






'''simple docstring'''
import math
import sys


class    _snake_case   :

					"""simple docstring"""





					def __init__(     self     )      ->	Tuple:
										a_									=   0
										a_									=   []
										a_									=   {}  # To store the pos of node in array




					def  __SCREAMING_SNAKE_CASE (     self     )      ->	Optional[int]:
										return self.cur_size == 0




					def  __SCREAMING_SNAKE_CASE (     self   , UpperCAmelCase__     )      ->	str:
										a_									=   self.left(__SCREAMING_SNAKE_CASE     )
										a_									=   self.right(__SCREAMING_SNAKE_CASE     )
										if lc < self.cur_size and self.array(__SCREAMING_SNAKE_CASE     )[0] < self.array(__SCREAMING_SNAKE_CASE     )[0]:
															a_									=   lc
										else:
															a_									=   idx
										if rc < self.cur_size and self.array(__SCREAMING_SNAKE_CASE     )[0] < self.array(__SCREAMING_SNAKE_CASE     )[0]:
															a_									=   rc
										if smallest != idx:
															self.swap(__SCREAMING_SNAKE_CASE   , __SCREAMING_SNAKE_CASE     )
															self.min_heapify(__SCREAMING_SNAKE_CASE     )




					def  __SCREAMING_SNAKE_CASE (     self   , UpperCAmelCase__     )      ->	str:
										a_									=   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:
										a_									=   self.array[0][1]
										a_									=   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   , UpperCAmelCase__     )      ->	Union[str, Any]:
										return 2 * i + 1




					def  __SCREAMING_SNAKE_CASE (     self   , UpperCAmelCase__     )      ->	Dict:
										return 2 * i + 2




					def  __SCREAMING_SNAKE_CASE (     self   , UpperCAmelCase__     )      ->	str:
										return math.floor(i / 2     )




					def  __SCREAMING_SNAKE_CASE (     self   , UpperCAmelCase__   , UpperCAmelCase__     )      ->	Dict:
										a_									=   j
										a_									=   i
										a_									=   self.array[i]
										a_									=   self.array[j]
										a_									=   temp




					def  __SCREAMING_SNAKE_CASE (     self   , UpperCAmelCase__   , UpperCAmelCase__     )      ->	Union[str, Any]:
										a_									=   self.pos[tup[1]]
										# assuming the new_d is atmost old_d
										a_									=   (new_d, tup[1])
										while idx > 0 and self.array[self.par(__SCREAMING_SNAKE_CASE     )][0] > self.array[idx][0]:
															self.swap(__SCREAMING_SNAKE_CASE   , self.par(__SCREAMING_SNAKE_CASE     )     )
															a_									=   self.par(__SCREAMING_SNAKE_CASE     )



class    _snake_case   :

					"""simple docstring"""





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




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

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

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




					def  __SCREAMING_SNAKE_CASE (     self     )      ->	int:

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




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

										while not q.is_empty():
															a_									=   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]:
																				a_									=   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)   , __SCREAMING_SNAKE_CASE     )
																									a_									=   new_dist
																									a_									=   u

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




					def  __SCREAMING_SNAKE_CASE (     self   , UpperCAmelCase__     )      ->	Union[str, Any]:
										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   , UpperCAmelCase__   , UpperCAmelCase__     )      ->	Any:
										a_									=   []
										a_									=   0
										a_									=   dest
										# Backtracking from dest to src
										while self.par[temp] != -1:
															path.append(__SCREAMING_SNAKE_CASE     )
															if temp != src:
																				for v, w in self.adjList[temp]:
																									if v == self.par[temp]:
																														cost += w
																														break
															a_									=   self.par[temp]
										path.append(__SCREAMING_SNAKE_CASE     )
										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: '   , __SCREAMING_SNAKE_CASE     )


