Homework 2 Solutions

hw02.py solution

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 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
    """
    curr, next = 0, 1
    while n > 0:
        curr, next = next, curr + next
        n -= 1
    return curr

Use OK to test your code:

python3 ok -q fib

Question 2: Shopping Total Cost

A shopping cart is represented as a list of 3-element tuples like this:

[(item1, cost1, quantity1), (item2, cost2, quantity2), ..., (itemN, costN, quantityN)]

Complete the function total_cost which takes in a list that represents a shopping cart called shopping_cart and returns the total cost of all the items before tax in that shopping cart. 

def total_cost(shopping_cart):
    """ Returns a float that is the total cost of all items in the shopping cart.
    >>> fruit_cart = [("apple", 0.5, 3), ("banana", 0.25, 4)]
    >>> total_cost(fruit_cart)
    2.5
    >>> cal_cart = [("oski", 1000, 1), ("go", 1.25, 2), ("bears", 3.5, 2)]
    >>> total_cost(cal_cart)
    1009.5
    """
    return sum([price*quantity for (name, price, quantity) in shopping_cart])

Use OK to test your code:

python3 ok -q total_cost

Question 3: Shopping Cart Tax

Complete the function tax which takes in a list that represents a shopping cart called shopping_cart and return a new list that also represents the same shopping cart but with a percent tax added to the price of each item. 
def tax(shopping_cart, percent):
    """ Returns a new list where a `percent` tax is added to each item's price in a shopping cart.
    >>> fruit_cart = [("apple", 0.5, 3), ("banana", 0.25, 4)]
    >>> tax(fruit_cart, 10)
    [('apple', 0.55, 3), ('banana', 0.275, 4)]
    >>> cal_cart = [("oski", 1000, 1), ("go", 1.25, 2), ("bears", 3.5, 2)]
    >>> tax(cal_cart, 100)
    [('oski', 2000.0, 1), ('go', 2.5, 2), ('bears', 7.0, 2)]
    """
    tax_multiplier= 1 + (percent / 100)
    return [(name, price * tax_multiplier, quantity) for (name, price, quantity) in shopping_cart]

Use OK to test your code:

python3 ok -q tax

Question 4: Deck of cards

Write a list comprehension that will create a deck of cards, given a list of suits and a list of numbers. Each element in the list will be a card, which is represented by a 2-element list of the form [suit, number].

def deck(suits, numbers):
    """Creates a deck of cards (a list of 2-element lists) with the given
    suits and numbers. Each element in the returned list should be of the form
    [suit, number].

    >>> deck(['S', 'C'], [1, 2, 3])
    [['S', 1], ['S', 2], ['S', 3], ['C', 1], ['C', 2], ['C', 3]]
    >>> deck(['S', 'C'], [3, 2, 1])
    [['S', 3], ['S', 2], ['S', 1], ['C', 3], ['C', 2], ['C', 1]]
    >>> deck([], [3, 2, 1])
    []
    >>> deck(['S', 'C'], [])
    []
    """
    return [[suit, number] for suit in suits
                           for number in numbers]

Use OK to test your code:

python3 ok -q deck

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]

    """
    value = start
    result = []
    while value < end:
        result.append(value)
        value += step

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]
    """
    rev_lst = []
    for e in lst:
        rev_lst = [e] + rev_lst
    return rev_lst

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):
        rev_lst = [lst[i]] + rev_lst
        i += 1
    return rev_lst

Use OK to test your code:

python3 ok -q reverse_iter_while