



"""simple docstring"""





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


lowerCamelCase            =		logging.get_logger(__name__)
class    lowercase__     (					__lowerCamelCase   ):







       '''simple docstring'''


       UpperCamelCase		=  '''linear'''
       UpperCamelCase		=  '''cosine'''
       UpperCamelCase		=  '''cosine_with_restarts'''
       UpperCamelCase		=  '''polynomial'''
       UpperCamelCase		=  '''constant'''
       UpperCamelCase		=  '''constant_with_warmup'''
       UpperCamelCase		=  '''piecewise_constant'''



def      a__			(   lowerCAmelCase__			,    lowerCAmelCase__ = -1   ):
      return LambdaLR(lowerCamelCase_			,    lambda lowerCAmelCase__   : 1			,    last_epoch=lowerCamelCase_   )
def      a__			(   lowerCAmelCase__			,    lowerCAmelCase__			,    lowerCAmelCase__ = -1   ):

      def lr_lambda(lowerCAmelCase__   ):
            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__			,    lowerCAmelCase__			,    lowerCAmelCase__ = -1   ):
      UpperCAmelCase_    				=							{}
      UpperCAmelCase_    				=							step_rules.split(","   )
      for rule_str in rule_list[:-1]:
            UpperCAmelCase_    				=							rule_str.split(":"   )
            UpperCAmelCase_    				=							int(lowerCamelCase_   )
            UpperCAmelCase_    				=							float(lowerCamelCase_   )
            UpperCAmelCase_    				=							value
      UpperCAmelCase_    				=							float(rule_list[-1]   )

      def create_rules_function(lowerCAmelCase__			,    lowerCAmelCase__   ):
            def rule_func(lowerCAmelCase__   ) -> float:
                  UpperCAmelCase_    				=							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

      UpperCAmelCase_    				=							create_rules_function(lowerCamelCase_			,    lowerCamelCase_   )

      return LambdaLR(lowerCamelCase_			,    lowerCamelCase_			,    last_epoch=lowerCamelCase_   )
def      a__			(   lowerCAmelCase__			,    lowerCAmelCase__			,    lowerCAmelCase__			,    lowerCAmelCase__=-1   ):

      def lr_lambda(lowerCAmelCase__   ):
            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__			,    lowerCAmelCase__			,    lowerCAmelCase__			,    lowerCAmelCase__ = 0.5			,    lowerCAmelCase__ = -1   ):

      def lr_lambda(lowerCAmelCase__   ):
            if current_step < num_warmup_steps:
                  return float(lowerCamelCase_   ) / float(max(1			,    lowerCamelCase_   )   )
            UpperCAmelCase_    				=							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__			,    lowerCAmelCase__			,    lowerCAmelCase__			,    lowerCAmelCase__ = 1			,    lowerCAmelCase__ = -1   ):

      def lr_lambda(lowerCAmelCase__   ):
            if current_step < num_warmup_steps:
                  return float(lowerCamelCase_   ) / float(max(1			,    lowerCamelCase_   )   )
            UpperCAmelCase_    				=							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__			,    lowerCAmelCase__			,    lowerCAmelCase__			,    lowerCAmelCase__=1e-7			,    lowerCAmelCase__=1.0			,    lowerCAmelCase__=-1   ):
      UpperCAmelCase_    				=							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__   ):
            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:
                  UpperCAmelCase_    				=							lr_init - lr_end
                  UpperCAmelCase_    				=							num_training_steps - num_warmup_steps
                  UpperCAmelCase_    				=							1 - (current_step - num_warmup_steps) / decay_steps
                  UpperCAmelCase_    				=							lr_range * pct_remaining**power + lr_end
                  return decay / lr_init  # as LambdaLR multiplies by lr_init

      return LambdaLR(lowerCamelCase_			,    lowerCamelCase_			,    lowerCamelCase_   )


lowerCamelCase            =		{
    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__			,    lowerCAmelCase__			,    lowerCAmelCase__ = None			,    lowerCAmelCase__ = None			,    lowerCAmelCase__ = None			,    lowerCAmelCase__ = 1			,    lowerCAmelCase__ = 1.0			,    lowerCAmelCase__ = -1			,    ):
      UpperCAmelCase_    				=							SchedulerType(lowerCamelCase_   )
      UpperCAmelCase_    				=							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_   )









"""simple docstring"""





def      a__			(   lowerCAmelCase__   ):
      if not head:
            return True
      # split the list to two parts
      UpperCAmelCase_				,					UpperCAmelCase_    				=							head.next, head
      while fast and fast.next:
            UpperCAmelCase_    				=							fast.next.next
            UpperCAmelCase_    				=							slow.next
      UpperCAmelCase_    				=							slow.next
      UpperCAmelCase_    				=							None  # Don't forget here! But forget still works!
      # reverse the second part
      UpperCAmelCase_    				=							None
      while second:
            UpperCAmelCase_    				=							second.next
            UpperCAmelCase_    				=							node
            UpperCAmelCase_    				=							second
            UpperCAmelCase_    				=							nxt
      # compare two parts
      # second part has the same or one less node
      while node:
            if node.val != head.val:
                  return False
            UpperCAmelCase_    				=							node.next
            UpperCAmelCase_    				=							head.next
      return True
def      a__			(   lowerCAmelCase__   ):
      if not head or not head.next:
            return True

      # 1. Get the midpoint (slow)
      UpperCAmelCase_    				=							UpperCAmelCase_    				=							UpperCAmelCase_    				=							head
      while fast and fast.next:
            UpperCAmelCase_				,					UpperCAmelCase_    				=							fast.next.next, slow.next

      # 2. Push the second half into the stack
      UpperCAmelCase_    				=							[slow.val]
      while slow.next:
            UpperCAmelCase_    				=							slow.next
            stack.append(slow.val   )

      # 3. Comparison
      while stack:
            if stack.pop() != cur.val:
                  return False
            UpperCAmelCase_    				=							cur.next

      return True


def      a__			(   lowerCAmelCase__   ):
      if not head or not head.next:
            return True
      UpperCAmelCase_    				=							{}
      UpperCAmelCase_    				=							0
      while head:
            if head.val in d:
                  d[head.val].append(lowerCAmelCase__   )
            else:
                  UpperCAmelCase_    				=							[pos]
            UpperCAmelCase_    				=							head.next
            pos += 1
      UpperCAmelCase_    				=							pos - 1
      UpperCAmelCase_    				=							0
      for v in d.values():
            if len(lowerCAmelCase__   ) % 2 != 0:
                  middle += 1
            else:
                  UpperCAmelCase_    				=							0
                  for i in range(0			,    len(lowerCAmelCase__   )   ):
                        if v[i] + v[len(lowerCAmelCase__   ) - 1 - step] != checksum:
                              return False
                        step += 1
            if middle > 1:
                  return False
      return True




