


'''simple docstring'''


import math
import sys






class 						lowerCAmelCase__      :




			def __init__(		self	:  str			) ->List[Any]:



					'''simple docstring'''







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




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



					'''simple docstring'''







					return self.cur_size == 0




			def 				lowerCAmelCase__     (		self	:  Union[str, Any]						,	lowerCamelCase__	:  Optional[Any]			) ->Any:



					'''simple docstring'''







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




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



					'''simple docstring'''







					_UpperCAmelCase		:							Union[str, 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 				lowerCAmelCase__     (		self	:  str			) ->int:



					'''simple docstring'''







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




			def 				lowerCAmelCase__     (		self	:  Dict						,	lowerCamelCase__	:  str			) ->Optional[Any]:



					'''simple docstring'''







					return 2 * i + 1




			def 				lowerCAmelCase__     (		self	:  str						,	lowerCamelCase__	:  Tuple			) ->Dict:



					'''simple docstring'''







					return 2 * i + 2




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



					'''simple docstring'''







					return math.floor(i / 2			)




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



					'''simple docstring'''







					_UpperCAmelCase		:							Union[str, Any]             =   j
					_UpperCAmelCase		:							Any             =   i
					_UpperCAmelCase		:							Union[str, Any]             =   self.array[i]
					_UpperCAmelCase		:							Optional[int]             =   self.array[j]
					_UpperCAmelCase		:							Optional[Any]             =   temp






			def 				lowerCAmelCase__     (		self	:  int						,	lowerCamelCase__	:  Tuple						,	lowerCamelCase__	:  Any			) ->Any:



					'''simple docstring'''







					_UpperCAmelCase		:							Optional[Any]             =   self.pos[tup[1]]
					# assuming the new_d is atmost old_d
					_UpperCAmelCase		:							Optional[Any]             =   (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		:							int             =   self.par(lowerCamelCase__			)






class 						lowerCAmelCase__      :




			def __init__(		self	:  List[Any]						,	lowerCamelCase__	:  Tuple			) ->str:



					'''simple docstring'''







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




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



					'''simple docstring'''







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

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




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



					'''simple docstring'''







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




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



					'''simple docstring'''







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

					while not q.is_empty():
							_UpperCAmelCase		:							List[Any]             =   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		:							Optional[Any]             =   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		:							Optional[Any]             =   new_dist
											_UpperCAmelCase		:							List[str]             =   u

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




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



					'''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 				lowerCAmelCase__     (		self	:  List[Any]						,	lowerCamelCase__	:  Union[str, Any]						,	lowerCamelCase__	:  Any			) ->Any:



					'''simple docstring'''







					_UpperCAmelCase		:							Union[str, Any]             =   []
					_UpperCAmelCase		:							List[Any]             =   0
					_UpperCAmelCase		:							Optional[int]             =   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		:							List[Any]             =   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__":
						lowerCamelCase__     						=  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'''


import torch
from torch import autograd






class 						lowerCAmelCase__      (      autograd.Function						):




			@staticmethod
			def 				lowerCAmelCase__     (		lowerCamelCase__	:  Optional[int]						,	lowerCamelCase__	:  torch.tensor						,	lowerCamelCase__	:  float						,	lowerCamelCase__	:  bool			) ->Optional[Any]:



					'''simple docstring'''







					_UpperCAmelCase		:							Optional[int]             =   inputs.numel()
					_UpperCAmelCase		:							Any             =   int(0.0_0_5 * nb_elems			) + 1
					if sigmoid:
							_UpperCAmelCase		:							List[str]             =   (torch.sigmoid(lowerCamelCase__			) > threshold).type(inputs.type()			)
					else:
							_UpperCAmelCase		:							List[Any]             =   (inputs > threshold).type(inputs.type()			)
					if mask.sum() < nb_min:
							# We limit the pruning so that at least 0.5% (half a percent) of the weights are remaining
							_UpperCAmelCase		:							str             =   inputs.flatten().kthvalue(max(nb_elems - nb_min						,	1			)			).values
							_UpperCAmelCase		:							str             =   (inputs > k_threshold).type(inputs.type()			)
					return mask






			@staticmethod
			def 				lowerCAmelCase__     (		lowerCamelCase__	:  List[Any]						,	lowerCamelCase__	:  Optional[int]			) ->Dict:



					'''simple docstring'''







					return gradOutput, None, None






class 						lowerCAmelCase__      (      autograd.Function						):




			@staticmethod
			def 				lowerCAmelCase__     (		lowerCamelCase__	:  Optional[int]						,	lowerCamelCase__	:  torch.tensor						,	lowerCamelCase__	:  float			) ->List[str]:



					'''simple docstring'''







					_UpperCAmelCase		:							Optional[int]             =   inputs.clone()
					_UpperCAmelCase       ,     _UpperCAmelCase		:							Tuple             =   inputs.flatten().sort(descending=lowerCamelCase__			)
					_UpperCAmelCase		:							Optional[int]             =   int(threshold * inputs.numel()			)

					# flat_out and mask access the same memory.
					_UpperCAmelCase		:							str             =   mask.flatten()
					_UpperCAmelCase		:							Optional[int]             =   0
					_UpperCAmelCase		:							Optional[Any]             =   1
					return mask






			@staticmethod
			def 				lowerCAmelCase__     (		lowerCamelCase__	:  Optional[int]						,	lowerCamelCase__	:  Any			) ->Union[str, Any]:



					'''simple docstring'''







					return gradOutput, None






class 						lowerCAmelCase__      (      UpperCAmelCase__						):




			@staticmethod
			def 				lowerCAmelCase__     (		lowerCamelCase__	:  torch.tensor						,	lowerCamelCase__	:  float			) ->Tuple:



					'''simple docstring'''







					_UpperCAmelCase		:							List[Any]             =   inputs.clone()
					_UpperCAmelCase       ,     _UpperCAmelCase		:							Optional[Any]             =   inputs.abs().flatten().sort(descending=lowerCamelCase__			)
					_UpperCAmelCase		:							int             =   int(threshold * inputs.numel()			)

					# flat_out and mask access the same memory.
					_UpperCAmelCase		:							int             =   mask.flatten()
					_UpperCAmelCase		:							List[Any]             =   0
					_UpperCAmelCase		:							int             =   1
					return mask



