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Homework 5 | CS 61A Spring 2024

Homework 5: Generators​

Due by 11:59pm on Thursday, March 7

Instructions​

Download hw05.zip. Inside the archive, you will find a file called hw05.py, along with a copy of the ok autograder.

Submission: When you are done, submit the assignment by uploading all code files you've edited to Gradescope. 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 Gradescope. 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:

Grading: Homework is graded based on correctness. Each incorrect problem will decrease the total score by one point. This homework is out of 2 points.

Required Questions​

Getting Started Videos​

These videos may provide some helpful direction for tackling the coding problems on this assignment.

To see these videos, you should be logged into your berkeley.edu email.

YouTube link

Q1: Infinite Hailstone​

Write a generator function that yiels the elements of the hailstone sequence starting at number n. After reaching the end of the hailstone sequence, the generator should yield the value 1 indefinitely.

Here's a quick reminder of how the hailstone sequence is defined:

  1. Pick a positive integer n as the start.
  2. If n is even, divide it by 2.
  3. If n is odd, multiply it by 3 and add 1.
  4. Continue this process until n is 1.

Try to write this generator function recursively. If you're stuck, you can first try writing it iteratively and then seeing how you can turn that implementation into a recursive one.

Hint: Since hailstone returns a generator, you can yield from a call to hailstone!

def hailstone(n):
    """Q1: Yields the elements of the hailstone sequence starting at n.
       At the end of the sequence, yield 1 infinitely.

    >>> hail_gen = hailstone(10)
    >>> [next(hail_gen) for _ in range(10)]
    [10, 5, 16, 8, 4, 2, 1, 1, 1, 1]
    >>> next(hail_gen)
    1
    """
    "*** YOUR CODE HERE ***"

Use Ok to test your code:

python3 ok -q hailstone

Q2: Merge​

Write a generator function merge that takes in two infinite generators a and b that are in increasing order without duplicates and returns a generator that has all the elements of both generators, in increasing order, without duplicates.

def merge(a, b):
    """Q2:
    >>> def sequence(start, step):
    ...     while True:
    ...         yield start
    ...         start += step
    >>> a = sequence(2, 3) # 2, 5, 8, 11, 14, ...
    >>> b = sequence(3, 2) # 3, 5, 7, 9, 11, 13, 15, ...
    >>> result = merge(a, b) # 2, 3, 5, 7, 8, 9, 11, 13, 14, 15
    >>> [next(result) for _ in range(10)]
    [2, 3, 5, 7, 8, 9, 11, 13, 14, 15]
    """
    "*** YOUR CODE HERE ***"

Use Ok to test your code:

python3 ok -q merge

Q3: Yield Paths​

Define a generator function yield_paths which takes in a tree t, a value value, and returns a generator object which yields each path from the root of t to a node that has label value.

Each path should be represented as a list of the labels along that path in the tree. You may yield the paths in any order.

def yield_paths(t, value):
    """Q4: Yields all possible paths from the root of t to a node with the label
    value as a list.

    >>> t1 = tree(1, [tree(2, [tree(3), tree(4, [tree(6)]), tree(5)]), tree(5)])
    >>> print_tree(t1)
    1
      2
        3
        4
          6
        5
      5
    >>> next(yield_paths(t1, 6))
    [1, 2, 4, 6]
    >>> path_to_5 = yield_paths(t1, 5)
    >>> sorted(list(path_to_5))
    [[1, 2, 5], [1, 5]]

    >>> t2 = tree(0, [tree(2, [t1])])
    >>> print_tree(t2)
    0
      2
        1
          2
            3
            4
              6
            5
          5
    >>> path_to_2 = yield_paths(t2, 2)
    >>> sorted(list(path_to_2))
    [[0, 2], [0, 2, 1, 2]]
    """
    if label(t) == value:
        yield ____
    for b in branches(t):
        for ____ in ____:
            yield ____

Hint: If you're having trouble getting started, think about how you'd approach this problem if it wasn't a generator function. What would your recursive calls be? With a generator function, what happens if you make a "recursive call" within its body?

Hint: Try coming up with a few simple cases of your own! How should this function work when t is a leaf node?

Hint: Remember, it's possible to loop over generator objects because generators are iterators!

Note: Remember that this problem should yield paths -- do not return a list of paths!

Use Ok to test your code:

python3 ok -q yield_paths

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​

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

Exam Practice​

Homework assignments will also contain prior exam questions for you to try. These questions have no submission component; feel free to attempt them if you'd like some practice!

  1. Summer 2018 Final Q7a,b: Streams and Jennyrators
  2. Spring 2019 Final Q1: Iterators are inevitable
  3. Spring 2021 MT2 Q8: The Tree of L-I-F-E
  4. Summer 2016 Final Q8: Zhen-erators Produce Power
  5. Spring 2018 Final Q4a: Apply Yourself