Lab 13: Final Review
Due at 11:59pm on Friday, 12/01/17.
Starter Files
Download lab13.zip. Inside the archive, you will find starter files for the questions in this lab, along with a copy of the Ok autograder.
Submission
By the end of this lab, you should have submitted the lab with
python3 ok --submit
. You may submit more than once before the
deadline; only the final submission will be graded.
Check that you have successfully submitted your code on
okpy.org.
- To receive credit for this lab, you must complete Questions 1-4 in lab13.py and lab13.scm and submit through OK.
- Question 5-7 are considered extra practice. They can be found in the lab13_extra.scm and lab13_extra.sql files. It is recommended that you complete them on your own time.
Required Questions
Scheme
These questions are to be done in lab13.scm
.
Q1: Compose All
Implement compose-all
, which takes a list of one-argument functions and
returns a one-argument function that applies each function in that list in turn
to its argument. For example, if func
is the result of calling compose-all
on a list of functions (f g h)
, then (func x)
should be equivalent to the result of calling (h (g (f x)))
.
(define (compose-all funcs)
'YOUR-CODE-HERE
nil
(lambda (x)
(if (null? funcs)
x
((compose-all (cdr funcs)) ((car funcs) x)))))
Use Ok to test your code:
python3 ok -q compose-all
Q2: Deep Map
Write the function deep-map
, which takes a function fn
and a nested list
s
. A nested list is a list where each element is either a number or a list
(e.g. (1 (2) 3)
where 1
, (2)
, and 3
are the elements). It returns a list
with identical structure to s
, but replacing each non-list element by the
result of applying fn
on it, even for elements within sub-lists. For example:
scm> (define (double x) (* 2 x))
double
scm> (deep-map double '(2 (3 4)))
(4 (6 8))
Assume that the input has no dotted (malformed) lists.
Hint: You can use the function
list?
, which checks if a value is a list.
(define (deep-map fn s)
'YOUR-CODE-HERE
nil
(cond ((null? s) s)
((list? (car s)) (cons (deep-map fn (car s))
(deep-map fn (cdr s))))
(else (cons (fn (car s))
(deep-map fn (cdr s))))))
Use Ok to test your code:
python3 ok -q deep-map
Generators
These questions are to be done in lab13.py
.
Q3: Generators generator
Write the function make_generators_generator
, which takes a generator
function g
and defines a generator which yields generators. The i
th generator
yielded will generate items 1 through i
yielded by the
generator returned by g
.
def make_generators_generator(g):
"""Generates all the "sub"-generators of the generator returned by
the generator function g.
>>> def ints_to(n):
... for i in range(1, n + 1):
... yield i
...
>>> def ints_to_5():
... for item in ints_to(5):
... yield item
...
>>> for gen in make_generators_generator(ints_to_5):
... print("Next Generator:")
... for item in gen:
... print(item)
...
Next Generator:
1
Next Generator:
1
2
Next Generator:
1
2
3
Next Generator:
1
2
3
4
Next Generator:
1
2
3
4
5
"""
"*** YOUR CODE HERE ***"
def gen(i):
for item in g():
if i <= 0:
break
yield item
i -= 1
i = 1
for item in g():
yield gen(i)
i += 1
Use Ok to test your code:
python3 ok -q make_generators_generator
Q4: Generate Permutations
Given a list of unique elements, a permutation of the list is a
reordering of the elements. For example, [2, 1, 3]
, [1, 3, 2]
, and
[3, 2, 1]
are all permutations of the list [1, 2, 3]
.
Implement permutations
, a generator function that takes in a lst
and outputs
all permutations of lst
, each as a list (see doctest for an example).
def permutations(lst):
"""Generates all permutations of sequence LST. Each permutation is a
list of the elements in LST in a different order.
The order of the permutations does not matter.
