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-Homework 1: Functions, Control
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- - hw01.zip
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- Due by 11:59pm on Monday, September 9
- - - - - -Instructions
- -Download hw01.zip.
- -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:
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- Section 1.1 -
- Section 1.2 -
- Section 1.3 -
- Section 1.4 -
- Section 1.5 -
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.
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Getting Started Videos
- - -These videos may provide some helpful direction for tackling the -problems on this assignment.
- -To see these videos, you should be logged into your berkeley.edu email. - -
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Required Questions
- - - -Q1: A Plus Abs B
- - -Python's operator module contains two-argument functions such as add and
-sub for Python's built-in arithmetic operators. For example, add(2, 3)
-evalutes to 5, just like the expression 2 + 3.
Fill in the blanks in the following function for adding a to the
-absolute value of b, without calling abs. You may not modify any
-of the provided code other than the two blanks.
def a_plus_abs_b(a, b):
- """Return a+abs(b), but without calling abs.
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- >>> a_plus_abs_b(2, 3)
- 5
- >>> a_plus_abs_b(2, -3)
- 5
- >>> a_plus_abs_b(-1, 4)
- 3
- >>> a_plus_abs_b(-1, -4)
- 3
- """
- if b < 0:
- f = _____
- else:
- f = _____
- return f(a, b)Use Ok to test your code:
python3 ok -q a_plus_abs_b- -
Use Ok to run the local syntax checker (which checks that you didn't modify any of the provided code other than the two blanks):
- -python3 ok -q a_plus_abs_b_syntax_checkQ2: Two of Three
- - -Write a function that takes three positive numbers as arguments and returns -the sum of the squares of the two smallest numbers. Use only a single line -for the body of the function.
- -def two_of_three(i, j, k):
- """Return m*m + n*n, where m and n are the two smallest members of the
- positive numbers i, j, and k.
-
- >>> two_of_three(1, 2, 3)
- 5
- >>> two_of_three(5, 3, 1)
- 10
- >>> two_of_three(10, 2, 8)
- 68
- >>> two_of_three(5, 5, 5)
- 50
- """
- return _____
-- -Hint: Consider using the
- -maxorminfunction:>>> max(1, 2, 3) -3 ->>> min(-1, -2, -3) --3
Use Ok to test your code:
python3 ok -q two_of_three- -
Use Ok to run the local syntax checker (which checks that you used only a single line for the body of the function):
- -python3 ok -q two_of_three_syntax_checkQ3: Largest Factor
- - -Write a function that takes an integer n that is greater than 1 and
-returns the largest integer that is smaller than n and evenly divides n.
def largest_factor(n):
- """Return the largest factor of n that is smaller than n.
-
- >>> largest_factor(15) # factors are 1, 3, 5
- 5
- >>> largest_factor(80) # factors are 1, 2, 4, 5, 8, 10, 16, 20, 40
- 40
- >>> largest_factor(13) # factor is 1 since 13 is prime
- 1
- """
- "*** YOUR CODE HERE ***"
-- -Hint: To check if
bevenly dividesa, -use the expressiona % b == 0, which can be read as, -"the remainder when dividingabybis 0."
Use Ok to test your code:
python3 ok -q largest_factor- - - - -
Q4: Hailstone
- - -Douglas Hofstadter's Pulitzer-prize-winning book, Gödel, Escher, Bach, poses -the following mathematical puzzle.
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- Pick a positive integer
nas the start.
- - If
nis even, divide it by 2.
- - If
nis odd, multiply it by 3 and add 1.
- - Continue this process until
nis 1.
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The number n will travel up and down but eventually end at 1 (at least for
-all numbers that have ever been tried -- nobody has ever proved that the
-sequence will terminate). Analogously, a hailstone travels up and down in the
-atmosphere before eventually landing on earth.
This sequence of values of n is often called a Hailstone sequence. Write a
-function that takes a single argument with formal parameter name n, prints
-out the hailstone sequence starting at n, and returns the number of steps in
-the sequence:
def hailstone(n):
- """Print the hailstone sequence starting at n and return its
- length.
-
- >>> a = hailstone(10)
- 10
- 5
- 16
- 8
- 4
- 2
- 1
- >>> a
- 7
- >>> b = hailstone(1)
- 1
- >>> b
- 1
- """
- "*** YOUR CODE HERE ***"
-Hailstone sequences can get quite long! Try 27. What's the longest you can -find?
- -- -Note that if
n == 1initially, then the sequence is one step long.
-Hint: If you see 4.0 but want just 4, try using floor division//instead of regular division/.
Use Ok to test your code:
python3 ok -q hailstone- -
Curious about hailstones or hailstone sequences? Take a look at these articles:
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- Check out this article to learn more about how hailstones work! -
- In 2019, there was a major development in understanding how the hailstone conjecture works for most numbers! -
Check Your Score Locally
- -You can locally check your score on each question of this assignment by running
- -python3 ok --scoreThis 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.
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