





import math
from enum import Enum
from typing import Optional, Union

from torch.optim import Optimizer
from torch.optim.lr_scheduler import LambdaLR

from .utils import logging


snake_case__					:							Any													=     logging.get_logger(__name__)





class A_					(			_lowerCamelCase   ):
   lowerCAmelCase__        = """linear"""
   lowerCAmelCase__        = """cosine"""
   lowerCAmelCase__        = """cosine_with_restarts"""
   lowerCAmelCase__        = """polynomial"""
   lowerCAmelCase__        = """constant"""
   lowerCAmelCase__        = """constant_with_warmup"""
   lowerCAmelCase__        = """piecewise_constant"""





def _a				(	lowerCamelCase:   Optimizer					,				lowerCamelCase:   int = -1 )	->						List[Any]:







      '''simple docstring'''






      return LambdaLR(lowerCamelCase					,				lambda lowerCamelCase : 1					,				last_epoch=lowerCamelCase )



def _a				(	lowerCamelCase:   Optimizer					,				lowerCamelCase:   int					,				lowerCamelCase:   int = -1 )	->						Tuple:







      '''simple docstring'''






      def lr_lambda(lowerCamelCase:   int ):
            if current_step < num_warmup_steps:
                  return float(lowerCamelCase ) / float(max(1.0					,				lowerCamelCase ) )
            return 1.0

      return LambdaLR(lowerCamelCase					,				lowerCamelCase					,				last_epoch=lowerCamelCase )



def _a				(	lowerCamelCase:   Optimizer					,				lowerCamelCase:   str					,				lowerCamelCase:   int = -1 )	->						Dict:







      '''simple docstring'''






      __A          =				{}
      __A          =				step_rules.split(''',''' )
      for rule_str in rule_list[:-1]:
            __A   ,						__A          =				rule_str.split(''':''' )
            __A          =				int(lowerCamelCase )
            __A          =				float(lowerCamelCase )
            __A          =				value
      __A          =				float(rule_list[-1] )

      def create_rules_function(lowerCamelCase:   Optional[int]					,				lowerCamelCase:   Tuple ):
            def rule_func(lowerCamelCase:   int ) -> float:
                  __A          =				sorted(rules_dict.keys() )
                  for i, sorted_step in enumerate(lowerCamelCase ):
                        if steps < sorted_step:
                              return rules_dict[sorted_steps[i]]
                  return last_lr_multiple

            return rule_func

      __A          =				create_rules_function(lowerCamelCase					,				lowerCamelCase )

      return LambdaLR(lowerCamelCase					,				lowerCamelCase					,				last_epoch=lowerCamelCase )



def _a				(	lowerCamelCase:   List[Any]					,				lowerCamelCase:   Union[str, Any]					,				lowerCamelCase:   Optional[int]					,				lowerCamelCase:   Any=-1 )	->						Dict:







      '''simple docstring'''






      def lr_lambda(lowerCamelCase:   int ):
            if current_step < num_warmup_steps:
                  return float(lowerCamelCase ) / float(max(1					,				lowerCamelCase ) )
            return max(
                0.0					,				float(num_training_steps - current_step ) / float(max(1					,				num_training_steps - num_warmup_steps ) ) )

      return LambdaLR(lowerCamelCase					,				lowerCamelCase					,				lowerCamelCase )



def _a				(	lowerCamelCase:   Optimizer					,				lowerCamelCase:   int					,				lowerCamelCase:   int					,				lowerCamelCase:   float = 0.5					,				lowerCamelCase:   int = -1 )	->						Optional[int]:







