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Linked List Delete Element Problem

Implement a method, remove_first which takes a linked list as a parameter and removes the first element. Make sure to check all possible cases for the possible sizes of the linked list. Use assert statement(s). 

def remove_first(s):

  ''' Removes the first node in the given list

  >>> remove_first(link(4,link(3, link(2, link(1, 'empty')))))

  [3, [2, [1, 'empty']]]

  >>> remove_first(link(1, 'empty'))

  'empty'

  '''

  "*** YOUR CODE HERE ***"

Implement a method, remove_last which takes a linked list as a parameter and removes the last element. Make sure to check all possible cases for the possible sizes of the linked list. Use assert statement(s). 

def remove_last(s):

  ''' Removes the last node in the given list

  >>> remove_last(link(4,link(3, link(2, link(1, 'empty')))))

  [4, [3, [2, 'empty']]]

  >>> remove_last(link(1, 'empty'))

  'empty'

  '''

  "*** YOUR CODE HERE ***"

Implement delete_at which takes a linked-list, and a deletion index and returns the reconstructed list with the element at the given location removed.

def delete_at(s, idx):

  '''Delete element in a given list at provided index.

    Please fill in the provided assert statements and do not

    modify the printed msg.

  >>> lst = link(3, link(2, link(1, empty)))

  >>> delete_at(lst, 0)

  [2, [1, 'empty']]

  >>> delete_at(lst, 2)

  [3, [2, 'empty']]

  '''

  "*** YOUR CODE HERE ***"

IMPORTANT Information:

empty = 'empty'

def is_link(s):

  """s is a linked list if it is empty or a (first, rest) pair."""

  return s == empty or (len(s) == 2 and is_link(s[1]))

def link(first, rest):

  """Construct a linked list from its first element and the rest."""

  assert is_link(rest), "rest must be a linked list."

  return [first, rest]

def first(s):

  """Return the first element of a linked list s."""

  assert is_link(s), "first only applies to linked lists."

  assert s != empty, "empty linked list has no first element."

  return s[0]

def rest(s):

  """Return the rest of the elements of a linked list s."""

  assert is_link(s), "rest only applies to linked lists."

  assert s != empty, "empty linked list has no rest."

  return s[1]

# define length

def len_link(s):

  """Return the length of linked list s."""

  length = 0

  while s != empty:

    s, length = rest(s), length + 1

  return length

# getitem

def getitem(s, i):

  """Return the element at index i of linked list s."""

  while i > 0:

    s, i = rest(s), i - 1

  return first(s)

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