>>> sorted(permutations([1, 2, 3]))
[[1, 2, 3], [1, 3, 2], [2, 1, 3], [2, 3, 1], [3, 1, 2], [3, 2, 1]]
>>> type(permutations([1, 2, 3]))
<class 'generator'>
>>> sorted(permutations((10, 20, 30)))
[[10, 20, 30], [10, 30, 20], [20, 10, 30], [20, 30, 10], [30, 10, 20], [30, 20, 10]]
>>> sorted(permutations("ab"))
[['a', 'b'], ['b', 'a']]
"""
if not lst:
yield []
return
"*** YOUR CODE HERE ***"
for perm in permutations(lst[1:]):
for i in range(len(lst)):
yield perm[:i] + [lst[0]] + perm[i:]
The order in which you generate permutations is irrelevant.
Hint: If you had the permutations of
lst
minus one element, how could you use that to generate the permutations of the fulllst
?
Use Ok to test your code:
python3 ok -q permutations
Optional Questions
More Scheme
This question is to be done in lab13_extra.scm
.
Q5: Tally
Implement tally
, which takes a list of names
and returns a
list of pairs, one pair for each unique name in names
. Each pair should
contain a name and the number of times that the name appeared in names
. Each
name should appear only once in the output, and the names should be ordered by
when they first appear in names
.
Hint: Use the eq?
procedure to test if two names are the same.
(define (tally names)
'YOUR-CODE-HERE
nil
(map (lambda (name) (cons name (count name names))) (unique names)))
Hint: If you find the procedure getting too complicated,
you may want to try implementing the count
and unique
helper procedures to use in
your solution. You may also want to use map
and filter
in your solution.
; Using this helper procedure is optional. You are allowed to delete it.
(define (unique s)
'YOUR-CODE-HERE
nil
(if (null? s) nil
(cons (car s)
(unique (filter (lambda (x) (not (eq? (car s) x))) (cdr s))))))
; Using this helper procedure is optional. You are allowed to delete it.
(define (count name s)
'YOUR-CODE-HERE
nil
(if (null? s) 0
(+ (if (eq? name (car s)) 1 0)
(count name (cdr s)))))
Use Ok to test your code:
python3 ok -q tally
Streams
This question is to be done in lab13_extra.scm
.
Q6: Run-Length Encoding
Run-length encoding is a very simple data compression technique, whereby runs of data are compressed and stored as a single value. A run is defined to be a contiguous sequence of the same number. For example, in the (finite) sequence
1, 1, 1, 1, 1, 6, 6, 6, 6, 2, 5, 5, 5
there are four runs: one each of 1, 6, 2, and 5. We can represent the same sequence as a sequence of two-element lists:
(1 5), (6 4), (2 1), (5 3)
Notice that the first element of each list is the number of times a particular number appears in a run, and the second element is the number in the run.
We will extend this idea to (possibly infinite) streams. Write a
function called rle
that takes in a stream of data, and returns a
corresponding stream of two-element lists, which represents the run-length
encoded version of the stream. You do not have to consider compressing
infinite runs.
(define (rle s)
'YOUR-CODE-HERE
(define (track-run elem st len)
(cond ((null? st) (cons-stream (list elem len) nil))
((= elem (car st)) (track-run elem (cdr-stream st) (+ len 1)))
(else (cons-stream (list elem len) (rle st))))
)
(if (null? s)
nil
(track-run (car s) (cdr-stream s) 1)))
Use Ok to test your code:
python3 ok -q rle
SQL
This question is to be done in lab13_extra.sql
. Make sure you have your sqlite3.exe
file in the folder!
Q7: Pairs
Let’s figure out all possible pairs of numbers between 0 and 42 that sum to 42 (the answer to Life, the Universe, and Everything)!
To do this we can build a pairs
table that contains all pairs without duplicates. This means 2,3 appears but 3,2 doesn't. Then we can use a query to select from this pairs
table to find the ones that sum to 42.
The first 5 rows should look something like this:
sqlite> SELECT * FROM pairs LIMIT 5;
0|0
0|1
0|2
0|3
0|4
Hint: You may want to first create a helper table containing all the possible values you might want to include in your pairs.
CREATE TABLE pairs AS
SELECT "REPLACE THIS LINE WITH YOUR SOLUTION";
WITH
nums(n) as (
SELECT 0 UNION
SELECT n + 1 FROM nums WHERE n < 42
)
SELECT a.n AS x, b.n AS y FROM nums AS a, nums AS b WHERE a.n <= b.n;
Use Ok to test your code:
python3 ok -q pairs