      '''simple docstring'''






      def lr_lambda(lowerCamelCase:   int ):
            if current_step < num_warmup_steps:
                  return float(lowerCamelCase ) / float(max(1					,				lowerCamelCase ) )
            __A          =				float(current_step - num_warmup_steps ) / float(max(1					,				num_training_steps - num_warmup_steps ) )
            return max(0.0					,				0.5 * (1.0 + math.cos(math.pi * float(lowerCamelCase ) * 2.0 * progress )) )

      return LambdaLR(lowerCamelCase					,				lowerCamelCase					,				lowerCamelCase )



def _a				(	lowerCamelCase:   Optimizer					,				lowerCamelCase:   int					,				lowerCamelCase:   int					,				lowerCamelCase:   int = 1					,				lowerCamelCase:   int = -1 )	->						str:







      '''simple docstring'''






      def lr_lambda(lowerCamelCase:   List[Any] ):
            if current_step < num_warmup_steps:
                  return float(lowerCamelCase ) / float(max(1					,				lowerCamelCase ) )
            __A          =				float(current_step - num_warmup_steps ) / float(max(1					,				num_training_steps - num_warmup_steps ) )
            if progress >= 1.0:
                  return 0.0
            return max(0.0					,				0.5 * (1.0 + math.cos(math.pi * ((float(lowerCamelCase ) * progress) % 1.0) )) )

      return LambdaLR(lowerCamelCase					,				lowerCamelCase					,				lowerCamelCase )



def _a				(	lowerCamelCase:   Optional[Any]					,				lowerCamelCase:   int					,				lowerCamelCase:   Optional[Any]					,				lowerCamelCase:   str=1e-7					,				lowerCamelCase:   Optional[int]=1.0					,				lowerCamelCase:   Union[str, Any]=-1 )	->						Dict:







      '''simple docstring'''






      __A          =				optimizer.defaults['''lr''']
      if not (lr_init > lr_end):
            raise ValueError(F"""lr_end ({lr_end}) must be be smaller than initial lr ({lr_init})""" )

      def lr_lambda(lowerCamelCase:   int ):
            if current_step < num_warmup_steps:
                  return float(lowerCamelCase ) / float(max(1					,				lowerCamelCase ) )
            elif current_step > num_training_steps:
                  return lr_end / lr_init  # as LambdaLR multiplies by lr_init
            else:
                  __A          =				lr_init - lr_end
                  __A          =				num_training_steps - num_warmup_steps
                  __A          =				1 - (current_step - num_warmup_steps) / decay_steps
                  __A          =				lr_range * pct_remaining**power + lr_end
                  return decay / lr_init  # as LambdaLR multiplies by lr_init

      return LambdaLR(lowerCamelCase					,				lowerCamelCase					,				lowerCamelCase )


snake_case__					:							str													=     {
    SchedulerType.LINEAR: get_linear_schedule_with_warmup,
    SchedulerType.COSINE: get_cosine_schedule_with_warmup,
    SchedulerType.COSINE_WITH_RESTARTS: get_cosine_with_hard_restarts_schedule_with_warmup,
    SchedulerType.POLYNOMIAL: get_polynomial_decay_schedule_with_warmup,
    SchedulerType.CONSTANT: get_constant_schedule,
    SchedulerType.CONSTANT_WITH_WARMUP: get_constant_schedule_with_warmup,
    SchedulerType.PIECEWISE_CONSTANT: get_piecewise_constant_schedule,
}







def _a				(	lowerCamelCase:   Union[str, SchedulerType]					,				lowerCamelCase:   Optimizer					,				lowerCamelCase:   Optional[str] = None					,				lowerCamelCase:   Optional[int] = None					,				lowerCamelCase:   Optional[int] = None					,				lowerCamelCase:   int = 1					,				lowerCamelCase:   float = 1.0					,				lowerCamelCase:   int = -1					,				)	->						str:







      '''simple docstring'''






      __A          =				SchedulerType(lowerCamelCase )
      __A          =				TYPE_TO_SCHEDULER_FUNCTION[name]
      if name == SchedulerType.CONSTANT:
            return schedule_func(lowerCamelCase					,				last_epoch=lowerCamelCase )

      if name == SchedulerType.PIECEWISE_CONSTANT:
            return schedule_func(lowerCamelCase					,				step_rules=lowerCamelCase					,				last_epoch=lowerCamelCase )

