Programming and Computation II Lab #3

CMPSC-132: Programming and Computation II

Lab #3

Read the instructions carefully before starting the assignment. Make sure your code follows the
stated guidelines to ensure full credit for your work.
Instructions:
- The work in this lab must be completed alone and must be your own.
- Download the starter code file from the LAB3 Assignment on Canvas. Do not change
the function names on your script.
- A doctest is provided as an example of code functionality. Getting the same result as the
doctest does not guarantee full credit. You are responsible for debugging and testing your
code with enough data, you can share ideas and testing code during your recitation class.
As a reminder, Gradescope should not be used to debug and test code!
- Each function must return the output (Do not use print in your final submission, otherwise
your submissions will receive a -1 point deduction)
- Do not include test code outside any function in the upload. Printing unwanted or illformatted data to output will cause the test cases to fail. Remove all your testing code
before uploading your file (You can also remove the doctest). Do not include the
input() function in your submission.
- For this assignment, you can assume that the parameters will follow the specifications
for each function
Goal
[2.5 pts] Write the recursive function thirtyTwos(n) that takes an integer greater or equal to 0 and
returns an integer that represents the number of times that a 2 directly follows a 3 in the digits of
n. Hint: The % and // operations from sumDigits could be helpful here
>>> thirtyTwos(132432601)
2
[2.5 pts] Write the recursive function flat(aList) that takes a possibly deep list and flattens it. The
function should not mutate the original list. Hint: you can check if something is a list by using the
built-in functions type() or isinstance()
>>> x = [3, [[5, 2]], 6, [4]]
>>> flat(x)
[3, 5, 2, 6, 4]
>>> x
[3, [[5, 2]], 6, [4]]
[2.5 pts] In the starter code, there is a function called triangle that calls the function
recursiveTriangle(n,n) once. For this exercise you must write the recursive function
recursiveTriangle(x, n) that returns a string with the LAST x lines of a right triangle of base and
height n.
- recursiveTriangle(x, n) must be a recursive function, otherwise, no credit is given
- recursiveTriangle(x, n) must return the pattern as ' ***\n **\n *'. As shown in the
example, you can use the print method during testing to check if your pattern is correct.
- Don’t modify anything in the triangle function. If your recursive function is correct,
calling triangle(n) should return the complete right triangle.
>>> triangle(4)
'****\n ***\n **\n *'
>>> print(triangle(4))
****
***
 **
 *
>>> recursiveTriangle(2,4)
' **\n *'
>>> print(recursiveTriangle(2,4))
 **
 *
>>> triangle(6)
'******\n *****\n ****\n ***\n **\n *'
>>> print(triangle(6))
******
*****
 ****
 ***
 **
 *
>>> recursiveTriangle(3,6)
' ***\n **\n *'
>>> print(recursiveTriangle(3,6))
 ***
 **
 *
Notes:
• The doctest includes \\n instead of \n in order to keep consistent leading whitespace
required by the shell session, your code must return output with as \n, otherwise it will fail
the test cases!
This is the output that will be
graded, make sure your function
returns the value in this form
You can call the print method on
your function to see the
triangle pattern
[2.5 pts] Write the recursive function isPrime(num) that takes an integer as a parameter and
returns a boolean value, True if the number is prime, False otherwise. A prime number is a positive
integer that has exactly two positive integer factors, 1 and itself.
- You can assume the function only receives integers
- If needed, the function could take a second argument, but it will not be provided by the
user. This means it should be a preloaded value and the original function call will be fed
only with num
- Remember to consider the special cases 0 and 1
- Based on your recursive algorithm, you might encounter the runtime error ‘maximum
recursion depth exceeded’ when using large values of num. While changing the limit of
recursive calls could solve the error, you should try to optimize your code rather than
changing the recursion limit to accommodate an unoptimized algorithm. See the references
at the end of this file for ideas on how to optimize your algorithm if needed.
NOTE: All functions should not contain any for or while loops, or global variables. Use
recursion otherwise, no credit will be given
Deliverables:
• Submit your code in a file name LAB3.py to the Lab3 Gradescope assignment before the
due date
References:
http://mathandmultimedia.com/2012/06/02/determining-primes-through-square-root/
https://www.smartickmethod.com/blog/math/operations-and-algebraicthinking/divisibility/prime-numbers-sieve-eratosthenes/