Lists, Tuples, and Strings

General Information

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All work that is completed in this assignment is your own group's. You may talk to other students about the problems you are to solve, however, you may not share code in any way, except with your partner(s). What you submit must be your own group's work.

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About

The aim of this homework assignment is to practice working with sequence types. The focus in on getting comfortable working with strings, lists, and tuples.

Be aware that you will be required to use the knowledge and skills you have acquired so far to succeed in this assignment. This includes defining functions, evaluating boolean expressions, evaluating arithmetic expressions, taking user input among others.

Learning Objectives

1. Practice working with strings.
2. Practice working with lists and tuples.
3. Practice working with python string methods.

Estimated Size

This assignment requires you to implement $5$ Python files.

• Each file will have a few functions to implement.
• Each function can be reasonably implemented in $1 - 5$ lines of code.
• Many functions have simple computations, similar to the first assignment.
• Some functions require you to use other functions implemented by you in the same file.

Note

• You do not need to use any assert statements in this assignment.
• You do not need to do any type checking, sanity checking or input validity checking in this assignment.

Preamble

We are trying a sort of new approach to the homework assignments.

You will be presented with a bunch of options of things to work on and can choose what seems reasonable to try and work toward the point totals you want.

We do not expect you to do everything. Note that the exceeding threshold is at 18+ points, whereas there are 37 total points to possibly gain.

0. Setup

Make a folder on your computer and open it in VSCode.

You must create five files in this folder. Make sure that you do not rename any of these files.

• stats.py
• str_checks.py
• rps.py
• tup_frac.py
• cipher.py

Remember that for every file you need to have comments indicating the authors at the, for example:

# Authors   : Jared Yeager,         Tim Richards
# Emails    : jyeager@cs.umass.edu, richards@cs.umass.edu
# Spire IDs : 31415926,             27182818

The # Author/# Authors, # Email/# Emails, and # Spire ID/# Spire IDs are the only really necessary formatting details.

Some copying and pasting here will save you some time and sanity.

Note that these details are necessary for the auto-grader to recognize your solution.

1. Implement stats.py

This problem is a revisit to elementary statistics, and you will implement functions to operate on collections of data to understand certain quantities of interest.

1a. Implement Minimum (1 point)

The minimum value in a collection of data is the value with the smallest magnitude.

Your task is to implement a function with the following signature:

def list_min(l)

This function should take as input a list l and returns the minimum value in l.

Example:

list_min([1, 2, 3])           # This should return 1
list_min(['bb', 'cb', 'abc']) # This should return abc

Hint: Consider using the Python min() function.

1b. Implement Maximum (1 point)

The maximum value in a collection of data is the value with the largest magnitude.

Your task is to implement a function with the following signature:

def list_max(l)

This function should take as input a list l and returns the maximum value in l.

Example:

list_max([1, 2, 3])           # This should return 3
list_max(['bb', 'cb', 'abc']) # This should return 'cb'

Hint: Consider using the Python max() function.

1c. Implement Range (1 point)

The range of a collection of data is defined as the difference between the maximum value and the minimum value.

Your task is to implement a function with the following signature:

def list_range(l)

This function should take as input a list l and returns the range of l.

Example:

list_range([1, 2, 3])           # This should return 2
list_range([20, 40, 1, 3, 400]) # This should return 399

Hint: Consider using 1a. and 1b. to simplify your work.

1d. Implement Mean (1 point)

The mean of a collection of data is defined as the sum of the values in the collection divided by the total number of values in the collection.

Your task is to implement a function with the following signature:

def list_mean(l)

This function should take as input a list l and returns the mean of l.

Example:

list_mean([1, 2, 3])           # This should return 2
list_mean([5, 5, 4, 4])        # This should return 4.5

Hint: Consider using the Python sum() function.

1e. Implement Median (1 point)

The median of a collection of data is the middle-most value in the sorted collection.

Your task is to implement a function with the following signature:

def list_median(l)

This function should take as input a list l and returns the median of l. You may assume that l always contains an odd number of elements.

Example:

list_median([1, 2, 3])           # This should return 2
list_median([5, 5, 4, 4, 6])     # This should return 5
list_median(['abc', 'ab', 'bc']) # This should return 'abc'

Hint: Consider using the Python sorted() function.