      # All other schedulers require `num_warmup_steps`
      if num_warmup_steps is None:
            raise ValueError(F"""{name} requires `num_warmup_steps`, please provide that argument.""" )

      if name == SchedulerType.CONSTANT_WITH_WARMUP:
            return schedule_func(lowerCamelCase					,				num_warmup_steps=lowerCamelCase					,				last_epoch=lowerCamelCase )

      # All other schedulers require `num_training_steps`
      if num_training_steps is None:
            raise ValueError(F"""{name} requires `num_training_steps`, please provide that argument.""" )

      if name == SchedulerType.COSINE_WITH_RESTARTS:
            return schedule_func(
                lowerCamelCase					,				num_warmup_steps=lowerCamelCase					,				num_training_steps=lowerCamelCase					,				num_cycles=lowerCamelCase					,				last_epoch=lowerCamelCase					,				)

      if name == SchedulerType.POLYNOMIAL:
            return schedule_func(
                lowerCamelCase					,				num_warmup_steps=lowerCamelCase					,				num_training_steps=lowerCamelCase					,				power=lowerCamelCase					,				last_epoch=lowerCamelCase					,				)

      return schedule_func(
          lowerCamelCase					,				num_warmup_steps=lowerCamelCase					,				num_training_steps=lowerCamelCase					,				last_epoch=lowerCamelCase )












from __future__ import annotations



def _a				(	lowerCamelCase:   list[float]					,				lowerCamelCase:   Tuple )	->						List[str]:







      '''simple docstring'''






      print(F"""Vertex\tShortest Distance from vertex {src}""" )
      for i, d in enumerate(lowerCamelCase ):
            print(F"""{i}\t\t{d}""" )



def _a				(	lowerCamelCase:   list[dict[str, int]]					,				lowerCamelCase:   list[float]					,				lowerCamelCase:   int )	->						Union[str, Any]:







      '''simple docstring'''






      for j in range(lowerCamelCase ):
            __A   ,						__A   ,						__A          =				(graph[j][k] for k in ['''src''', '''dst''', '''weight'''])
            if distance[u] != float('''inf''' ) and distance[u] + w < distance[v]:
                  return True
      return False



def _a				(	lowerCamelCase:   list[dict[str, int]]					,				lowerCamelCase:   int					,				lowerCamelCase:   int					,				lowerCamelCase:   int )	->						list[float]:







      '''simple docstring'''






      __A          =				[float('''inf''' )] * vertex_count
      __A          =				0.0

      for _ in range(vertex_count - 1 ):
            for j in range(lowerCamelCase ):
                  __A   ,						__A   ,						__A          =				(graph[j][k] for k in ['''src''', '''dst''', '''weight'''])

                  if distance[u] != float('''inf''' ) and distance[u] + w < distance[v]:
                        __A          =				distance[u] + w

      __A          =				check_negative_cycle(lowerCamelCase					,				lowerCamelCase					,				lowerCamelCase )
      if negative_cycle_exists:
            raise Exception('''Negative cycle found''' )

      return distance


if __name__ == "__main__":
       import doctest

       doctest.testmod()

       snake_case__					:							Dict													=     int(input('Enter number of vertices: ').strip())
       snake_case__					:							Optional[int]													=     int(input('Enter number of edges: ').strip())

       snake_case__					:							list[dict[str, int]]													=     [{} for _ in range(E)]

       for i in range(E):
              print('Edge ', i + 1)
              snake_case__						,    snake_case__						,    snake_case__					:							Dict													=     (
                  int(x)
                  for x in input('Enter source, destination, weight: ').strip().split(' ')
              )
              snake_case__					:							List[Any]													=     {'src': src, 'dst': dest, 'weight': weight}

       snake_case__					:							Union[str, Any]													=     int(input('\nEnter shortest path source:').strip())
       snake_case__					:							List[Any]													=     bellman_ford(graph, V, E, source)
       print_distance(shortest_distance, 0)





