




'''simple docstring'''





class      UpperCamelCase       :



  def __init__(			self ):







      '''simple docstring'''


      _a				:							Optional[Any]							       =      [0]
      _a				:							Dict							       =      0



  def     a_							(			self		,     __lowerCAmelCase ):







      '''simple docstring'''


      _a				:							Tuple							       =      self.__heap[i]
      while i // 2 > 0:
          if self.__heap[i] > self.__heap[i // 2]:
              _a				:							Tuple							       =      self.__heap[i // 2]
              _a				:							str							       =      temporary
          i //= 2



  def     a_							(			self		,     __lowerCAmelCase ):







      '''simple docstring'''


      self.__heap.append(__lowerCAmelCase )
      self.__size += 1
      self.__swap_up(self.__size )



  def     a_							(			self		,     __lowerCAmelCase ):







      '''simple docstring'''


      while self.__size >= 2 * i:
          if 2 * i + 1 > self.__size:
              _a				:							Dict							       =      2 * i
          else:
              if self.__heap[2 * i] > self.__heap[2 * i + 1]:
                  _a				:							Union[str, Any]							       =      2 * i
              else:
                  _a				:							Dict							       =      2 * i + 1
          _a				:							List[Any]							       =      self.__heap[i]
          if self.__heap[i] < self.__heap[bigger_child]:
              _a				:							Tuple							       =      self.__heap[bigger_child]
              _a				:							Optional[int]							       =      temporary
          _a				:							Dict							       =      bigger_child



  def     a_							(			self ):







      '''simple docstring'''


      _a				:							List[Any]							       =      self.__heap[1]
      _a				:							str							       =      self.__heap[self.__size]
      self.__size -= 1
      self.__heap.pop()
      self.__swap_down(1 )
      return max_value



  @property
  def     a_							(			self ):







      '''simple docstring'''


      return self.__heap[1:]



  def __len__(			self ):







      '''simple docstring'''


      return self.__size


if __name__ == "__main__":
  import doctest

  doctest.testmod()
  # create an instance of BinaryHeap
  a		:	List[Any]       =      BinaryHeap()
  binary_heap.insert(6)
  binary_heap.insert(1_0)
  binary_heap.insert(1_5)
  binary_heap.insert(1_2)
  # pop root(max-values because it is max heap)
  print(binary_heap.pop())  # 15
  print(binary_heap.pop())  # 12
  # get the list and size after operations
  print(binary_heap.get_list)
  print(len(binary_heap))






'''simple docstring'''




import math
import sys





class _snake_case :
							"""simple docstring"""





							def __init__( self						)  ->int:



											"""simple docstring"""







											__lowerCamelCase		:   int           =       0
											__lowerCamelCase		:   str           =       []
											__lowerCamelCase		:   int           =       {}  # To store the pos of node in array







							def 		__SCREAMING_SNAKE_CASE( self						)  ->Union[str, Any]:



											"""simple docstring"""







											return self.cur_size == 0







							def 		__SCREAMING_SNAKE_CASE( self      ,					__A						)  ->Union[str, Any]:



											"""simple docstring"""







											__lowerCamelCase		:   Any           =       self.left(__A						)
											__lowerCamelCase		:   Any           =       self.right(__A						)
											if lc < self.cur_size and self.array(__A						)[0] < self.array(__A						)[0]:
															__lowerCamelCase		:   Dict           =       lc
											else:
															__lowerCamelCase		:   List[Any]           =       idx
											if rc < self.cur_size and self.array(__A						)[0] < self.array(__A						)[0]:
															__lowerCamelCase		:   List[str]           =       rc
											if smallest != idx:
															self.swap(__A      ,					__A						)
															self.min_heapify(__A						)







							def 		__SCREAMING_SNAKE_CASE( self      ,					__A						)  ->str:



											"""simple docstring"""







