Due by 11:59pm on Thursday, 10/6

Instructions

Download hw06.zip. The vitamin problems can be found in the vitamin directory and the homework problems can be found in the problems directory.

You must run python3 ok --submit two times: once inside the vitamin directory and once inside the problems directory.

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:

Vitamins

Question 1: Counter

Define a function make_counter that returns a counter function, which takes a string and returns the number of times that the function has been called on that string.

def make_counter():
    """Return a counter function.

    >>> c = make_counter()
    >>> c('a')
    1
    >>> c('a')
    2
    >>> c('b')
    1
    >>> c('a')
    3
    >>> c2 = make_counter()
    >>> c2('b')
    1
    >>> c2('b')
    2
    >>> c('b') + c2('b')
    5
    """
    "*** YOUR CODE HERE ***"

Use OK to test your code:

python3 ok -q make_counter

Question 2: Next Fibonacci

Write a function make_fib that returns a function that returns the next Fibonacci number each time it is called. Use a nonlocal statement!

def make_fib():
    """Returns a function that returns the next Fibonacci number
    every time it is called.

    >>> fib = make_fib()
    >>> fib()
    0
    >>> fib()
    1
    >>> fib()
    1
    >>> fib()
    2
    >>> fib()
    3
    >>> fib2 = make_fib()
    >>> fib() + sum([fib2() for _ in range(5)])
    12
    """
    "*** YOUR CODE HERE ***"

Use OK to test your code:

python3 ok -q make_fib

Question 3: Retirement

Add a time_to_retire method to the Account class that takes an amount. It returns how many years the holder would need to wait in order for the current balance to grow to at least amount, assuming that the bank adds balance times the interest rate at the end of every year.

class Account:
    """An account has a balance and a holder.

    >>> a = Account('John')
    >>> a.deposit(10)
    10
    >>> a.balance
    10
    >>> a.interest
    0.02

    >>> a.time_to_retire(10.25) # 10 -> 10.2 -> 10.404
    2
    >>> a.balance               # balance should not change
    10
    >>> a.time_to_retire(11)    # 10 -> 10.2 -> ... -> 11.040808032
    5
    >>> a.time_to_retire(100)
    117
    """

    interest = 0.02  # A class attribute

    def __init__(self, account_holder):
        self.holder = account_holder
        self.balance = 0

    def deposit(self, amount):
        """Add amount to balance."""
        self.balance = self.balance + amount
        return self.balance

    def withdraw(self, amount):
        """Subtract amount from balance if funds are available."""
        if amount > self.balance:
            return 'Insufficient funds'
        self.balance = self.balance - amount
        return self.balance

    def time_to_retire(self, amount):
        """Return the number of years until balance would grow to amount."""
        assert self.balance > 0 and amount > 0 and self.interest > 0
        "*** YOUR CODE HERE ***"

Use OK to test your code:

python3 ok -q Account

Question 4: Free Checking

Implement FreeChecking, which is like the CheckingAccount from lecture except that it only charges a withdraw fee after 2 free withdrawals. Such a deal! Even unsuccessful withdrawals count against the free quota, but only successful withdrawals actually incur a fee.

class FreeChecking(Account):
    """A bank account that charges for withdrawals, but the first two are free!

    >>> ch = FreeChecking('Jack')
    >>> ch.balance = 20
    >>> ch.withdraw(3)    # First one's free
    17
    >>> ch.withdraw(100)  # And the second
    'Insufficient funds'
    >>> ch.balance
    17
    >>> ch.withdraw(3)    # Ok, two free withdrawals is enough
    13
    >>> ch.withdraw(3)
    9
    >>> ch2 = FreeChecking('John')
    >>> ch2.balance = 10
    >>> ch2.withdraw(3) # No fee
    7
    >>> ch.withdraw(3)  # ch still charges a fee
    5
    """
    withdraw_fee = 1
    free_withdrawals = 2

    "*** YOUR CODE HERE ***"

Use OK to test your code:

python3 ok -q FreeChecking

Homework Questions

Mobiles

Acknowledgements. This mobile example is based on a classic problem from Structure and Interpretation of Computer Programs, Section 2.2.2.

