelCase__							(			__lowercase    ,      __lowercase    ,      __lowercase							):
     snake_case :			str					   = [(0, start)]  # cost from start node,end node
     snake_case :			Optional[int]					   = set()
     while heap:
          (snake_case) :			Optional[Any]					   = heapq.heappop(UpperCAmelCase_							)
          if u in visited:
               continue
          visited.add(UpperCAmelCase_							)
          if u == end:
               return cost
          for v, c in graph[u]:
               if v in visited:
                    continue
               snake_case :			Dict					   = cost + c
               heapq.heappush(UpperCAmelCase_    ,      (next_item, v)							)
     return -1


lowercase			:      Any			=					{
    """A""": [["""B""", 2], ["""C""", 5]],
    """B""": [["""A""", 2], ["""D""", 3], ["""E""", 1], ["""F""", 1]],
    """C""": [["""A""", 5], ["""F""", 3]],
    """D""": [["""B""", 3]],
    """E""": [["""B""", 4], ["""F""", 3]],
    """F""": [["""C""", 3], ["""E""", 3]],
}
lowercase			:      Optional[Any]			=					{
    """B""": [["""C""", 1]],
    """C""": [["""D""", 1]],
    """D""": [["""F""", 1]],
    """E""": [["""B""", 1], ["""F""", 3]],
    """F""": [],
}
lowercase			:      Any			=					{
    """B""": [["""C""", 1]],
    """C""": [["""D""", 1]],
    """D""": [["""F""", 1]],
    """E""": [["""B""", 1], ["""G""", 2]],
    """F""": [],
    """G""": [["""F""", 1]],
}

lowercase			:      Any			=					dijkstra(G, """E""", """C""")
print(short_distance)  # E -- 3 --> F -- 3 --> C == 6

lowercase			:      Optional[int]			=					dijkstra(Ga, """E""", """F""")
print(short_distance)  # E -- 3 --> F == 3

lowercase			:      Any			=					dijkstra(Ga, """E""", """F""")
print(short_distance)  # E -- 2 --> G -- 1 --> F == 3

if __name__ == "__main__":
      import doctest

      doctest.testmod()









'''simple docstring'''







from __future__ import annotations

from collections.abc import Iterable, Iterator
from typing import Any, Generic, TypeVar

lowercase			:      Union[str, Any]			=					TypeVar("""T""", bound=bool)







class 				_a   (Generic[T]  ):





     '''simple docstring'''



     def __init__(							self       ,__a       )			->							None:
          snake_case :			T					   = value
          snake_case :			SkewNode[T] | None					   = None
          snake_case :			SkewNode[T] | None					   = None







     @property
     def  snake_case_			(							self       )			->							T:
          return self._value







     @staticmethod
     def  snake_case_			(							__a       ,__a       )			->							SkewNode[T] | None:
          if not roota:
               return roota

          if not roota:
               return roota

          if roota.value > roota.value:
               snake_case   ,		snake_case :			Tuple					   = roota, roota

          snake_case :			Tuple					   = roota
          snake_case :			Union[str, Any]					   = roota.right
          snake_case :			Any					   = roota.left
          snake_case :			Union[str, Any]					   = SkewNode.merge(__a       ,__a       )

          return result







class 				_a   (Generic[T]  ):





     '''simple docstring'''



     def __init__(							self       ,__a = ()       )			->							None:
          snake_case :			SkewNode[T] | None					   = None
          if data:
               for item in data:
                    self.insert(__a       )







     def __bool__(							self       )			->							bool:
          return self._root is not None







     def __iter__(							self       )			->							Iterator[T]:
          snake_case :			list[Any]					   = []
          while self:
               result.append(self.pop()       )

          # Pushing items back to the heap not to clear it.
          for item in result:
               self.insert(__a       )

          return iter(__a       )







     def  snake_case_			(							self       ,__a       )			->							None:
          snake_case :			List[Any]					   = SkewNode.merge(self._root       ,SkewNode(__a       )       )







     def  snake_case_			(							self       )			->							T | None:
          snake_case :			Tuple					   = self.top()
          snake_case :			int					   = (
              SkewNode.merge(self._root.left       ,self._root.right       ) if self._root else None
          )

          return result







     def  snake_case_			(							self       )			->							T:
          if not self._root:
               raise IndexError("""Can't get top element for the empty heap."""       )
          return self._root.value







     def  snake_case_			(							self       )			->							None:
          snake_case :			Any					   = None


if __name__ == "__main__":
      import doctest

      doctest.testmod()



