Homework 2
Due by 11:59pm on Tuesday, 9/5
Instructions
Download hw02.zip. Inside the archive, you will find a file called
hw02.py, along with a copy of the ok
autograder.
Submission: When you are done, submit with
python3 ok --submit
.
You may submit more than once before the deadline; only the final submission
will be scored. Check that you have successfully submitted your code on
okpy.org.
See Lab 0
for more instructions on submitting assignments.
Using Ok: If you have any questions about using Ok, please refer to this guide.
Readings: You might find the following references useful:
The construct_check
module is used in this assignment, which defines a
function check
. For example, a call such as
check("foo.py", "func1", ["While", "For", "Recursion"])
checks that the function func1
in file foo.py
does not contain
any while
or for
constructs, and is not an overtly recursive function (i.e.,
one in which a function contains a call to itself by name.)
Several doctests refer to these one-argument functions:
from operator import add, mul
def square(x):
return x * x
def triple(x):
return 3 * x
def identity(x):
return x
def increment(x):
return x + 1
Q1: Product
The summation(n, term)
function from lecture adds up term(1) + ... + term(n)
.
Write a similar product(n, term)
function that returns term(1) * ... *
term(n)
. Show how to define the
factorial function in terms of
product
. Hint: try using the identity
function for factorial
.
def product(n, term):
"""Return the product of the first n terms in a sequence.
n -- a positive integer
term -- a function that takes one argument
>>> product(3, identity) # 1 * 2 * 3
6
>>> product(5, identity) # 1 * 2 * 3 * 4 * 5
120
>>> product(3, square) # 1^2 * 2^2 * 3^2
36
>>> product(5, square) # 1^2 * 2^2 * 3^2 * 4^2 * 5^2
14400
"""
"*** YOUR CODE HERE ***"
# The identity function, defined using a lambda expression!
identity = lambda k: k
def factorial(n):
"""Return n factorial for n >= 0 by calling product.
>>> factorial(4)
24
>>> factorial(6)
720
>>> from construct_check import check
>>> check(HW_SOURCE_FILE, 'factorial', ['Recursion', 'For', 'While'])
True
"""
"*** YOUR CODE HERE ***"
return _______
Use Ok to test your code:
python3 ok -q product
python3 ok -q factorial
Q2: Make Adder with a Lambda
Implement the make_adder
function below using a single return
statement that returns the value of a lambda
expression.
def make_adder(n):
"""Return a function that takes an argument K and returns N + K.
>>> add_three = make_adder(3)
>>> add_three(1) + add_three(2)
9
>>> make_adder(1)(2)
3
"""
"*** YOUR CODE HERE ***"
return lambda ________________
Use Ok to test your code:
python3 ok -q make_adder