Midterm 1 Review

Starter Files And Practice Exams

Download mt1_review.zip. Inside the archive you will find starter files for the questions in this lab, as well as practice exams (with keys) for the first and second midterms of a previous persion of this course.

Submission

There is no submission for this lab. It's just offered as practice.

All Questions Are Optional

The questions in this assignment are not graded, but they are highly recommended to help you prepare for the upcoming exam.

Suggested Questions

Control

Q1: Unique Digits

Write a function that returns the number of unique digits in a positive integer.

Hints: You can use // and % to separate a positive integer into its one's digit and the rest of its digits.

You may find it helpful to first define a function has_digit(n, k), which determines whether a number n has digit k.
def has_digit(n, k):
    """Returns whether K is a digit in N.
    >>> has_digit(10, 1)
    True
    >>> has_digit(12, 7)
    False
    """
    "*** YOUR CODE HERE ***"

def unique_digits(n):
    """Return the number of unique digits in positive integer n.

    >>> unique_digits(8675309) # All are unique
    7
    >>> unique_digits(1313131) # 1 and 3
    2
    >>> unique_digits(13173131) # 1, 3, and 7
    3
    >>> unique_digits(10000) # 0 and 1
    2
    >>> unique_digits(101) # 0 and 1
    2
    >>> unique_digits(10) # 0 and 1
    2
    """
    "*** YOUR CODE HERE ***"

Q2: 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.

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

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

Q3: K Runner (Challenge)

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):
    """
    >>> get_k_run_starter(123444345, 0) # example from description
    3
    >>> get_k_run_starter(123444345, 1)
    4
    >>> get_k_run_starter(123444345, 2)
    4
    >>> get_k_run_starter(123444345, 3)
    1
    >>> get_k_run_starter(123412341234, 1)
    1
    >>> get_k_run_starter(1234234534564567, 0)
    4
    >>> get_k_run_starter(1234234534564567, 1)
    3
    >>> get_k_run_starter(1234234534564567, 2)
    2
    """
    "*** YOUR CODE HERE ***"

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

Q4: 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)
    8
    >>> make_repeater(triple, 5)(1) # 3 * 3 * 3 * 3 * 3 * 1
    243
    >>> make_repeater(square, 2)(5) # square(square(5))
    625
    >>> make_repeater(square, 4)(5) # square(square(square(square(5))))
    152587890625
    >>> make_repeater(square, 0)(5) # Yes, it makes sense to apply the function zero times!
    5
    """
    "*** YOUR CODE HERE ***"

Hint: We've defined this function for you that composes two functions.

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

Q5: 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)
    16
    """
    "*** YOUR CODE HERE ***"

Environment Diagrams

Q6: 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.

Show PythonTutor

Q7: 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)

Self Reference

Q8: Protected Secret

Write a function protected_secret which takes in a password, secret, and num_attempts.

protected_secret should return another function which takes in a password and prints secret if the password entered matches the password given as an argument to protected_secret. Otherwise, the returned function should print "INCORRECT PASSWORD". After num_attempts incorrect passwords are used, the secret is locked forever and the function should print "SECRET LOCKED".

For example:

>>> my_secret = protected_secret("cosmo2023", "The view from the top of Y Mountain.", 1)
>>> my_secret = my_secret("cosmo2023")
The view from the top of Y Mountain.
>>> my_secret = my_secret("goCougs!")
INCORRECT PASSWORD # 0 Attempts left
>>> my_secret = my_secret("beatUtah!")
SECRET LOCKED

See the doctests for a detailed example.

def protected_secret(password, secret, num_attempts):
    """
    Returns a function which takes in a password and prints the SECRET if the password entered matches
    the PASSWORD given to protected_secret. Otherwise it prints "INCORRECT PASSWORD". After NUM_ATTEMPTS
    incorrect passwords are entered, the secret is locked and the function should print "SECRET LOCKED".

    >>> my_secret = protected_secret("correcthorsebatterystaple", "I love BYU", 2)
    >>> my_secret = my_secret("hax0r_1") # 2 attempts left
    INCORRECT PASSWORD
    >>> my_secret = my_secret("correcthorsebatterystaple")
    I love BYU
    >>> my_secret = my_secret("hax0r_2") # 1 attempt left
    INCORRECT PASSWORD
    >>> my_secret = my_secret("hax0r_3") # No attempts left
    SECRET LOCKED
    >>> my_secret = my_secret("correcthorsebatterystaple")
    SECRET LOCKED
    """
    def get_secret(password_attempt):
        "*** YOUR CODE HERE ***"
    return get_secret