2. Implement str_checks.py

In this problem, you will use functions to perform some simple checks on strings. Any background information that you may need is provided to you.

2a. Palindrome Strings (2 points)

Palindromes are strings that read the same backwards as forwards. For example, madam and racecar.

Your task is to implement a function with the following signature:

def is_palindrome(s) 

The function should take as input a string s and returns if s is a palindrome or not.

Example:

is_palindrome('foo')   # This should return False
is_palindrome('madam') # This should return True

2b. Anagrams (2 points)

A string is said to be an anagram of another string if it can be created by rearranging the letters of the other string. For example, fried is an anagram of fired and vice versa. Another example is listen and silent.

Your task is to implement a function with the following signature:

def is_anagram(s, t)

The function should take as input two strings s and t and return if the two strings are anagrams of each other.

Example:

is_anagram('fired', 'fried')   # This should return True
is_anagram('fired', 'silent')  # This should return False

2c. 'Same' Strings (2 points)

For this problem, we define two strings to be 'same' if they have the same alphabets in the same order irrespective of whether the letters are in upper or lower case. For example, foo, Foo, fOO, FoO are all 'same' strings.

Your task is to implement a function with the following signature:

def same_word(s, t)

The function should take as input two strings s and t and returns whether the two strings are 'same' or not.

Example:

same_word('foo', 'Foo') # This should return True
same_word('foo', 'bar') # This should return False

Hint: Consider using the Python String .lower() function.

3. Implement rps.py

Do you remember playing Rock, Paper, Scissors? Here's a quick reminder: At the same time, two players display one of three symbols - a rock, paper, or scissors. A rock beats scissors by destroying it, scissors beat paper by cutting it, and paper beats rock by covering it.

In this problem, you will implement functions to simulate this game using a python program.

Btw, this problem will involve using boolean expressions! You might want to refresh your knowledge before moving ahead.

3a. Get input from the user (2 points)

Your task is to implement a function with the following signature:

def get_input()

The function does not take any argument. It should ask the user for an input string (which would be either rock, paper or scissors) and return the user's choice in lower case.

Example:

get_input() # If the user types 'rock' when prompted, this should return 'rock'
get_input() # If the user types 'PaPeR' when prompted, this should return 'paper'

3b. Check if player 1 wins (1 point)

Your task is to implement a function with the following signature:

def p1_wins(p1, p2)

The function should take as input two strings p1 and p2 corresponding to the choices of player 1 and player 2 respectively (This means they could be either rock, paper or scissors). It should return whether player 1 wins or not based on p1 and p2.

Example:

p1_wins('rock', 'scissors')  # This should return True
p1_wins('paper', 'scissors') # This should return False

3c. Check if player 2 wins (1 point)

Your task is to implement a function with the following signature:

def p2_wins(p1, p2)

The function should take as input two strings p1 and p2 corresponding to the choices of player 1 and player 2 respectively (This means they could be either rock, paper or scissors). It should return whether player 2 wins or not based on p1 and p2.

Example:

p2_wins('rock', 'scissors')  # This should return False
p2_wins('paper', 'scissors') # This should return True

3d. Check for a tie (1 point)

Your task is to implement a function with the following signature:

def tie(p1, p2)

The function should take as input two strings p1 and p2 corresponding to the choices of player 1 and player 2 respectively (This means they could be either rock, paper or scissors). It should return if there is a tie based p1 and p2.

Example:

tie('paper', 'paper')      # This should return True
tie('paper', 'rock')       # This should return False

Play the game!

You can play your game to test it. Use the following code snippet after implementing $3a. - 3d.$

import random

p1 = get_input()
p2 = random.choice(["rock", "paper", "scissors"])

print(f"Player 1: {p1}")
print(f"Player 2: {p2}")
print(f"P1 Winner : {p1_wins(p1, p2)}")
print(f"P2 Winner : {p2_wins(p1, p2)}")
print(f"No Winner : {tie(p1, p2)}")

4. Implement tup_frac.py

Do you remember fractions from pre-calculus? In this problem, we will implement some basic operations on fractions. Don't worry if you don't remember! We will reintroduce the operations for your assistance.

All the necessary mathematical background you may need is provided below.

4a. Simplify fractions (1 point)

To simplify a fraction, we divide the top and bottom by the highest number that can divide into both numbers exactly i.e. the greatest common divisor (gcd). For example, $\frac{2}{10}$ in simplified form is $\frac{1}{5}$.

