Homework 2
Due at 11:59:59 pm on 9/18/2020 .
Instructions
Download hw02.zip. Inside the archive, you will find starter files for the questions in this homework, 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 this article for more instructions on okpy and submitting assignments.
Readings: This homework relies on following references:
To submit: run ok
with the --submit
option:
python3 ok --submit
Questions
Question 1: Fibonacci
The Fibonacci sequence is a famous sequence in mathematics. The first element in the sequence is 0 and the second element is 1. The nth element is defined as Fn = Fn-1 + Fn-2.
Implement the fib
function, which takes an integer n
and returns
the n
th Fibonacci number. Use a while
loop in your solution.
def fib(n):
"""Returns the nth Fibonacci number.
>>> fib(0)
0
>>> fib(1)
1
>>> fib(2)
1
>>> fib(3)
2
>>> fib(4)
3
>>> fib(5)
5
>>> fib(6)
8
>>> fib(100)
354224848179261915075
"""
"*** YOUR CODE HERE ***"
Use OK to test your code:
python3 ok -q fib
Question 2: Right Triangle
Write a function that takes in 3 sides a
, b
, and c
and checks to see if they can be possible lenths of the sides of a right triangle. Recall Pythagorean's Theorem:
x^2 + y^2 = z^2 # where z is the hypotenuse
Hint: Find the smallest and largest side first
def right_triangle(a, b, c):
"""Determine whether a, b, and c can be sides of a right triangle
>>> right_triangle(1, 1, 1)
False
>>> right_triangle(5, 3, 4)
True
>>> right_triangle(8, 10, 6)
True
"""
"*** YOUR CODE HERE ***"
Use OK to test your code:
python3 ok -q right_triangle
Question 3: Disneyland Discounts
Disneyland is having a special where they give discounts for
grandparents accompanying their grandchildren. Help Disneyland figure
out when the discount should be given. Define a function
gets_discount
that takes two numbers as input (representing the two
ages) and returns True
if one of them is a senior citizen (age 65 or above)
and the other is a child (age 12 or below). You should not use if
in your
solution.
def gets_discount(x, y):
""" Returns True if this is a combination of a senior citizen
and a child, False otherwise.
>>> gets_discount(65, 12)
True
>>> gets_discount(9, 70)
True
>>> gets_discount(40, 45)
False
>>> gets_discount(40, 75)
False
>>> gets_discount(65, 13)
False
>>> gets_discount(7, 9)
False
>>> gets_discount(73, 77)
False
>>> gets_discount(70, 31)
False
>>> gets_discount(10, 25)
False
"""
"*** YOUR CODE HERE ***"
Use OK to test your code:
python3 ok -q gets_discount
Question 4: Mul_by_num
Using higher order functions, complete the mul_by_num
function. This
function should take an argument and return a one argument function
that multiplies any value passed to it by the original number.
def mul_by_num(factor):
"""
Returns a function that takes one argument and returns num
times that argument.
>>> x = mul_by_num(5)
>>> y = mul_by_num(2)
>>> x(3)
15
>>> y(-4)
-8
"""
"*** YOUR CODE HERE ***"
Use OK to test your code:
python3 ok -q mul_by_num
Question 5: Count van Count
Consider the following implementations of count_factors
and count_primes
:
def count_factors(n):
"""Return the number of positive factors that n has."""
i, count = 1, 0
while i <= n:
if n % i == 0:
count += 1
i += 1
return count
def count_primes(n):
"""Return the number of prime numbers up to and including n."""
i, count = 1, 0
while i <= n:
if is_prime(i):
count += 1
i += 1
return count
def is_prime(n):
return count_factors(n) == 2 # only factors are 1 and n
The implementations look quite similar! Generalize this logic by writing a
function count_cond
, which takes in a two-argument predicate function mystery_function(n,
i)
. count_cond
returns a count of all the numbers from 1 to n
that satisfy
condition
.
Note: A predicate function is a function that returns a boolean (True
or False
).
def count_cond(mystery_function, n):
"""
>>> def divisible(n, i):
... return n % i == 0
>>> count_cond(divisible, 2) # 1, 2
2
>>> count_cond(divisible, 4) # 1, 2, 4
3
>>> count_cond(divisible, 12) # 1, 2, 3, 4, 6, 12
6
>>> def is_prime(n, i):
... return count_cond(divisible, i) == 2
>>> count_cond(is_prime, 2) # 2
1
>>> count_cond(is_prime, 3) # 2, 3
2
>>> count_cond(is_prime, 4) # 2, 3
2
>>> count_cond(is_prime, 5) # 2, 3, 5
3
>>> count_cond(is_prime, 20) # 2, 3, 5, 7, 11, 13, 17, 19
8
"""
"*** YOUR CODE HERE ***"
Use OK to test your code:
python3 ok -q count_cond