





'''simple docstring'''

import math
import sys
class        __lowerCAmelCase  :






							"""simple docstring"""





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

												'''simple docstring'''




												_UpperCamelCase       					= 0
												_UpperCamelCase       					= []
												_UpperCamelCase       					= {}  # To store the pos of node in array





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

												'''simple docstring'''




												return self.cur_size == 0





							def snake_case__		(							self     :	int ,				lowerCAmelCase__     :	Optional[int]  )					->  Tuple:

												'''simple docstring'''




												_UpperCamelCase       					= self.left(lowerCAmelCase__  )
												_UpperCamelCase       					= self.right(lowerCAmelCase__  )
												if lc < self.cur_size and self.array(lowerCAmelCase__  )[0] < self.array(lowerCAmelCase__  )[0]:
																	_UpperCamelCase       					= lc
												else:
																	_UpperCamelCase       					= idx
												if rc < self.cur_size and self.array(lowerCAmelCase__  )[0] < self.array(lowerCAmelCase__  )[0]:
																	_UpperCamelCase       					= rc
												if smallest != idx:
																	self.swap(lowerCAmelCase__ ,				lowerCAmelCase__  )
																	self.min_heapify(lowerCAmelCase__  )





							def snake_case__		(							self     :	Any ,				lowerCAmelCase__     :	List[str]  )					->  int:

												'''simple docstring'''




												_UpperCamelCase       					= self.cur_size
												self.cur_size += 1
												self.array.append((sys.maxsize, tup[1])  )
												self.decrease_key((sys.maxsize, tup[1]) ,				tup[0]  )





							def snake_case__		(							self     :	List[str]  )					->  int:

												'''simple docstring'''




												_UpperCamelCase       					= self.array[0][1]
												_UpperCamelCase       					= self.array[self.cur_size - 1]
												self.cur_size -= 1
												self.min_heapify(1  )
												del self.pos[min_node]
												return min_node





							def snake_case__		(							self     :	Dict ,				lowerCAmelCase__     :	Dict  )					->  Any:

												'''simple docstring'''




												return 2 * i + 1





							def snake_case__		(							self     :	Optional[int] ,				lowerCAmelCase__     :	Optional[Any]  )					->  Optional[Any]:

												'''simple docstring'''




												return 2 * i + 2





							def snake_case__		(							self     :	Dict ,				lowerCAmelCase__     :	List[str]  )					->  Any:

												'''simple docstring'''




												return math.floor(i / 2  )





							def snake_case__		(							self     :	Optional[Any] ,				lowerCAmelCase__     :	str ,				lowerCAmelCase__     :	List[Any]  )					->  Tuple:

												'''simple docstring'''




												_UpperCamelCase       					= j
												_UpperCamelCase       					= i
												_UpperCamelCase       					= self.array[i]
												_UpperCamelCase       					= self.array[j]
												_UpperCamelCase       					= temp







							def snake_case__		(							self     :	List[Any] ,				lowerCAmelCase__     :	List[Any] ,				lowerCAmelCase__     :	Optional[int]  )					->  Optional[int]:

												'''simple docstring'''




												_UpperCamelCase       					= self.pos[tup[1]]
												# assuming the new_d is atmost old_d
												_UpperCamelCase       					= (new_d, tup[1])
												while idx > 0 and self.array[self.par(lowerCAmelCase__  )][0] > self.array[idx][0]:
																	self.swap(lowerCAmelCase__ ,				self.par(lowerCAmelCase__  )  )
																	_UpperCamelCase       					= self.par(lowerCAmelCase__  )

class        __lowerCAmelCase  :






							"""simple docstring"""





							def __init__(							self     :	Optional[int] ,				lowerCAmelCase__     :	List[Any]  )					->  Dict:

												'''simple docstring'''




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





							def snake_case__		(							self     :	List[str] ,				lowerCAmelCase__     :	List[str] ,				lowerCAmelCase__     :	Any ,				lowerCAmelCase__     :	int  )					->  Optional[Any]:

												'''simple docstring'''




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

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





							def snake_case__		(							self     :	str  )					->  str:

												'''simple docstring'''




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





							def snake_case__		(							self     :	Tuple ,				lowerCAmelCase__     :	str  )					->  List[str]:

												'''simple docstring'''




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

												while not q.is_empty():
																	_UpperCamelCase       					= 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]:
																						_UpperCamelCase       					= 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) ,				lowerCAmelCase__  )
																											_UpperCamelCase       					= new_dist
																											_UpperCamelCase       					= u

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





							def snake_case__		(							self     :	Tuple ,				lowerCAmelCase__     :	Union[str, Any]  )					->  List[str]:

												'''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 snake_case__		(							self     :	int ,				lowerCAmelCase__     :	Dict ,				lowerCAmelCase__     :	Optional[int]  )					->  int:

												'''simple docstring'''




												_UpperCamelCase       					= []
												_UpperCamelCase       					= 0
												_UpperCamelCase       					= dest
												# Backtracking from dest to src
												while self.par[temp] != -1:
																	path.append(lowerCAmelCase__  )
																	if temp != src:
																						for v, w in self.adjList[temp]:
																											if v == self.par[temp]:
																																cost += w
																																break
																	_UpperCamelCase       					= self.par[temp]
												path.append(lowerCAmelCase__  )
												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: ''' ,				lowerCAmelCase__  )


if __name__ == "__main__":
			lowercase__		:    Union[str, 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










'''simple docstring'''

lowercase__		:    Tuple =       '\n# Transformers installation\n! pip install transformers datasets evaluate\n# To install from source instead of the last release, comment the command above and uncomment the following one.\n# ! pip install git+https://github.com/huggingface/transformers.git\n'

lowercase__		:    Union[str, Any] =       [{'type': 'code', 'content': INSTALL_CONTENT}]
lowercase__		:    str =       {
    '{processor_class}': 'FakeProcessorClass',
    '{model_class}': 'FakeModelClass',
    '{object_class}': 'FakeObjectClass',
}



