Midsemester Survey

We have posted an optional survey that you can complete to give us feedback and help us make the course even better! Completing this survey will yield 1 Extra Credit Point that will be added at the end of the semester.

Linked Lists

A linked list is either an empty linked list (Link.empty) or a first value and the rest of the linked list.

class Link:
    """
    >>> s = Link(1, Link(2, Link(3)))
    >>> s
    Link(1, Link(2, Link(3)))
    """
    empty = ()

    def __init__(self, first, rest=empty):
        assert rest is Link.empty or isinstance(rest, Link)
        self.first = first
        self.rest = rest

    def __repr__(self):
        if self.rest is not Link.empty:
            rest_str = ', ' + repr(self.rest)
        else:
            rest_str = ''
        return 'Link({0}{1})'.format(repr(self.first), rest_str)

To check if a Link is empty, compare it against the class attribute Link.empty. For example, the below function prints out whether or not the link it is handed is empty:

def test_empty(link):
    if link is Link.empty:
        print('This linked list is empty!')
    else:
        print('This linked list is not empty!')

Note: Linked lists are recursive data structures! A linked list contains the first element of the list (first) and a reference to another linked list (rest) which contains the rest of the values in the list.

Question 1: WWPP: Linked Lists

Use OK to test your knowledge with the following "What Would Python Print?" questions:

python3 ok -q link -u

If you get stuck, try loading lab09.py into an interpreter or drawing out the diagram for the linked list on a piece of paper.

>>> from lab09 import *
>>> link = Link(1, Link(2, Link(3)))
>>> link.first
______
1
>>> link.rest.first
______
2
>>> link.rest.rest.rest is Link.empty
______
True
>>> link.first = 9001 >>> link.first
______
9001
>>> link.rest = link.rest.rest >>> link.rest.first
______
3
>>> link = Link(1) >>> link.rest = link >>> link.rest.rest.rest.rest.first
______
1
>>> link = Link(2, Link(3, Link(4))) >>> link2 = Link(1, link) >>> link2.first
______
1
>>> link2.rest.first
______
2
>>> print_link(link2) # Look at print_link in lab09.py
______
<1 2 3 4>

Question 2: Link to List

Write a function link_to_list that converts a given Link to a Python list.

def link_to_list(link):
    """Takes a Link and returns a Python list with the same elements.

    >>> link = Link(1, Link(2, Link(3, Link(4))))
    >>> link_to_list(link)
    [1, 2, 3, 4]
    >>> link_to_list(Link.empty)
    []
    """
"*** YOUR CODE HERE ***"
# Recursive solution if link is Link.empty: return [] return [link.first] + link_to_list(link.rest) # Iterative solution def link_to_list(link): result = [] while link is not Link.empty: result.append(link.first) link = link.rest return result

Use OK to test your code:

python3 ok -q link_to_list

Question 3: Deep Map

Implement deep_map, which takes a function f and a link. It returns a new linked list with the same structure as link, but with f applied to any element within link or any Link instance contained in link.

The deep_map function should recursively apply fn to each of that Link's elements rather than to that Link itself.

Hint: You may find the built-in isinstance function useful.

def deep_map(f, link):
    """Return a Link with the same structure as link but with fn mapped over
    its elements. If an element is an instance of a linked list, recursively
    apply f inside that linked list as well.

    >>> s = Link(1, Link(Link(2, Link(3)), Link(4)))
    >>> print_link(deep_map(lambda x: x * x, s))
    <1 <4 9> 16>
    >>> print_link(s) # unchanged
    <1 <2 3> 4>
    >>> print_link(deep_map(lambda x: 2 * x, Link(s, Link(Link(Link(5))))))
    <<2 <4 6> 8> <<10>>>
    """
"*** YOUR CODE HERE ***"
if link is Link.empty: return link if isinstance(link.first, Link): first = deep_map(f, link.first) else: first = f(link.first) return Link(first, deep_map(f, link.rest))

Use OK to test your code:

python3 ok -q deep_map

Question 4: Add Links

Let's implement a method in order to add together items of link1 and link2. Do not assume that the links are the same length.

def add_links(link1, link2):
    """Adds two Links, returning a new Link

    >>> l1 = Link(1, Link(2))  
    >>> l2 = Link(3, Link(4, Link(5)))
    >>> new = add_links(l1,l2)
    >>> print_link(new)
    <1 2 3 4 5>
    """
"*** YOUR CODE HERE ***"
if link1 is not Link.empty: return Link(link1.first, add_links(link1.rest, link2)) elif link2 is not Link.empty: return Link(link2.first, add_links(link1, link2.rest)) else: return Link.empty # Iterative version (using reverse) def add_links(link1, link2): result = Link.empty while link1 is not Link.empty: result = Link(link1.first, result) link1 = link1.rest while link2 is not Link.empty: result = Link(link2.first, result) link2 = link2.rest return reverse(result)

Use OK to test your code:

python3 ok -q add_links

Question 5: Every Other

Implement every_other, which takes a linked list s. It mutates s such that all of the odd-indexed elements (using 0-based indexing) are removed from the list. For example:

>>> s = Link('a', Link('b', Link('c', Link('d'))))
>>> every_other(s)
>>> s.first
'a'
>>> s.rest.first
'c'
>>> s.rest.rest is Link.empty
True

If s contains fewer than two elements, s remains unchanged.

