Description
2) Introduction
Have you heard of Six Degrees of Separation? This simple theory states that at most 6 people separate you
from any other person in the world. (Facebook actually showed that the number among their users is
significantly lower, at about 4.6. You can read more about it in a research paper
(http://arxiv.org/abs/1111.4570).)
Hollywood has its own version: Kevin Bacon is the center of the universe (not really, but let’s let him feel good
about himself). Every actor who has acted with Kevin Bacon in a movie is assigned a “Bacon number” of 1,
every actor who acted with someone who acted with Kevin Bacon is given a “Bacon number” of 2, and so on.
(What Bacon number does Kevin Bacon have? Think about it for a second.)
Note that if George Clooney acts in a movie with Julia Roberts, who has acted with Kevin Bacon in a different
film, George has a Bacon number of 2 through this relationship. If George himself has also acted in a movie
with Kevin, however, then his Bacon number is 1, and the connection through Julia is irrelevant. We define the
notion of a “Bacon number” to be the smallest number of films separating a given actor (or actress) from Kevin
Bacon.
In this lab, we will explore the notion of the Bacon number. We have prepared an ambitious database of
approximately 37,000 actors and 10,000 films so that you may look up your favorites. Did Julia Roberts and
Kevin Bacon act in the same movie? And what does Robert De Niro have to do with Frozen? Let’s find out!
2.1) The Film Database
We’ve mined a large database of actors and films from IMDB (https://www.imdb.com/) via the
www.themoviedb.org (http://www.themoviedb.org/) API. We present this data set to you as a list of records (3-
element lists), each of the form [actor_id_1, actor_id_2, film_id] , which tells us that actor_id_2 acted
with actor_id_1 in a film denoted by film_id .
Keep in mind that “acts with” is a symmetric relationship. So if [a1, a2, f] is in the list, it is true both that a1
acted with a2 and that a2 acted with a1 , even if [a2, a1, f] is not explicitly represented in the list.
We store this data as JSON files (https://en.wikipedia.org/wiki/JSON). The server tests will use small.json
and large.json , but we have also included a tiny.json that you will use to write your own tests.
2.2) The Names Database
The methods in lab.py expect you to use integer actor IDs, but the tests we give you on this page will have
actor names as inputs and outputs.
We include a file, resources/names.json , which has a JSON (https://en.wikipedia.org/wiki/JSON)
representation of the mapping between actor IDs and names. You can use the load method of Python’s json
module to get the data out of the file and into Python. For an example of this, check out how we load
databases in the setUp functions of test.py .
Which of the following best describes the Python object that results from loading resources/names.json ?
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What is Terry Notary’s ID number?
Which actor has the ID 1250109?
2.3) Using the UI
Your code will be loaded into a small server ( server.py ) and will serve up a visualization website. To use the
visualization, run server.py and use your web browser navigate to localhost:8000 (http://localhost:8000/). You
will need to restart server.py in order to reload your code if you make changes.
You will be able to see actors as circular nodes (hover above the node to see the actor’s name) and the movies
as edges linking nodes together.
Above the graph, we define three different tabs, one for each component of the lab. Each tab sets up the
visualization appropriate for its aspect of the lab.
2.4) lab.py and test.py
These files are yours to edit in order to complete this lab. You should implement the main functionality of the
lab in lab.py , and you should implement additional test cases (as described throughout the assignment) in
test.py .
In lab.py , you will find a skeleton for the functions we expect you to write.
3) Acting Together
Complete the definition of did_x_and_y_act_together in lab.py . This function should take three arguments,
in order:
The database to be used (a list of records of actors who have acted together in a film, as well as a film
ID: [actor_id_1, actor_id_2, film_id] ),
Two IDs representing actors
This function should return True if the two given actors ever acted together in a film, and False otherwise.
For example, Kevin Bacon ( id=4724 ) and Steve Park ( id=4025 ) did not act in a film together, meaning
did_x_and_y_act_together(…, 4724, 4025) should return False .
Inside test.py , we have included a TestTiny class which has a setUp method but no tests. Add at least
one test testing did_x_and_y_act_together on the tiny database (you can open tiny.json in a text editor to
see the data it contains).
When you are done implementing this method and it passes the associated tests, use your code to answer the
following questions according to the data in the resources/small.json database. (Hint: You will need to load
names.json to get the mapping from actors to IDs, then find the actor corresponding to the ID. Consider
writing a helper method that does this automatically.)
