
"""simple docstring"""




import math
import sys







class 	_lowercase    :


     '''simple docstring'''





     def __init__(   self	)->       Optional[int]:
          UpperCAmelCase__				:			str							=    0
          UpperCAmelCase__				:			str							=    []
          UpperCAmelCase__				:			List[Any]							=    {}  # To store the pos of node in array



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



     def 			lowerCAmelCase__							(   self			,      __UpperCamelCase	)->       List[str]:
          UpperCAmelCase__				:			List[Any]							=    self.left(UpperCAmelCase_	)
          UpperCAmelCase__				:			List[str]							=    self.right(UpperCAmelCase_	)
          if lc < self.cur_size and self.array(UpperCAmelCase_	)[0] < self.array(UpperCAmelCase_	)[0]:
               UpperCAmelCase__				:			int							=    lc
          else:
               UpperCAmelCase__				:			Union[str, Any]							=    idx
          if rc < self.cur_size and self.array(UpperCAmelCase_	)[0] < self.array(UpperCAmelCase_	)[0]:
               UpperCAmelCase__				:			Dict							=    rc
          if smallest != idx:
               self.swap(UpperCAmelCase_			,      UpperCAmelCase_	)
               self.min_heapify(UpperCAmelCase_	)



     def 			lowerCAmelCase__							(   self			,      __UpperCamelCase	)->       Any:
          UpperCAmelCase__				:			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 			lowerCAmelCase__							(   self	)->       str:
          UpperCAmelCase__				:			List[Any]							=    self.array[0][1]
          UpperCAmelCase__				:			int							=    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			,      __UpperCamelCase	)->       Any:
          return 2 * i + 1



     def 			lowerCAmelCase__							(   self			,      __UpperCamelCase	)->       Tuple:
          return 2 * i + 2



     def 			lowerCAmelCase__							(   self			,      __UpperCamelCase	)->       int:
          return math.floor(i / 2	)



     def 			lowerCAmelCase__							(   self			,      __UpperCamelCase			,      __UpperCamelCase	)->       List[Any]:
          UpperCAmelCase__				:			Union[str, Any]							=    j
          UpperCAmelCase__				:			Optional[Any]							=    i
          UpperCAmelCase__				:			int							=    self.array[i]
          UpperCAmelCase__				:			int							=    self.array[j]
          UpperCAmelCase__				:			Tuple							=    temp



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







class 	_lowercase    :


     '''simple docstring'''





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



     def 			lowerCAmelCase__							(   self			,      __UpperCamelCase			,      __UpperCamelCase			,      __UpperCamelCase	)->       Tuple:



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

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



     def 			lowerCAmelCase__							(   self	)->       int:



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



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

          while not q.is_empty():
               UpperCAmelCase__				:			Optional[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__				:			Dict							=    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)			,      UpperCAmelCase_	)
                         UpperCAmelCase__				:			Tuple							=    new_dist
                         UpperCAmelCase__				:			Optional[int]							=    u

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



     def 			lowerCAmelCase__							(   self			,      __UpperCamelCase	)->       Any:
          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			,      __UpperCamelCase			,      __UpperCamelCase	)->       Tuple:
          UpperCAmelCase__				:			int							=    []
          UpperCAmelCase__				:			Any							=    0
          UpperCAmelCase__				:			List[str]							=    dest
          # Backtracking from dest to src
          while self.par[temp] != -1:
               path.append(UpperCAmelCase_	)
               if temp != src:
                    for v, w in self.adjList[temp]:
                         if v == self.par[temp]:
                              cost += w
                              break
               UpperCAmelCase__				:			Tuple							=    self.par[temp]
          path.append(UpperCAmelCase_	)
          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: "			,      UpperCAmelCase_	)


if __name__ == "__main__":
    A__   :						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"""
import importlib
import importlib.metadata
import os
import warnings
from distutils.util import strtobool
from functools import lru_cache

import torch
from packaging import version
from packaging.version import parse

from .environment import parse_flag_from_env
from .versions import compare_versions, is_torch_version


try:
				import torch_xla.core.xla_model as xm  # noqa: F401

				__SCREAMING_SNAKE_CASE				:     List[Any]		=     True
except ImportError:
				__SCREAMING_SNAKE_CASE				:     Dict		=     False


