"""simple docstring"""







from __future__ import annotations

from queue import Queue






class 							__snake_case:


    '''simple docstring'''





    def __init__(  self	):




         '''simple docstring'''



         __A					:					dict[int, list[int]]								=		{}
    def 						_a							(  self	):




         '''simple docstring'''



         for i in self.vertices:
              print(__lowerCamelCase					,       ' : '					,       ' -> '.join([str(__lowerCamelCase	) for j in self.vertices[i]]	)	)
    def 						_a							(  self					,       __lowerCamelCase					,       __lowerCamelCase	):




         '''simple docstring'''



         if from_vertex in self.vertices:
              self.vertices[from_vertex].append(__lowerCamelCase	)
         else:
              __A					:					List[str]								=		[to_vertex]

    def 						_a							(  self					,       __lowerCamelCase	):




         '''simple docstring'''



         __A					:					Optional[int]								=		set()

         # create a first in first out queue to store all the vertices for BFS
         __A					:					Queue								=		Queue()

         # mark the source node as visited and enqueue it
         visited.add(__lowerCamelCase	)
         queue.put(__lowerCamelCase	)

         while not queue.empty():
              __A					:					Any								=		queue.get()

              # loop through all adjacent vertex and enqueue it if not yet visited
              for adjacent_vertex in self.vertices[vertex]:
                   if adjacent_vertex not in visited:
                        queue.put(__lowerCamelCase	)
                        visited.add(__lowerCamelCase	)
         return visited


if __name__ == "__main__":
       from doctest import testmod

       testmod(verbose=True)

       lowerCamelCase      : Any       =Graph()
       g.add_edge(0, 1)
       g.add_edge(0, 2)
       g.add_edge(1, 2)
       g.add_edge(2, 0)
       g.add_edge(2, 3)
       g.add_edge(3, 3)

       g.print_graph()
       # 0  :  1 -> 2
       # 1  :  2
       # 2  :  0 -> 3
       # 3  :  3

       assert sorted(g.bfs(2)) == [0, 1, 2, 3]




"""simple docstring"""







from __future__ import annotations

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

lowerCamelCase      : List[str]       =TypeVar('''T''', bound=bool)






class 							__snake_case(					Generic[T]	):


    '''simple docstring'''





    def __init__(  self					,       __lowerCamelCase	):




         '''simple docstring'''



         __A					:					T								=		value
         __A					:					RandomizedHeapNode[T] | None								=		None
         __A					:					RandomizedHeapNode[T] | None								=		None
    @property
    def 						_a							(  self	):




         '''simple docstring'''



         return self._value

    @staticmethod
    def 						_a							(  __lowerCamelCase					,       __lowerCamelCase	):




         '''simple docstring'''



         if not roota:
              return roota

         if not roota:
              return roota

         if roota.value > roota.value:
              __A						,		__A					:					List[str]								=		roota, roota

         if random.choice([True, False]	):
              __A						,		__A					:					Dict								=		roota.right, roota.left

         __A					:					Dict								=		RandomizedHeapNode.merge(roota.left					,       __lowerCamelCase	)

         return roota







class 							__snake_case(					Generic[T]	):


    '''simple docstring'''





    def __init__(  self					,       __lowerCamelCase = ()	):




         '''simple docstring'''



         __A					:					RandomizedHeapNode[T] | None								=		None

         if data:
              for item in data:
                   self.insert(__lowerCamelCase	)
    def 						_a							(  self					,       __lowerCamelCase	):




         '''simple docstring'''



         __A					:					List[str]								=		RandomizedHeapNode.merge(self._root					,       RandomizedHeapNode(__lowerCamelCase	)	)
    def 						_a							(  self	):




         '''simple docstring'''



         __A					:					int								=		self.top()

         if self._root is None:
              return None

         __A					:					Dict								=		RandomizedHeapNode.merge(self._root.left					,       self._root.right	)

         return result
    def 						_a							(  self	):




         '''simple docstring'''



         if not self._root:
              raise IndexError('Can\'t get top element for the empty heap.'	)
         return self._root.value
    def 						_a							(  self	):




         '''simple docstring'''



         __A					:					Dict								=		None
    def 						_a							(  self	):




         '''simple docstring'''



         __A					:					Tuple								=		[]
         while self:
              result.append(self.pop()	)

         return result

    def __bool__(  self	):




         '''simple docstring'''



         return self._root is not None


if __name__ == "__main__":
       import doctest

       doctest.testmod()