According to the small.json database, have Christian Stoehr and Craig Bierko acted together?
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According to the small.json database, have Scott Subiono and Paule Annen acted together?
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According to the small.json database, have Stephen Blackehart and Lew Knopp acted together?
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According to the small.json database, have Philip Bosco and Patrick Malahide acted together?
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Please note that did_x_and_y_act_together is a warmup and was given to help you to get familiar with the
structure of the databases. You don’t have to use the function in subsequent sections.
4) Bacon Number
Complete the definition of get_actors_with_bacon_number in lab.py . This function should take two
arguments, in order:
The database to be used (the same structure as before)
The desired Bacon number
This function should return a Python list containing the ID numbers of all the actors with that Bacon number.
The order of the elements doesn’t matter. Note that we’ll define the Bacon number to be the smallest number
of films separating a given actor from Kevin Bacon, whose actor ID is 4724 .
Look at the data in tiny.json and answer these questions:
What are the IDs of the actors who have a Bacon number of 0 in tiny.json ? Enter your answer below, as a
Python list of integers:
What are the IDs of the actors who have a Bacon number of 1 in tiny.json ? Enter your answer below, as a
Python list of integers:
What are the IDs of the actors who have a Bacon number of 2 in tiny.json ? Enter your answer below, as a
Python list of integers:
Add the three above questions as tests in the TestTiny class, using your get_actors_with_bacon_number
function to compute the lists of actors with Bacon numbers 0, 1, and 2; and comparing against the results you
just found above.
Now you’re ready to write your Bacon number code! Here are some things to think about when writing your
implementation. Consider the set of actors with a Bacon number of 1. Here is a visual representation of the
data from the small.json database:
Given the set of actors with a Bacon number of 1, think of how you can find the set of actors with a Bacon
number of 2:
Once you get a sense for how to get the Bacon number 2 actors from the Bacon number 1 actors, try to
generalize to getting the Bacon number i+1 actors from the Bacon number i actors.
Make sure that your function doesn’t assign multiple Bacon numbers to the same actor.
Note that the test cases in test.py run against small and large databases of actors and films, and that your
implementation needs to be efficient enough to handle the large database in a timely manner.
When you’re done writing this method and it passed all of your tests, answer the following questions:
In the small.json database, what is the list of actors with Bacon number 3? Enter your answer below, as a
Python list of actor names:
In the small.json database, what is the list of actors with Bacon number 4? Enter your answer below, as a
Python list of actor names:
In the large.json database, what is the list of actors with Bacon number 5? Enter your answer below, as a
Python list of actor names:
In the large.json database, what is the list of actors with Bacon number 6? Enter your answer below, as a
Python list of actor names:
5) Paths
Now we’ll turn our attention to finding the chain of actors that connects Kevin Bacon to someone else.
5.1) Bacon Paths
Complete the definition of get_bacon_path in lab.py . The function should take two arguments, in order:
The database to be used (a list of records of actors who have acted together in a film, as well as a film
ID: [actor_id_1, actor_id_2, film_id] ),
An ID representing an actor
Your function should produce a list of actor IDs (any such shortest list, if there are several) detailing a “Bacon
path” from Kevin Bacon to the actor denoted by actor_id . If no path exists, return None .
Please note that the paths are not necessarily unique, and so any shortest list that connects Bacon to the actor
denoted by actor_id is valid. The tester does not hard-code the correct paths and only verifies the length of
the path you find (also that it is indeed a path that exists in the database).
For example, if we run this method with Julia Roberts’s ID ( actor_id=1204 ), one valid path is [4724, 3087,
1204] , showing that Kevin Bacon ( 4724 ) has acted with Robert Duvall ( 3087 ), who in turn acted with Julia
Roberts ( 1204 ).
Take look at the data in tiny.json . What’s the shortest path that connects actor 4724 to actor 46866 ? Enter
your answer below, as a Python list of ID numbers:
Add a test for the case above to the TestTiny class. You can use this test to help make sure your function is
implemented correctly.
5.1.1) Speed
When implementing the path-finding algorithm, you should optimize your code to handle the large database,
which our testing infrastructure will use when testing your code.
In particular, here are a few ideas about speed:
Membership tests (the in operator) on long lists can be very slow. By contrast, the in operator is very
fast on sets and dictionaries (regardless of the lengths of these objects). However, sets and dictionaries
do not retain information about the order of their elements. Consider whether there are cases in your
code where a set or dictionary can be used in place of a list.
