Lab 5: Midterm Review

Due by 11:59pm on Wednesday, July 13.

Starter Files

Download Inside the archive, you will find starter files for the questions in this lab, along with a copy of the Ok autograder.

Midsemester Survey

Please fill out the course-wide midsemester survey by Wednesday, 7/13 @ 11:59pm PT. This survey is designed to help us make short term adjustments to the course so that it works better for you. We appreciate your feedback. We may not be able to make every change that you request, but we will read all the feedback and consider it.

Required Questions

Let's say we'd like to model a bank account that can handle interactions such as depositing funds or gaining interest on current funds. In the following questions, we will be building off of the Account class. Here's our current definition of the class:

class Account:
    """An account has a balance and a holder.
    >>> a = Account('John')
    >>> a.deposit(10)
    >>> a.balance
    >>> a.interest
    >>> a.time_to_retire(10.25) # 10 -> 10.2 -> 10.404
    >>> a.balance               # balance should not change
    >>> a.time_to_retire(11)    # 10 -> 10.2 -> ... -> 11.040808032
    >>> a.time_to_retire(100)
    max_withdrawal = 10
    interest = 0.02

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

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

    def withdraw(self, amount):
        if amount > self.balance:
            return "Insufficient funds"
        if amount > self.max_withdrawal:
            return "Can't withdraw that amount"
        self.balance = self.balance - amount
        return self.balance

Q1: Retirement

Add a time_to_retire method to the Account class. This method takes in an amount and 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 to the total balance at the end of every year.

    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

Q2: FreeChecking

Implement the FreeChecking class, which is like the Account class from lecture except that it charges a withdraw fee after 2 withdrawals. If a withdrawal is unsuccessful, it still counts towards the number of free withdrawals remaining, but no fee for the withdrawal will be charged.

Hint: Don't forget that FreeChecking inherits from Account! Check the Inheritance section in Topics for a refresher.

class FreeChecking(Account):
    """A bank account that charges for withdrawals, but the first two are free!
    >>> ch = FreeChecking('Jack')
    >>> ch.balance = 20
    >>> ch.withdraw(100)  # First one's free
    'Insufficient funds'
    >>> ch.withdraw(3)    # And the second
    >>> ch.balance
    >>> ch.withdraw(3)    # Ok, two free withdrawals is enough
    >>> ch.withdraw(3)
    >>> ch2 = FreeChecking('John')
    >>> ch2.balance = 10
    >>> ch2.withdraw(3) # No fee
    >>> ch.withdraw(3)  # ch still charges a fee
    >>> ch.withdraw(5)  # Not enough to cover fee + withdraw
    'Insufficient funds'
    withdraw_fee = 1
    free_withdrawals = 2

    "*** YOUR CODE HERE ***"

Use Ok to test your code:

python3 ok -q FreeChecking


Make sure to submit this assignment by running:

python3 ok --submit

Suggested Questions


Q3: Ordered Digits

Implement the function ordered_digits, which takes as input a positive integer and returns True if its digits, read left to right, are in non-decreasing order, and False otherwise. For example, the digits of 5, 11, 127, 1357 are ordered, but not those of 21 or 1375.

Note: You can solve this with either iteration or recursion. We recommend trying both for practice purposes but you will credit for either one.

def ordered_digits(x):
    """Return True if the (base 10) digits of X>0 are in non-decreasing
    order, and False otherwise.

    >>> ordered_digits(5)
    >>> ordered_digits(11)
    >>> ordered_digits(127)
    >>> ordered_digits(1357)
    >>> ordered_digits(21)
    >>> result = ordered_digits(1375) # Return, don't print
    >>> result

    "*** YOUR CODE HERE ***"

Use Ok to test your code:

python3 ok -q ordered_digits

Q4: K Runner

An increasing run of an integer is a sequence of consecutive digits in which each digit is larger than the last. For example, the number 123444345 has four increasing runs: 1234, 4, 4 and 345. Each run can be indexed from the end of the number, starting with index 0. In the example, the 0th run is 345, the first run is 4, the second run is 4 and the third run is 1234.

Implement get_k_run_starter, which takes in integers n and k and returns the 0th digit of the kth increasing run within n. The 0th digit is the leftmost number in the run. You may assume that there are at least k+1 increasing runs in n.

def get_k_run_starter(n, k):
    """Returns the 0th digit of the kth increasing run within n.
    >>> get_k_run_starter(123444345, 0) # example from description
    >>> get_k_run_starter(123444345, 1)
    >>> get_k_run_starter(123444345, 2)
    >>> get_k_run_starter(123444345, 3)
    >>> get_k_run_starter(123412341234, 1)
    >>> get_k_run_starter(1234234534564567, 0)
    >>> get_k_run_starter(1234234534564567, 1)
    >>> get_k_run_starter(1234234534564567, 2)
    i = 0
    final = None
    while ____________________________:
        while ____________________________:
        final = ____________________________
        i = ____________________________
        n = ____________________________
    return final

Use Ok to test your code:

python3 ok -q get_k_run_starter

Higher Order Functions

These are some utility function definitions you may see being used as part of the doctests for the following problems.

from operator import add, mul

square = lambda x: x * x

identity = lambda x: x

triple = lambda x: 3 * x

increment = lambda x: x + 1

Q5: Make Repeater

Implement the function make_repeater so that make_repeater(func, n)(x) returns func(func(...func(x)...)), where func is applied n times. That is, make_repeater(func, n) returns another function that can then be applied to another argument. For example, make_repeater(square, 3)(42) evaluates to square(square(square(42))).

def make_repeater(func, n):
    """Return the function that computes the nth application of func.