# Cache this result has it's a C FFI call which can be pretty time-consuming
__SCREAMING_SNAKE_CASE				:     Optional[Any]		=     torch.distributed.is_available()







def     _a					(   _SCREAMING_SNAKE_CASE					)     ->					int:
							# Check we're not importing a "pkg_name" directory somewhere but the actual library by trying to grab the version
							snake_case_     							=		importlib.util.find_spec(_SCREAMING_SNAKE_CASE					) is not None
							if package_exists:
														try:
																					snake_case_     							=		importlib.metadata.metadata(_SCREAMING_SNAKE_CASE					)
																					return True
														except importlib.metadata.PackageNotFoundError:
																					return False







def     _a					(   )     ->					bool:
							return _torch_distributed_available







def     _a					(   )     ->					Union[str, Any]:
							try:
														pass
							except ImportError:
														print(
														    """Intel(R) oneCCL Bindings for PyTorch* is required to run DDP on Intel(R) GPUs, but it is not"""
														    """ detected. If you see \"ValueError: Invalid backend: 'ccl'\" error, please install Intel(R) oneCCL"""
														    """ Bindings for PyTorch*."""					)
							return (
							    importlib.util.find_spec("""torch_ccl"""					) is not None
							    or importlib.util.find_spec("""oneccl_bindings_for_pytorch"""					) is not None
							)







def     _a					(   )     ->					Optional[Any]:
							return importlib.metadata.version("""oneccl_bind_pt"""					)







def     _a					(   )     ->					Optional[Any]:
							return _is_package_available("""transformer_engine"""					)







@lru_cache
def     _a					(   _SCREAMING_SNAKE_CASE=True					)     ->					int:
							# Due to bugs on the amp series GPUs, we disable torch-xla on them
							if torch.cuda.is_available():
														return False
							if _tpu_available and check_device:
														try:
																					# Will raise a RuntimeError if no XLA configuration is found
																					snake_case_     							=		xm.xla_device()
																					return True
														except RuntimeError:
																					return False
							return _tpu_available







def     _a					(   )     ->					List[str]:
							return _is_package_available("""deepspeed"""					)







def     _a					(   _SCREAMING_SNAKE_CASE=False					)     ->					Optional[int]:
							if is_tpu_available():
														return not ignore_tpu
							if torch.cuda.is_available():
														return torch.cuda.is_bfaa_supported()
							if is_npu_available():
														return False
							return True







def     _a					(   )     ->					Any:
							snake_case_     							=		_is_package_available("""bitsandbytes"""					)
							if package_exists:
														snake_case_     							=		version.parse(importlib.metadata.version("""bitsandbytes"""					)					)
														return compare_versions(_SCREAMING_SNAKE_CASE					,			""">="""					,			"""0.39.0"""					)
							return False







def     _a					(   )     ->					List[Any]:
							snake_case_     							=		_is_package_available("""bitsandbytes"""					)
							if package_exists:
														snake_case_     							=		version.parse(importlib.metadata.version("""bitsandbytes"""					)					)
														return compare_versions(_SCREAMING_SNAKE_CASE					,			""">="""					,			"""0.37.2"""					)
							return False







def     _a					(   )     ->					Union[str, Any]:
							return _is_package_available("""bitsandbytes"""					)







def     _a					(   )     ->					Optional[int]:
							if strtobool(os.environ.get("""ACCELERATE_USE_MEGATRON_LM"""					,			"""False"""					)					) == 1:
														snake_case_     							=		importlib.util.find_spec("""megatron"""					) is not None
														if package_exists:
																					try:
																												snake_case_     							=		parse(importlib.metadata.version("""megatron-lm"""					)					)
																												return compare_versions(_SCREAMING_SNAKE_CASE					,			""">="""					,			"""2.2.0"""					)
																					except Exception as e:
																												warnings.warn(f"""Parse Megatron version failed. Exception:{e}"""					)
																												return False







def     _a					(   )     ->					str:
							return _is_package_available("""safetensors"""					)







def     _a					(   )     ->					str:
							return _is_package_available("""transformers"""					)







def     _a					(   )     ->					Union[str, Any]:
							return _is_package_available("""datasets"""					)







