Due by 11:59pm on Friday, February 27.

Starter Files

Download lab05.zip.

Required Questions

Recursion!

Q1: Symmetric List

A list is symmetric if it is the same from left to right as from right to left. For example, [1, 2, 3, 4, 3, 2, 1] is symmetric. Implement symmetric, a function that takes list l and check if l is a symmetric list, Use recursion!

def symmetric(l):
    """Returns whether a list is symmetric.
    >>> symmetric([])
    True
    >>> symmetric([1])
    True
    >>> symmetric([1, 4, 5, 1])
    False
    >>> symmetric([1, 4, 4, 1])
    True
    >>> symmetric(['l', 'o', 'l'])
    True
    """
    "*** YOUR CODE HERE ***"

Use Ok to test your code:

python3 ok -q symmetric
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✂️

Q2: GCD

The greatest common divisor of two positive integers a and b is the largest integer which evenly divides both numbers (with no remainder). Euclid, a Greek mathematician in 300 B.C., realized that the greatest common divisor of a and b is one of the following:

• the smaller value if it evenly divides the larger value, or
• the greatest common divisor of the smaller value and the remainder of the larger value divided by the smaller value

In other words, if a is greater than b and a is not divisible by b, then

gcd(a, b) = gcd(b, a % b)

Write the gcd function recursively using Euclid's algorithm.

def gcd(a, b):
    """Returns the greatest common divisor of a and b.
    Should be implemented using recursion.

    >>> gcd(34, 19)
    1
    >>> gcd(39, 91)
    13
    >>> gcd(20, 30)
    10
    >>> gcd(40, 40)
    40
    """
    "*** YOUR CODE HERE ***"

Use Ok to test your code:

python3 ok -q gcd
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✂️

Q3: Has Seven

Write a recursive function has_seven that takes a positive integer n and returns whether n contains the digit 7. Use recursion - the tests will fail if you use any assignment statements.

def has_seven(k):
    """Returns True if at least one of the digits of k is a 7, False otherwise.

    >>> has_seven(3)
    False
    >>> has_seven(7)
    True
    >>> has_seven(2734)
    True
    >>> has_seven(2634)
    False
    >>> has_seven(374)
    True
    >>> has_seven(140)
    False
    >>> from construct_check import check
    >>> # ban all assignments
    >>> check(SOURCE_FILE, 'has_seven',
    ...       ['Assign', 'AugAssign'])
    True
    """
    "*** YOUR CODE HERE ***"

Use Ok to test your code:

python3 ok -q has_seven
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✂️

Check Your Score Locally

You can locally check your score on each question of this assignment by running

python3 ok --score

This does NOT submit the assignment! When you are satisfied with your score, submit the assignment to Gradescope to receive credit for it.

Submit Assignment

Submit this assignment by uploading any files you've edited to the appropriate Gradescope assignment. Lab 00 has detailed instructions.