
'''simple docstring'''

import math
import sys






class 				A       :





	def __init__(   self     :    str							):


				"""simple docstring"""

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





	def 							__SCREAMING_SNAKE_CASE					(   self     :    str							):


				"""simple docstring"""

				return self.cur_size == 0





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


				"""simple docstring"""

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





	def 							__SCREAMING_SNAKE_CASE					(   self     :    List[Any] ,							__magic_name__     :    Union[str, Any]							):


				"""simple docstring"""

				lowerCAmelCase__									=							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     :    Tuple							):


				"""simple docstring"""

				lowerCAmelCase__									=							self.array[0][1]
				lowerCAmelCase__									=							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     :    List[Any] ,							__magic_name__     :    Any							):


				"""simple docstring"""

				return 2 * i + 1





	def 							__SCREAMING_SNAKE_CASE					(   self     :    List[Any] ,							__magic_name__     :    str							):


				"""simple docstring"""

				return 2 * i + 2





	def 							__SCREAMING_SNAKE_CASE					(   self     :    Tuple ,							__magic_name__     :    Dict							):


				"""simple docstring"""

				return math.floor(i / 2							)





	def 							__SCREAMING_SNAKE_CASE					(   self     :    List[Any] ,							__magic_name__     :    str ,							__magic_name__     :    List[Any]							):


				"""simple docstring"""

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







	def 							__SCREAMING_SNAKE_CASE					(   self     :    int ,							__magic_name__     :    str ,							__magic_name__     :    List[Any]							):


				"""simple docstring"""

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






class 				A       :





	def __init__(   self     :    Dict ,							__magic_name__     :    str							):


				"""simple docstring"""

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





	def 							__SCREAMING_SNAKE_CASE					(   self     :    Optional[Any] ,							__magic_name__     :    List[str] ,							__magic_name__     :    Optional[Any] ,							__magic_name__     :    Optional[Any]							):


				"""simple docstring"""

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

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





	def 							__SCREAMING_SNAKE_CASE					(   self     :    int							):


				"""simple docstring"""

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





	def 							__SCREAMING_SNAKE_CASE					(   self     :    List[str] ,							__magic_name__     :    Any							):


				"""simple docstring"""

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

				while not q.is_empty():
							lowerCAmelCase__									=							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__									=							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) ,							__magic_name__							)
													lowerCAmelCase__									=							new_dist
													lowerCAmelCase__									=							u

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





	def 							__SCREAMING_SNAKE_CASE					(   self     :    List[str] ,							__magic_name__     :    Optional[Any]							):


				"""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     :    str ,							__magic_name__     :    Tuple ,							__magic_name__     :    Union[str, Any]							):


				"""simple docstring"""

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


if __name__ == "__main__":
		UpperCAmelCase__				:	int					=						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'''

UpperCAmelCase__				:	List[str]					=						"\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"

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