A mobile is a type of hanging sculpture. A binary mobile consists of two sides. Each side is a rod of a certain length, from which hangs either a weight or another mobile.

We will represent a binary mobile using the data abstractions below, which use the tree data abstraction for their representation.

A mobile has a left side (index 0) and a right side (index 1).
A side has a length and a structure, which is either a mobile or weight.
A weight has a size, which is a positive number.

Question 5: Weights

Implement the weight data abstraction by completing the weight constructor, the size selector, and the is_weight predicate so that a weight is represented using a tree. The total_weight example is provided to demonstrate use of the mobile, side, and weight abstractions.

def mobile(left, right):
    """Construct a mobile from a left side and a right side."""
    return tree(None, [left, right])

def sides(m):
    """Select the sides of a mobile."""
    return branches(m)

def side(length, mobile_or_weight):
    """Construct a side: a length of rod with a mobile or weight at the end."""
    return tree(length, [mobile_or_weight])

def length(s):
    """Select the length of a side."""
    return root(s)

def end(s):
    """Select the mobile or weight hanging at the end of a side."""
    return branches(s)[0]

def weight(size):
    """Construct a weight of some size."""
    assert size > 0
    "*** YOUR CODE HERE ***"

def size(w):
    """Select the size of a weight."""
    "*** YOUR CODE HERE ***"

def is_weight(w):
    """Whether w is a weight, not a mobile."""
    "*** YOUR CODE HERE ***"

Use OK to test your code:

python3 ok -q total_weight

Question 6: Balanced

Implement the balanced function, which returns whether m is a balanced mobile. A mobile is said to be balanced if the torque applied by its left side is equal to that applied by its right side (that is, if the length of the left rod multiplied by the total weight hanging from that rod is equal to the corresponding product for the right side) and if each of the submobiles hanging off its sides is balanced.

def balanced(m):
    """Return whether m is balanced.

    >>> t, u, v = examples()
    >>> balanced(t)
    True
    >>> balanced(v)
    True
    >>> w = mobile(side(3, t), side(2, u))
    >>> balanced(w)
    False
    >>> balanced(mobile(side(1, v), side(1, w)))
    False
    >>> balanced(mobile(side(1, w), side(1, v)))
    False
    """
    "*** YOUR CODE HERE ***"

Use OK to test your code:

python3 ok -q balanced

Question 7: Totals

Implement the with_totals function, which takes a mobile and returns a tree representation of that same mobile in which the root label of each mobile tree is the total weight of the mobile it represents (instead of None).

Note: This function needs to assume that a mobile is represented as a tree.

def with_totals(m):
    """Return a mobile with total weights stored as the root of each mobile.

    >>> t, _, v = examples()
    >>> root(with_totals(t))
    3
    >>> print(root(t))                           # t should not change
    None
    >>> root(with_totals(v))
    9
    >>> [root(end(s)) for s in sides(with_totals(v))]
    [3, 6]
    >>> [root(end(s)) for s in sides(v)]         # v should not change
    [None, None]
    """
    "*** YOUR CODE HERE ***"

Use OK to test your code:

python3 ok -q with_totals

Mutation

Question 8: Password Protected Account

In lecture, we saw how to use functions to create mutable objects. Here, for example, is the function make_withdraw which produces a function that can withdraw money from an account:

def make_withdraw(balance):
    """Return a withdraw function with BALANCE as its starting balance.
    >>> withdraw = make_withdraw(1000)
    >>> withdraw(100)
    900
    >>> withdraw(100)
    800
    >>> withdraw(900)
    'Insufficient funds'
    """
    def withdraw(amount):
        nonlocal balance
        if amount > balance:
           return 'Insufficient funds'
        balance = balance - amount
        return balance
    return withdraw

Write a version of the make_withdraw function that returns password-protected withdraw functions. That is, make_withdraw should take a password argument (a string) in addition to an initial balance. The returned function should take two arguments: an amount to withdraw and a password.