Do not return anything! every_other should mutate the original list.

def every_other(s):
    """Mutates a linked list so that all the odd-indiced elements are removed
    (using 0-based indexing).

    >>> s = Link(1, Link(2, Link(3, Link(4))))
    >>> every_other(s)
    >>> s
    Link(1, Link(3))
    >>> odd_length = Link(5, Link(3, Link(1)))
    >>> every_other(odd_length)
    >>> odd_length
    Link(5, Link(1))
    >>> singleton = Link(4)
    >>> every_other(singleton)
    >>> singleton
    Link(4)
    """
"*** YOUR CODE HERE ***"
if s is Link.empty or s.rest is Link.empty: return else: s.rest = s.rest.rest every_other(s.rest)

Use OK to test your code:

python3 ok -q every_other

Extra Questions

The following questions are for extra practice — they can be found in the the lab08_extra.py file. It is recommended that you complete these problems on your own time.

Question 6: Find Intersection

Implement intersection, which takes two linked lists, xs and ys, and finds the Link at which the two linked list begin to intersect (or overlap). Remember that all Links end with Link.empty, so there will always be some overlap.

For the two linked lists below, z1 should be the start of the linked list that you return. Note that you should be comparing with identity, rather than equality; an intersection means that some part of the Link is shared between xs and ys, not just that they have the same elements.

Try to aim for θ(n) runtime (where n is the sum of the lengths of xs and ys), and even θ(1) additional space.

xs:  x1 -> x2 -> z1 -> z2 -> z3 -> ...
                 ^
                 |
ys:        y1 ---+
def intersection(xs, ys):
    """
    >>> a = Link(1)
    >>> intersection(a, Link.empty) is Link.empty
    True

    >>> b = a
    >>> intersection(a, b).first # intersection begins at a
    1

    >>> looks_like_a = Link(1)
    >>> intersection(a, looks_like_a) is Link.empty # no intersection! (identity vs value)
    True

    >>> b = Link(1, Link(2, Link(3, a)))
    >>> a.first = 5
    >>> intersection(a, b).first # intersection begins at a
    5

    >>> c = Link(3, b)
    >>> intersection(b, c).first # intersection begins at b
    1
    >>> intersection(c, b).first # intersection begins at b
    1

    >>> intersection(a, c).first # intersection begins at a
    5
    """
"*** YOUR CODE HERE ***"
if xs is Link.empty or ys is Link.empty: return Link.empty # make xs and ys the same size if len(xs) < len(ys): return intersection(xs, ys.rest) elif len(xs) > len(ys): return intersection(xs.rest, ys) # comparison while xs is not ys: xs, ys = xs.rest, ys.rest return xs

Use OK to test your code:

python3 ok -q intersection

Question 7: Cycles

The Link class can represent lists with cycles. That is, a list may contain itself as a sublist.

>>> s = Link(1, Link(2, Link(3)))
>>> s.rest.rest.rest = s
>>> s.rest.rest.rest.rest.rest.first
3

Implement has_cycle that returns whether its argument, a Link instance, contains a cycle.

Hint: Iterate through the linked list and try keeping track of which Link objects you've already seen.

def has_cycle(link):
    """Return whether link contains a cycle.

    >>> s = Link(1, Link(2, Link(3)))
    >>> s.rest.rest.rest = s
    >>> has_cycle(s)
    True
    >>> t = Link(1, Link(2, Link(3)))
    >>> has_cycle(t)
    False
    >>> u = Link(2, Link(2, Link(2)))
    >>> has_cycle(u)
    False
    """
"*** YOUR CODE HERE ***"
lists = set() while link is not Link.empty: if link in lists: return True lists.add(link) link = link.rest return False

Use OK to test your code:

python3 ok -q has_cycle

Extra for experts: Implement has_cycle with only constant space. (If you followed the hint above, you will use linear space.) The solution is short (less than 20 lines of code), but requires a clever idea. Try to discover the solution yourself before asking around:

def has_cycle_constant(link):
    """Return whether link contains a cycle.

    >>> s = Link(1, Link(2, Link(3)))
    >>> s.rest.rest.rest = s
    >>> has_cycle_constant(s)
    True
    >>> t = Link(1, Link(2, Link(3)))
    >>> has_cycle_constant(t)
    False
    """
"*** YOUR CODE HERE ***"
if link is Link.empty: return False slow, fast = link, link.rest while fast is not Link.empty: if fast.rest == Link.empty: return False elif fast == slow or fast.rest == slow: return True else: slow, fast = slow.rest, fast.rest.rest return False

Use OK to test your code:

python3 ok -q has_cycle_constant

Submit

Make sure to submit this assignment by running:

python3 ok --submit

Extra Credit Practice Open in a new window

These questions are new this semester. They're a mix of Parsons Problems, Code Tracing questions, and Code Writing questions.

Confused about how to use the tool? Check out https://codestyle.herokuapp.com/cs88-lab01 for some problems designed to demonstrate how to solve these types of problems.

These cover some similar material to lab, so can be helpful to further review or try to learn the material. Unlike lab and homework, after you've worked for long enough and tested your code enough times on any of these questions, you'll have the option to view an instructor solution. You'll unlock each question one at a time, either by correctly answering the previous question or by viewing an instructor solution.

Starting from lab 2 onward, each set of questions are worth half (0.5) a point per lab, for a total opportunity of 4-5 points throughout the semester.

Use OK to test your code:

python3 ok -q extra_credit