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 random
from typing import List, Optional, Union

import numpy as np
import torch

from ..state import AcceleratorState
from .constants import CUDA_DISTRIBUTED_TYPES
from .dataclasses import DistributedType, RNGType
from .imports import is_npu_available, is_tpu_available, is_xpu_available


if is_tpu_available(check_device=False):
						import torch_xla.core.xla_model as xm

def 							a	(   _UpperCAmelCase					,  _UpperCAmelCase = False )				->				List[str]:






					"""simple docstring"""







					if device_specific:
										seed += AcceleratorState().process_index
					random.seed(_UpperCAmelCase )
					np.random.seed(_UpperCAmelCase )
					torch.manual_seed(_UpperCAmelCase )
					if is_xpu_available():
										torch.xpu.manual_seed_all(_UpperCAmelCase )
					elif is_npu_available():
										torch.npu.manual_seed_all(_UpperCAmelCase )
					else:
										torch.cuda.manual_seed_all(_UpperCAmelCase )
					# ^^ safe to call this function even if cuda is not available
					if is_tpu_available():
										xm.set_rng_state(_UpperCAmelCase )

def 							a	(   _UpperCAmelCase = None					,  _UpperCAmelCase = None )				->				Tuple:






					"""simple docstring"""







					if rng_type == RNGType.TORCH:
										a_									=   torch.get_rng_state()
					elif rng_type == RNGType.CUDA:
										a_									=   torch.cuda.get_rng_state()
					elif rng_type == RNGType.XLA:
										assert is_tpu_available(), "Can't synchronize XLA seeds on an environment without TPUs."
										a_									=   torch.tensor(xm.get_rng_state() )
					elif rng_type == RNGType.NPU:
										assert is_npu_available(), "Can't synchronize NPU seeds on an environment without NPUs."
										a_									=   torch.npu.get_rng_state()
					elif rng_type == RNGType.XPU:
										assert is_xpu_available(), "Can't synchronize XPU seeds on an environment without XPUs."
										a_									=   torch.xpu.get_rng_state()
					elif rng_type == RNGType.GENERATOR:
										assert generator is not None, "Need a generator to synchronize its seed."
										a_									=   generator.get_state()

					# Broadcast the rng state from device 0 to other devices
					a_									=   AcceleratorState()
					if state.distributed_type == DistributedType.TPU:
										a_									=   rng_state.to(xm.xla_device() )
										xm.collective_broadcast([rng_state] )
										xm.mark_step()
										a_									=   rng_state.cpu()
					elif (
					    state.distributed_type in CUDA_DISTRIBUTED_TYPES
					    or state.distributed_type == DistributedType.MULTI_NPU
					    or state.distributed_type == DistributedType.MULTI_XPU
					):
										a_									=   rng_state.to(state.device )
										torch.distributed.broadcast(_UpperCAmelCase					,  0 )
										a_									=   rng_state.cpu()
					elif state.distributed_type == DistributedType.MULTI_CPU:
										torch.distributed.broadcast(_UpperCAmelCase					,  0 )

					# Set the broadcast rng state
					if rng_type == RNGType.TORCH:
										torch.set_rng_state(_UpperCAmelCase )
					elif rng_type == RNGType.CUDA:
										torch.cuda.set_rng_state(_UpperCAmelCase )
					elif rng_type == RNGType.NPU:
										torch.npu.set_rng_state(_UpperCAmelCase )
					elif rng_type == RNGType.XPU:
										torch.xpu.set_rng_state(_UpperCAmelCase )
					elif rng_type == RNGType.XLA:
										xm.set_rng_state(rng_state.item() )
					elif rng_type == RNGType.GENERATOR:
										generator.set_state(_UpperCAmelCase )





def 							a	(   _UpperCAmelCase					,  _UpperCAmelCase = None )				->				Any:






					"""simple docstring"""







					for rng_type in rng_types:
										synchronize_rng_state(RNGType(_UpperCAmelCase )					,  generator=_UpperCAmelCase )

