

'''simple docstring'''

from __future__ import annotations

from collections.abc import Iterator
from typing import Any





class 							_snake_case :
   def __init__( self			:      Optional[int]     ,SCREAMING_SNAKE_CASE__			:      Any							):
     SCREAMING_SNAKE_CASE:Any						      =					data
     SCREAMING_SNAKE_CASE:Node | None						      =					None





class 							_snake_case :
   def __init__( self			:      Optional[int]							):
     SCREAMING_SNAKE_CASE:List[Any]						      =					None
     SCREAMING_SNAKE_CASE:List[str]						      =					None
   def __iter__( self			:      Optional[Any]							):
     SCREAMING_SNAKE_CASE:Tuple						      =					self.head
     while self.head:
       yield node.data
       SCREAMING_SNAKE_CASE:List[str]						      =					node.next
       if node == self.head:
         break
   def __len__( self			:      List[str]							):
     return sum(1 for _ in self							)
   def __repr__( self			:      List[Any]							):
     return "->".join(str(SCREAMING_SNAKE_CASE__							) for item in iter(self							)							)
   def     __UpperCamelCase						( self			:      Union[str, Any]     ,SCREAMING_SNAKE_CASE__			:      Any							):
     self.insert_nth(len(self							)     ,SCREAMING_SNAKE_CASE__							)
   def     __UpperCamelCase						( self			:      Union[str, Any]     ,SCREAMING_SNAKE_CASE__			:      Any							):
     self.insert_nth(0     ,SCREAMING_SNAKE_CASE__							)
   def     __UpperCamelCase						( self			:      List[str]     ,SCREAMING_SNAKE_CASE__			:      int     ,SCREAMING_SNAKE_CASE__			:      Any							):
     if index < 0 or index > len(self							):
       raise IndexError("list index out of range."							)
     SCREAMING_SNAKE_CASE:List[str]						      =					Node(SCREAMING_SNAKE_CASE__							)
     if self.head is None:
       SCREAMING_SNAKE_CASE:Any						      =					new_node  # first node points itself
       SCREAMING_SNAKE_CASE:Optional[int]						      =					new_node
     elif index == 0:  # insert at head
       SCREAMING_SNAKE_CASE:Optional[int]						      =					self.head
       SCREAMING_SNAKE_CASE:Tuple						      =					new_node
     else:
       SCREAMING_SNAKE_CASE:List[str]						      =					self.head
       for _ in range(index - 1							):
         SCREAMING_SNAKE_CASE:Optional[Any]						      =					temp.next
       SCREAMING_SNAKE_CASE:str						      =					temp.next
       SCREAMING_SNAKE_CASE:Union[str, Any]						      =					new_node
       if index == len(self							) - 1:  # insert at tail
         SCREAMING_SNAKE_CASE:Dict						      =					new_node
   def     __UpperCamelCase						( self			:      int							):
     return self.delete_nth(0							)
   def     __UpperCamelCase						( self			:      Union[str, Any]							):
     return self.delete_nth(len(self							) - 1							)
   def     __UpperCamelCase						( self			:      Union[str, Any]     ,SCREAMING_SNAKE_CASE__			:      int = 0							):
     if not 0 <= index < len(self							):
       raise IndexError("list index out of range."							)
     SCREAMING_SNAKE_CASE:List[Any]						      =					self.head
     if self.head == self.tail:  # just one node
       SCREAMING_SNAKE_CASE:List[str]						      =					None
     elif index == 0:  # delete head node
       SCREAMING_SNAKE_CASE:Union[str, Any]						      =					self.tail.next.next
       SCREAMING_SNAKE_CASE:Optional[int]						      =					self.head.next
     else:
       SCREAMING_SNAKE_CASE:Any						      =					self.head
       for _ in range(index - 1							):
         SCREAMING_SNAKE_CASE:Tuple						      =					temp.next
       SCREAMING_SNAKE_CASE:List[Any]						      =					temp.next
       SCREAMING_SNAKE_CASE:Optional[int]						      =					temp.next.next
       if index == len(self							) - 1:  # delete at tail
         SCREAMING_SNAKE_CASE:Union[str, Any]						      =					temp
     return delete_node.data







   def     __UpperCamelCase						( self			:      List[Any]							):
     return len(self							) == 0





def    A_  ( ):
  SCREAMING_SNAKE_CASE:Union[str, Any]						      =					CircularLinkedList()
  assert len(snake_case ) == 0
  assert circular_linked_list.is_empty() is True
  assert str(snake_case ) == ""

  try:
    circular_linked_list.delete_front()
    raise AssertionError  # This should not happen
  except IndexError:
    assert True  # This should happen

  try:
    circular_linked_list.delete_tail()
    raise AssertionError  # This should not happen
  except IndexError:
    assert True  # This should happen

  try:
    circular_linked_list.delete_nth(-1 )
    raise AssertionError
  except IndexError:
    assert True

  try:
    circular_linked_list.delete_nth(0 )
    raise AssertionError
  except IndexError:
    assert True

  assert circular_linked_list.is_empty() is True
  for i in range(5 ):
    assert len(snake_case ) == i
    circular_linked_list.insert_nth(snake_case      ,       i + 1 )
  assert str(snake_case ) == "->".join(str(snake_case ) for i in range(1      ,       6 ) )

  circular_linked_list.insert_tail(6 )
  assert str(snake_case ) == "->".join(str(snake_case ) for i in range(1      ,       7 ) )
  circular_linked_list.insert_head(0 )
  assert str(snake_case ) == "->".join(str(snake_case ) for i in range(0      ,       7 ) )

  assert circular_linked_list.delete_front() == 0
  assert circular_linked_list.delete_tail() == 6
  assert str(snake_case ) == "->".join(str(snake_case ) for i in range(1      ,       6 ) )
  assert circular_linked_list.delete_nth(2 ) == 3

  circular_linked_list.insert_nth(2      ,       3 )
  assert str(snake_case ) == "->".join(str(snake_case ) for i in range(1      ,       6 ) )

  assert circular_linked_list.is_empty() is False


if __name__ == "__main__":
    import doctest

    doctest.testmod()









'''simple docstring'''

import random





def    A_  ( snake_case      ,       snake_case      ,       snake_case = False ):
  SCREAMING_SNAKE_CASE:dict						      =					{i: [] for i in range(snake_case )}

  # if probability is greater or equal than 1, then generate a complete graph
  if probability >= 1:
    return complete_graph(snake_case )
  # if probability is lower or equal than 0, then return a graph without edges
  if probability <= 0:
    return graph

  # for each couple of nodes, add an edge from u to v
  # if the number randomly generated is greater than probability probability
  for i in range(snake_case ):
    for j in range(i + 1      ,       snake_case ):
      if random.random() < probability:
        graph[i].append(snake_case )
        if not directed:
          # if the graph is undirected, add an edge in from j to i, either
          graph[j].append(snake_case )
  return graph





def    A_  ( snake_case ):
  return {
      i: [j for j in range(snake_case ) if i != j] for i in range(snake_case )
  }


if __name__ == "__main__":
    import doctest

    doctest.testmod()