    >>> add_three = make_repeater(increment, 3)
    >>> add_three(5)
    >>> make_repeater(triple, 5)(1) # 3 * 3 * 3 * 3 * 3 * 1
    >>> make_repeater(square, 2)(5) # square(square(5))
    >>> make_repeater(square, 4)(5) # square(square(square(square(5))))
    >>> make_repeater(square, 0)(5) # Yes, it makes sense to apply the function zero times!
    "*** YOUR CODE HERE ***"

def composer(func1, func2):
    """Return a function f, such that f(x) = func1(func2(x))."""
    def f(x):
        return func1(func2(x))
    return f

Use Ok to test your code:

python3 ok -q make_repeater

Q6: Apply Twice

Using make_repeater define a function apply_twice that takes a function of one argument as an argument and returns a function that applies the original function twice. For example, if inc is a function that returns 1 more than its argument, then double(inc) should be a function that returns two more:

def apply_twice(func):
    """ Return a function that applies func twice.

    func -- a function that takes one argument

    >>> apply_twice(square)(2)
    "*** YOUR CODE HERE ***"

Use Ok to test your code:

python3 ok -q apply_twice

Environment Diagrams

Q7: Doge

Draw the environment diagram for the following code.

wow = 6

def much(wow):
    if much == wow:
        such = lambda wow: 5
        def wow():
            return such
        return wow
    such = lambda wow: 4
    return wow()

wow = much(much(much))(wow)

You can check out what happens when you run the code block using Python Tutor. Please ignore the “ambiguous parent frame” message on step 18. The parent is in fact f1.

Q8: Environment Diagrams - Challenge

These questions were originally developed by Albert Wu and are included here for extra practice. We recommend checking your work in PythonTutor after filling in the diagrams for the code below.

Challenge 1

Draw the environment diagram that results from executing the code below.

Guiding Notes: Pay special attention to the names of the frames!

Multiple assignments in a single line: We will first evaluate the expressions on the right of the assignment, and then assign those values to the expressions on the left of the assignment. For example, if we had x, y = a, b, the process of evaluating this would be to first evaluate a and b, and then assign the value of a to x, and the value of b to y.

def funny(joke):
    hoax = joke + 1
    return funny(hoax)

def sad(joke):
    hoax = joke - 1
    return hoax + hoax

funny, sad = sad, funny
result = funny(sad(1))

Challenge 2

Draw the environment diagram that results from executing the code below.

def double(x):
    return double(x + x)

first = double

def double(y):
    return y + y

result = first(10)


Q9: Add Characters

Given two words, w1 and w2, we say w1 is a subsequence of w2 if all the letters in w1 appear in w2 in the same order (but not necessarily all together). That is, you can add letters to any position in w1 to get w2. For example, "sing" is a substring of "absorbing" and "cat" is a substring of "contrast".

Implement add_chars, which takes in w1 and w2, where w1 is a substring of w2. This means that w1 is shorter than w2. It should return a string containing the characters you need to add to w1 to get w2. Your solution must use recursion.

In the example above, you need to add the characters "aborb" to "sing" to get "absorbing", and you need to add "ontrs" to "cat" to get "contrast".

The letters in the string you return should be in the order you have to add them from left to right. If there are multiple characters in the w2 that could correspond to characters in w1, use the leftmost one. For example, add_words("coy", "cacophony") should return "acphon", not "caphon" because the first "c" in "coy" corresponds to the first "c" in "cacophony".

def add_chars(w1, w2):
    Return a string containing the characters you need to add to w1 to get w2.

    You may assume that w1 is a subsequence of w2.

    >>> add_chars("owl", "howl")
    >>> add_chars("want", "wanton")
    >>> add_chars("rat", "radiate")
    >>> add_chars("a", "prepare")
    >>> add_chars("resin", "recursion")
    >>> add_chars("fin", "effusion")
    >>> add_chars("coy", "cacophony")
    >>> from construct_check import check
    >>> # ban iteration and sets
    >>> check(LAB_SOURCE_FILE, 'add_chars',
    ...       ['For', 'While', 'Set', 'SetComp']) # Must use recursion
    "*** YOUR CODE HERE ***"

Use Ok to test your code:

python3 ok -q add_chars


Q10: Replace All

Given a dictionary d, replace all occurrences of x as a value (not a key) with y.

Hint: You can iterate through the keys of a dictionary using a for statement:

>>> for k in {1: 2, 3: 4, 5: 6}:
...     print(k)
def replace_all(d, x, y):
    """Replace all occurrences of x as a value (not a key) in d with y.
    >>> d = {3: '3', 'foo': 2, 'bar': 3, 'garply': 3, 'xyzzy': 99}
    >>> replace_all(d, 3, 'poof')
    >>> d == {3: '3', 'foo': 2, 'bar': 'poof', 'garply': 'poof', 'xyzzy': 99}
    "*** YOUR CODE HERE ***"

Use Ok to test your code:

python3 ok -q replace_all