def     _a					(   )     ->					List[str]:
							return _is_package_available("""aim"""					)







def     _a					(   )     ->					List[str]:
							return _is_package_available("""tensorboard"""					) or _is_package_available("""tensorboardX"""					)







def     _a					(   )     ->					int:
							return _is_package_available("""wandb"""					)







def     _a					(   )     ->					List[Any]:
							return _is_package_available("""comet_ml"""					)







def     _a					(   )     ->					Union[str, Any]:
							return _is_package_available("""boto3"""					)







def     _a					(   )     ->					Optional[Any]:
							if _is_package_available("""rich"""					):
														if "ACCELERATE_DISABLE_RICH" in os.environ:
																					warnings.warn(
																					    """`ACCELERATE_DISABLE_RICH` is deprecated and will be removed in v0.22.0 and deactivated by default. Please use `ACCELERATE_ENABLE_RICH` if you wish to use `rich`."""					)
																					return not parse_flag_from_env("""ACCELERATE_DISABLE_RICH"""					,			_SCREAMING_SNAKE_CASE					)
														return parse_flag_from_env("""ACCELERATE_ENABLE_RICH"""					,			_SCREAMING_SNAKE_CASE					)
							return False







def     _a					(   )     ->					List[Any]:
							return _is_package_available("""sagemaker"""					)







def     _a					(   )     ->					int:
							return _is_package_available("""tqdm"""					)







def     _a					(   )     ->					List[Any]:
							return _is_package_available("""mlflow"""					)







def     _a					(   )     ->					int:
							return is_torch_version(""">="""					,			"""1.12"""					) and torch.backends.mps.is_available() and torch.backends.mps.is_built()







def     _a					(   )     ->					Any:
							def get_major_and_minor_from_version(_SCREAMING_SNAKE_CASE					):
														return str(version.parse(_SCREAMING_SNAKE_CASE					).major					) + "." + str(version.parse(_SCREAMING_SNAKE_CASE					).minor					)

							snake_case_     							=		importlib.metadata.version("""torch"""					)
							if importlib.util.find_spec("""intel_extension_for_pytorch"""					) is None:
														return False
							snake_case_     							=		"""N/A"""
							try:
														snake_case_     							=		importlib.metadata.version("""intel_extension_for_pytorch"""					)
							except importlib.metadata.PackageNotFoundError:
														return False
							snake_case_     							=		get_major_and_minor_from_version(_torch_version					)
							snake_case_     							=		get_major_and_minor_from_version(_ipex_version					)
							if torch_major_and_minor != ipex_major_and_minor:
														warnings.warn(
														    f"""Intel Extension for PyTorch {ipex_major_and_minor} needs to work with PyTorch {ipex_major_and_minor}.*,"""
														    f""" but PyTorch {_torch_version} is found. Please switch to the matching version and run again."""					)
														return False
							return True







@lru_cache
def     _a					(   _SCREAMING_SNAKE_CASE=False					)     ->					List[str]:
							if importlib.util.find_spec("""torch"""					) is None or importlib.util.find_spec("""torch_npu"""					) is None:
														return False

							import torch
							import torch_npu  # noqa: F401

							if check_device:
														try:
																					# Will raise a RuntimeError if no NPU is found
																					snake_case_     							=		torch.npu.device_count()
																					return torch.npu.is_available()
														except RuntimeError:
																					return False
							return hasattr(_SCREAMING_SNAKE_CASE					,			"""npu"""					) and torch.npu.is_available()







@lru_cache
def     _a					(   _SCREAMING_SNAKE_CASE=False					)     ->					int:
							if not parse_flag_from_env("""ACCELERATE_USE_XPU"""					,			default=_SCREAMING_SNAKE_CASE					):
														return False
							if is_ipex_available():
														import torch

														if is_torch_version("""<="""					,			"""1.12"""					):
																					return False
							else:
														return False

							import intel_extension_for_pytorch  # noqa: F401

							if check_device:
														try:
																					# Will raise a RuntimeError if no XPU  is found
																					snake_case_     							=		torch.xpu.device_count()
																					return torch.xpu.is_available()
														except RuntimeError:
																					return False
							return hasattr(_SCREAMING_SNAKE_CASE					,			"""xpu"""					) and torch.xpu.is_available()