											__lowerCamelCase		:   Optional[Any]           =       self.cur_size
											self.cur_size += 1
											self.array.append((sys.maxsize, tup[1])						)
											self.decrease_key((sys.maxsize, tup[1])      ,					tup[0]						)







							def 		__SCREAMING_SNAKE_CASE( self						)  ->int:



											"""simple docstring"""







											__lowerCamelCase		:   Tuple           =       self.array[0][1]
											__lowerCamelCase		:   str           =       self.array[self.cur_size - 1]
											self.cur_size -= 1
											self.min_heapify(1						)
											del self.pos[min_node]
											return min_node







							def 		__SCREAMING_SNAKE_CASE( self      ,					__A						)  ->int:



											"""simple docstring"""







											return 2 * i + 1







							def 		__SCREAMING_SNAKE_CASE( self      ,					__A						)  ->Optional[Any]:



											"""simple docstring"""







											return 2 * i + 2







							def 		__SCREAMING_SNAKE_CASE( self      ,					__A						)  ->Tuple:



											"""simple docstring"""







											return math.floor(i / 2						)







							def 		__SCREAMING_SNAKE_CASE( self      ,					__A      ,					__A						)  ->List[Any]:



											"""simple docstring"""







											__lowerCamelCase		:   Union[str, Any]           =       j
											__lowerCamelCase		:   str           =       i
											__lowerCamelCase		:   Dict           =       self.array[i]
											__lowerCamelCase		:   Union[str, Any]           =       self.array[j]
											__lowerCamelCase		:   str           =       temp







							def 		__SCREAMING_SNAKE_CASE( self      ,					__A      ,					__A						)  ->Optional[Any]:



											"""simple docstring"""







											__lowerCamelCase		:   str           =       self.pos[tup[1]]
											# assuming the new_d is atmost old_d
											__lowerCamelCase		:   Union[str, Any]           =       (new_d, tup[1])
											while idx > 0 and self.array[self.par(__A						)][0] > self.array[idx][0]:
															self.swap(__A      ,					self.par(__A						)						)
															__lowerCamelCase		:   List[Any]           =       self.par(__A						)





class _snake_case :
							"""simple docstring"""





							def __init__( self      ,					__A						)  ->Any:



											"""simple docstring"""







											__lowerCamelCase		:   Dict           =       {}  # To store graph: u -> (v,w)
											__lowerCamelCase		:   Optional[Any]           =       num  # Number of nodes in graph
											# To store the distance from source vertex
											__lowerCamelCase		:   Dict           =       [0] * self.num_nodes
											__lowerCamelCase		:   List[str]           =       [-1] * self.num_nodes  # To store the path







							def 		__SCREAMING_SNAKE_CASE( self      ,					__A      ,					__A      ,					__A						)  ->Optional[Any]:



											"""simple docstring"""







											if u in self.adjList:
															self.adjList[u].append((v, w)						)
											else:
															__lowerCamelCase		:   Dict           =       [(v, w)]

											# Assuming undirected graph
											if v in self.adjList:
															self.adjList[v].append((u, w)						)
											else:
															__lowerCamelCase		:   List[Any]           =       [(u, w)]







							def 		__SCREAMING_SNAKE_CASE( self						)  ->Tuple:



											"""simple docstring"""







											for u in self.adjList:
															print(__A      ,					"->"      ,					" -> ".join(str(f'{v}({w})'						) for v, w in self.adjList[u]						)						)







							def 		__SCREAMING_SNAKE_CASE( self      ,					__A						)  ->int:



											"""simple docstring"""







