Homework 2
Due at 11:59:59 pm on 09/14/2023.

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.

Readings: This homework relies on following references:

• Section 1.5
• Section 2.3.1-2.3.5

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 F_n = F_n-1 + F_n-2.

Implement the fib function, which takes an integer n and returns the nth 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: Nonzero

Write a function that takes in a list and returns the first nonzero entry.

def nonzero(lst):
    """ Returns the first nonzero element of a list

    >>> nonzero([1, 2, 3])
    1
    >>> nonzero([0, 1, 2])
    1
    >>> nonzero([0, 0, 0, 0, 0, 0, 5, 0, 6])
    5
    """
    "*** YOUR CODE HERE ***"

Use OK to test your code:

python3 ok -q nonzero

Question 3: Contains N

Write a function that takes in a list and a number, and returns whether or not the list contains the value n.

def has_n(lst, n):
    """ Returns whether or not a list contains the value n.

    >>> has_n([1, 2, 2], 2)
    True
    >>> has_n([0, 1, 2], 3)
    False
    >>> has_n([], 5)
    False
    """
    "*** YOUR CODE HERE ***"

Use OK to test your code:

python3 ok -q has_n

Question 4: Total Price

Implement the function total_price, which takes in a list of prices of individual products and needs to find the total price. Unfortunately, any product that is priced greater than or equal to $20 has a 50 percent tax, so include that in the final price.

Try to do this in one line!

Cast your final answer to an integer to avoid floating point precision errors. For example, if x contains your final answer, return int(x)!

def total_price(prices):
    """
    Finds the total price of all products in prices including a
    50% tax on products with a price greater than or equal to 20.
    >>> total_price([5, 20, 30, 7])
    87
    >>> total_price([8, 4, 3])
    15
    >>> total_price([10, 100, 4])
    164
    """
    "*** YOUR CODE HERE ***"

Use OK to test your code:

python3 ok -q total_price

Question 5: arange

Implement the function arange, which behaves just like np.arange(start, end, step) from Data 8. You only need to support positive values for step.

def arange(start, end, step=1):
    """
    arange behaves just like np.arange(start, end, step).
    You only need to support positive values for step.

    >>> arange(1, 3)
    [1, 2]
    >>> arange(0, 25, 2)
    [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24]
    >>> arange(999, 1231, 34)
    [999, 1033, 1067, 1101, 1135, 1169, 1203]

    """
    "*** YOUR CODE HERE ***"
    

Use OK to test your code:

python3 ok -q arange

Question 6: Reverse (iteratively)

Write a function reverse_iter_for that takes a list and returns a new list that is the reverse of the original using a for loop. You should not need any indexing notation.

def reverse_iter_for(lst):
    """Returns the reverse of the given list.

    >>> reverse_iter_for([1, 2, 3, 4])
    [4, 3, 2, 1]
    """
    "*** YOUR CODE HERE ***"

Use OK to test your code:

python3 ok -q reverse_iter_for

Complete the function reverse_iter_while that behaves identically to reverse_iter_for but is implemented as using a while loop. You may use indexing or slicing notation. Do not use lst[::-1]!

def reverse_iter_while(lst):
    """Returns the reverse of the given list.

    >>> reverse_iter_while([1, 2, 3, 4])
    [4, 3, 2, 1]
    """
    rev_lst = []
    i = 0
    while i < len(lst):
        "*** YOUR CODE HERE ***"

Use OK to test your code:

python3 ok -q reverse_iter_while

Submission

When you are done, submit your file to Gradescope. You only need to upload the following files:

• hw02.py