Python 3 Linked List Insert Element Problem

Implement two functions

1. insert_last: takes a linked list as a parameter and elem, and returns a new list, where elem was inserted as a last node.

def insert_last(s, elem):

'''

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

>>> insert_last(lst,100)

[2, [1, [100, 'empty']]]

'''

"*** YOUR CODE HERE ***"

2. insert_at: takes a linked-list, an element elem and an insertion index idx and returns the list with the element inserted at the correct location.

def insert_at(s, elem, idx):

'''

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

>>> insert_at(lst, 4, 0)

[4, [3, [2, [1, 'empty']]]]

>>> insert_at(lst, 4, 2)

[3, [2, [4, [1, 'empty']]]]

'''

"*** YOUR CODE HERE ***"

ONLY USE FUNTIONS BELOW:

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]

def len_link(s):

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

length = 0

while s != empty:

s, length = rest(s), length + 1

return length

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)