											__lowerCamelCase		:   List[str]           =       [-1] * self.num_nodes
											# src is the source node
											__lowerCamelCase		:   str           =       0
											__lowerCamelCase		:   int           =       PriorityQueue()
											q.insert((0, src)						)  # (dist from src, node)
											for u in self.adjList:
															if u != src:
																			__lowerCamelCase		:   List[Any]           =       sys.maxsize  # Infinity
																			__lowerCamelCase		:   Dict           =       -1

											while not q.is_empty():
															__lowerCamelCase		:   int           =       q.extract_min()  # Returns node with the min dist from source
															# Update the distance of all the neighbours of u and
															# if their prev dist was INFINITY then push them in Q
															for v, w in self.adjList[u]:
																			__lowerCamelCase		:   str           =       self.dist[u] + w
																			if self.dist[v] > new_dist:
																							if self.dist[v] == sys.maxsize:
																											q.insert((new_dist, v)						)
																							else:
																											q.decrease_key((self.dist[v], v)      ,					__A						)
																							__lowerCamelCase		:   str           =       new_dist
																							__lowerCamelCase		:   Tuple           =       u

        # Show the shortest distances from src
											self.show_distances(__A						)







							def 		__SCREAMING_SNAKE_CASE( self      ,					__A						)  ->int:



											"""simple docstring"""







											print(f'Distance from node: {src}'						)
											for u in range(self.num_nodes						):
															print(f'Node {u} has distance: {self.dist[u]}'						)







							def 		__SCREAMING_SNAKE_CASE( self      ,					__A      ,					__A						)  ->Optional[int]:



											"""simple docstring"""







											__lowerCamelCase		:   List[Any]           =       []
											__lowerCamelCase		:   Tuple           =       0
											__lowerCamelCase		:   List[str]           =       dest
											# Backtracking from dest to src
											while self.par[temp] != -1:
															path.append(__A						)
															if temp != src:
																			for v, w in self.adjList[temp]:
																							if v == self.par[temp]:
																											cost += w
																											break
															__lowerCamelCase		:   int           =       self.par[temp]
											path.append(__A						)
											path.reverse()

											print(f'----Path to reach {dest} from {src}----'						)
											for u in path:
															print(f'{u}'      ,					end=" "						)
															if u != dest:
																			print("-> "      ,					end=""						)

											print("\nTotal cost of path: "      ,					__A						)


if __name__ == "__main__":
				__lowercase	:   Optional[Any]   		=					Graph(9)
				graph.add_edge(0, 1, 4)
				graph.add_edge(0, 7, 8)
				graph.add_edge(1, 2, 8)
				graph.add_edge(1, 7, 11)
				graph.add_edge(2, 3, 7)
				graph.add_edge(2, 8, 2)
				graph.add_edge(2, 5, 4)
				graph.add_edge(3, 4, 9)
				graph.add_edge(3, 5, 14)
				graph.add_edge(4, 5, 10)
				graph.add_edge(5, 6, 2)
				graph.add_edge(6, 7, 1)
				graph.add_edge(6, 8, 6)
				graph.add_edge(7, 8, 7)
				graph.show_graph()
				graph.dijkstra(0)
				graph.show_path(0, 4)

# OUTPUT
# 0 -> 1(4) -> 7(8)
# 1 -> 0(4) -> 2(8) -> 7(11)
# 7 -> 0(8) -> 1(11) -> 6(1) -> 8(7)
# 2 -> 1(8) -> 3(7) -> 8(2) -> 5(4)
# 3 -> 2(7) -> 4(9) -> 5(14)
# 8 -> 2(2) -> 6(6) -> 7(7)
# 5 -> 2(4) -> 3(14) -> 4(10) -> 6(2)
# 4 -> 3(9) -> 5(10)
# 6 -> 5(2) -> 7(1) -> 8(6)
# Distance from node: 0
# Node 0 has distance: 0
# Node 1 has distance: 4
# Node 2 has distance: 12
# Node 3 has distance: 19
# Node 4 has distance: 21
# Node 5 has distance: 11
# Node 6 has distance: 9
# Node 7 has distance: 8
# Node 8 has distance: 14
# ----Path to reach 4 from 0----
# 0 -> 7 -> 6 -> 5 -> 4
# Total cost of path:  21





