Description
Introduction
The goal of this homework is to allow you to practice and understand how to use
recursion to solve problems. Refer to the rubric to see how points will be rewarded for
each function. You have been given HW11.py to fill out with instructions in the
docstrings. However, below you will find more detailed information on how to complete
the assignment. Read it thoroughly before you begin. You have until Monday,
December 4th at 11:55pm to complete this assignment.
CS1301 – HOMEWORK 11: RECURSION
NOTE: YOU MUST USE RECURSION TO WRITE EVERY FUNCTION
(NOT ITERATION) TO RECEIVE CREDIT FOR THIS ASSIGNMENT!
Function name: leaning_pyramid
Parameters: int
Returns: None
Description: Write a function that takes in a positive integer n (n ≥ 1). Use this integer to
draw a leaning pyramid made out of stars (*). The base of the pyramid will consist of n
stars, the next level of the pyramid will consist of n – 1 stars, etc. The top will be a single
star.
Test Cases:
>>> leaning_pyramid(5)
*
**
***
****
*****
>>> leaning_pyramid(3)
*
**
***
Function name: reverse_phrase
Parameters: string
Returns: string
Description: Write a function that accepts one parameter, a string. Use recursion to
reverse all the characters in the phrase. Keep in mind that you are reversing the entire
string regardless of what it contains.
Test Cases:
>>> test_one = reverse_phrase(“car”)
>>> print(test_one)
rac
>>> test_two = reverse_phrase(“Karoline likes chocolate”)
>>> print(test_two)
etalocohc sekil eniloraK
>>> test_three = reverse_phrase(“123456789”)
>>> print(test_three)
987654321
CS1301 – HOMEWORK 11: RECURSION
Function name: find_parenthesized_string
Parameters: string
Returns: string
Description: Given a string that contains a single pair of parenthesis, compute
recursively a new string made up of only the parenthesis and the contents between
them. Assume the single pair of parentheses will always be included in the string and
that no other parenthesis will exist in the string. Return the computed string. You may
not use .find in your solution.
Test Cases:
>>> test_one = find_parenthesized_string(‘(cs1301)abcdefg’)
>>> print(test_one)
(cs1301)
>>> test_two =
find_parenthesized_string(‘aaldsfj(riverdale)lkjadlksfj’)
>>> print(test_two)
(riverdale)
>>> test_three = find_parenthesized_string(‘()’)
>>> print(test_three)
()
Function name: factorial_dictionary
Parameters: int
Returns: dict
Description: Define a recursive function that accepts a positive integer parameter n
(n ≥ 1) and returns a dictionary. The dictionary should contain, as a key, every number
from 1 to the number passed in (inclusive). The corresponding value for each key
should be the factorial of that number. You may not use looping in your solution.
Hint: When trying to solve factorial_dictionary(n), you first need to recursively get
factorial_dictionary(n – 1). How would you get from factorial_dictionary(n – 1) to factorial
dictionary(n)?
Test Cases:
>>> test_one = factorial_dictionary(5)
>>> print(test_one)
{1: 1, 2: 2, 3: 6, 4: 24, 5: 120}
>>> test_two = factorial_dictionary(2)
>>> print(test_two)
{1: 1, 2: 2}
CS1301 – HOMEWORK 11: RECURSION
>>> test_three = factorial_dictionary(1)
>>> print(test_three)
{1: 1}
Function name: pascal_triangle
Parameters: int
Returns: list of ints
Description: Write a function that takes in an integer parameter n (n ≥ 0) and returns a
list of the elements of that row (the nth row) in the Pascal Triangle. Here is a link to what
a Pascal Triangle looks like, and the rules behind making one:
http://mathforum.org/workshops/usi/pascal/pascal_intro.html!
Hint: When trying to solve pascal_triangle(n), you first need to recursively get
pascal_triangle(n – 1). How would you get from pascal_triangle(n – 1) to
pascal_triangle(n)?
Test Cases:
>>> test_one = pascal_triangle(6)
>>> print(test_one)
[1, 6, 15, 20, 15, 6, 1]
>>> test_two = pascal_triangle(10)
>>> print(test_two)
[1, 10, 45, 120, 210, 252, 210, 120, 45, 10, 1]
>>> test_three = pascal_triangle(0)
>>> print(test_three)
[1]
CS1301 – HOMEWORK 11: RECURSION
Grading Rubric
NOTE: ALL FUNCTIONS IN THIS HOMEWORK MUST BE SOLVED USING
RECURSION OR NO CREDIT WILL BE RECEIVED FOR THAT FUNCTION.
leaning_pyramid: 10 pts
reverse_phrase: 20 pts
find_parenthesized_string: 20 pts
factorial_dictionary: 25 pts
pascal_triangle: 25 pts
Provided
The following file(s) have been provided to you.
1. HW11.py
This is the file you will edit and implement. All instructions for what the methods
should do are in the docstrings.
Deliverables
You must submit all of the following file(s). Please make sure the filename matches the filename(s)
below. Be sure you receive the confirmation email from T-Square, and then download your uploaded
files to a new folder and run them.
1. HW11.py
If this file does not run (if it encounters an error while trying to run), you will get no
credit on the assignment.