Running L.pop(0) on a long list is also slow. If you find yourself doing this, ask: do you really need to
pop? Or can you just use an index to keep track of which list element you’re working on?
Searching through data using a for loop can be slow. Can you reorganize the data so that your search
can be implemented with a single dictionary lookup or set containment check?
You will also need to be careful about your overall algorithm. In particular, avoid repeatedly iterating through
all of data . For example, consider the following graph, with a path highlighted:
Here we’ve started from Kevin Bacon and successfully expanded out our search until we got to the actor we
were looking for. What do we need to keep track of during our search if we want to get the path without looking
for the actor again?
When you have implemented your function and it passes your tests, use it to answer the questions below:
According to the large.json database, what is the path of actors from Kevin Bacon to Ron Howard? Enter
your answer as a Python list of actor names below:
According to the large.json database, what is the path of actors from Kevin Bacon to Jack Hoxie? Enter your
answer as a Python list of actor names below:
According to the large.json database, what is the path of actors from Kevin Bacon to Anton Radacic? Enter
your answer as a Python list of actor names below:
5.2) Arbitrary Paths
What we’ve done so far is pretty good, but it raises an important question: what makes Kevin Bacon so
special? So far, everything we’ve done has centered around him… but let’s expand things a bit, to be able to
find the path that connects two arbitrary actors to each other.
Complete the definition of get_path in lab.py . The function should take three arguments, in order:
The database to be used (a list of records of actors who have acted together in a film, as well as a film
ID: [actor_id_1, actor_id_2, film_id] ),
Two IDs representing actors
Your function should produce a list of actor IDs (any such shortest list, if there are several) detailing a path
from one actor to the other.
Add at least one test case for get_path to TestTiny , based on the contents of the tiny.json database. It
should find the minimal path between two non-Bacon actors.
When you have implemented this function and it passes your tests, use it to answer the questions below:
According to the large.json database, what is the minimal path of actors from Beau Bridges to Vjeran Tin
Turk? Enter your answer as a Python list of actor names below:
According to the large.json database, what is the minimal path of actors from Martin Ljung to Michael
Yarmush? Enter your answer as a Python list of actor names below:
6) Movie Paths
After completing the work above, you might be interested to know what sequence of movies you could watch in
order to traverse the path from one actor to another. For example, to move from Kevin Bacon to Julia Roberts,
one could watch movie ID 94671 (“Jayne Mansfield’s Car,” which connects Kevin Bacon to Robert Duvall) and
18402 (“Something to Talk About,” which connects Robert Duvall to Julia Roberts).
Add some code to your lab.py to determine the list of movie names that connect two arbitrary actors. To this
end, we have included the movies.json database, which maps movie names to ID numbers.
When you have finished this code, use it to answer the following questions:
According to the large.json database, what is the minimal path of movie titles connecting Iva Ilakovac to
Unknown Actor 15? Enter your answer as a Python list of movie names below:
According to the large.json database, what is the minimal path of movie titles connecting Jessica James to
Ric Walker? Enter your answer as a Python list of movie names below:
7) Code Submission
When you have tested your code sufficiently on your own machine, submit your modified lab.py by clicking
on “Choose File”, then clicking the Submit button to send the file to the 6.009 server. The server will run the
tests and report back the results (including timing) below.
Select File No file selected
8) Feedback
When you are finished with the lab, please help us out by answering the following questions:
How many hours, approximately, did you spend working on this lab?
On a scale of 1-7, how difficult was this lab?
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On a scale of 1-7, how much did you learn from completing this lab?
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9) Checkoff
Once you are finished with the code, please come to a tutorial, lab session, or office hour and add yourself to
the queue asking for a checkoff. You must be ready to discuss your code and test cases in detail before
asking for a checkoff.
You should be prepared to demonstrate your code (which should be well-commented, should avoid repetition,
and should make good use of helper functions). In particular, be prepared to discuss:
Your additional test cases in the TestTiny class.
Your implementation of did_x_and_y_act_together .
Your implementation of get_actors_with_bacon_number .
Your implementation of get_path and get_bacon_path , and your test cases for get_path .
How you transformed actor/movie names into ID numbers, and vice versa.
Any additional code you wrote to compute the paths of actor/movie names.
9.1) Grade
You have not yet received this checkoff. When you have completed this checkoff, you will see a grade here.