A password-protected withdraw function should only process withdrawals that include a password that matches the original. Upon receiving an incorrect password, the function should:

Store that incorrect password in a list, and
Return the string 'Incorrect password'.

If a withdraw function has been called three times with incorrect passwords p1, p2, and p3, then it is locked. All subsequent calls to the function should return:

"Your account is locked. Attempts: [<p1>, <p2>, <p3>]"

The incorrect passwords may be the same or different:

def make_withdraw(balance, password):
    """Return a password-protected withdraw function.

    >>> w = make_withdraw(100, 'hax0r')
    >>> w(25, 'hax0r')
    75
    >>> w(90, 'hax0r')
    'Insufficient funds'
    >>> w(25, 'hwat')
    'Incorrect password'
    >>> w(25, 'hax0r')
    50
    >>> w(75, 'a')
    'Incorrect password'
    >>> w(10, 'hax0r')
    40
    >>> w(20, 'n00b')
    'Incorrect password'
    >>> w(10, 'hax0r')
    "Your account is locked. Attempts: ['hwat', 'a', 'n00b']"
    >>> w(10, 'l33t')
    "Your account is locked. Attempts: ['hwat', 'a', 'n00b']"
    """
    "*** YOUR CODE HERE ***"

Use OK to test your code:

python3 ok -q make_withdraw

Question 9: Joint Account

Suppose that our banking system requires the ability to make joint accounts. Define a function make_joint that takes three arguments.

A password-protected withdraw function,
The password with which that withdraw function was defined, and
A new password that can also access the original account.

The make_joint function returns a withdraw function that provides additional access to the original account using either the new or old password. Both functions draw down the same balance. Incorrect passwords provided to either function will be stored and cause the functions to be locked after three wrong attempts.

Hint: The solution is short (less than 10 lines) and contains no string literals! The key is to call withdraw with the right password and amount, then interpret the result. You may assume that all failed attempts to withdraw will return some string (for incorrect passwords, locked accounts, or insufficient funds), while successful withdrawals will return a number.

Use type(value) == str to test if some value is a string:

def make_joint(withdraw, old_password, new_password):
    """Return a password-protected withdraw function that has joint access to
    the balance of withdraw.

    >>> w = make_withdraw(100, 'hax0r')
    >>> w(25, 'hax0r')
    75
    >>> make_joint(w, 'my', 'secret')
    'Incorrect password'
    >>> j = make_joint(w, 'hax0r', 'secret')
    >>> w(25, 'secret')
    'Incorrect password'
    >>> j(25, 'secret')
    50
    >>> j(25, 'hax0r')
    25
    >>> j(100, 'secret')
    'Insufficient funds'

    >>> j2 = make_joint(j, 'secret', 'code')
    >>> j2(5, 'code')
    20
    >>> j2(5, 'secret')
    15
    >>> j2(5, 'hax0r')
    10

    >>> j2(25, 'password')
    'Incorrect password'
    >>> j2(5, 'secret')
    "Your account is locked. Attempts: ['my', 'secret', 'password']"
    >>> j(5, 'secret')
    "Your account is locked. Attempts: ['my', 'secret', 'password']"
    >>> w(5, 'hax0r')
    "Your account is locked. Attempts: ['my', 'secret', 'password']"
    >>> make_joint(w, 'hax0r', 'hello')
    "Your account is locked. Attempts: ['my', 'secret', 'password']"
    """
    "*** YOUR CODE HERE ***"

Use OK to test your code:

python3 ok -q make_joint

Homework 6

Instructions

Vitamins

Question 1: Counter

Question 2: Next Fibonacci

Question 3: Retirement

Question 4: Free Checking

Homework Questions

Mobiles

Question 5: Weights

Question 6: Balanced

Question 7: Totals

Mutation

Question 8: Password Protected Account

Question 9: Joint Account