Your task is to implement a function with the following signature:

def simplify(frac)

The function take as argument a tuple frac that stores the top as the first element and bottom as the second element. It should simplify the fraction and return a tuple with the first element as the simplified top and the second element as the simplified bottom.

Example:

simplify((2, 10))  # This should return (1, 5)
simplify((5, 13))  # This should return (5, 13)

Hint: Consider using the Python math.gcd() function.

4b. Create Fractions (1 point)

Your task is to implement a function with the following signature:

def make_fraction(top, bottom)

The function take as argument two integers top and bottom. Note that bottom cannot be negative. It should return a simplified fraction created from top and bottom as a tuple.

Example:

make_fraction(1, 5)   # This should return (1, 5)
make_fraction(2, 10)  # This should return (1, 5)

4c. Addition of Fractions (1 point)

Addition of two fractions $\frac{a}{b}$ and $\frac{c}{d}$ involves several steps:

• Step $1$: Find the least common multiple of $b$ and $d$. Let's call this $l$. This is the bottom of the sum of the two fractions.
• Step $2$: Multiply $a$ by $\frac{l}{b}$
• Step $3$: Multiply $c$ by $\frac{l}{d}$
• Step $4$: Add the two numbers obtained in Step $2$ and Step $3$. This is the top of the sum of the two fractions.
• Step $5$: Simplify the fraction.

Your task is to implement a function with the following signature:

def add(frac1, frac2)

The function take as argument two fractions stored as tuples frac1 and frac2 where the first element of the tuple stores the top and the second element stores the bottom. It should add the two fractions according to the steps described above and return the new fraction as a tuple where the first element of the tuple stores the top and the second element stores the bottom.

Example:

add((1, 5), (3, 5))  # This should return (4, 5)
add((1, 6), (3, 4))  # This should return (11, 12)

Hint: Consider using the Python math.lcm() function.

4d. Negate Fractions (1 point)

The negation of a fraction $\frac{a}{b}$ is the fraction $\frac{-a}{b}$.

Your task is to implement a function with the following signature:

def negate(frac)

The function take as argument a fraction stored as a tuple frac where the first element of the tuple stores the top and the second element stores the bottom. It should return the negation of frac as a tuple where the first element of the tuple stores the top and the second element stores the bottom.

Example:

negate((1, 5))   # This should return (-1, 5)
negate((-1, 5))  # This should return (1, 5)

4e. Subtraction of Fractions (1 point)

Subtraction of two fractions follows almost the same procedure as addition. The only difference is that in Step $4$, instead of adding we subtract the number obtained in Step $3$ from that obtained in Step $2$.

Your task is to implement a function with the following signature:

def sub(frac1, frac2)

The function take as argument two fractions stored as tuples frac1 and frac2 where the first element of the tuple stores the top and the second element stores the bottom. It should subtract frac2 from frac1 according to the steps described above and return the new fraction as a tuple where the first element of the tuple stores the top and the second element stores the bottom.

Example:

sub((3, 5), (1, 5))  # This should return (2, 5)
sub((3, 4), (1, 6))  # This should return (7, 12)

Hint: There exists a one/two line solution for this problem by using 4c. and 4d.

4f. Multiplication of Fractions (1 point)

Multiplication of two fractions $\frac{a}{b}$ and $\frac{c}{d}$ involves several steps:

• Step $1$: Multiply $a$ by $c$. This becomes the new top.
• Step $2$: Multiply $b$ by $d$. This becomes the new bottom.
• Step $3$: Simplify the fraction.

Remember that multiplying a negative number with another negative number results in a positive number.

Your task is to implement a function with the following signature:

def mul(frac1, frac2)

The function take as argument two fractions stored as tuples frac1 and frac2 where the first element of the tuple stores the top and the second element stores the bottom. It should multiply frac1 by frac2 according to the steps described above and return the new fraction as a tuple where the first element of the tuple stores the top and the second element stores the bottom.

Example:

mul((3, 5), (1, 5))  # This should return (3, 25)
mul((3, 4), (1, 6))  # This should return (1, 8)

4g. Multiplicative Inverse of Fractions (2 points)

The multiplicative inverse of a fraction $\frac{a}{b}$ is the fraction $\frac{b}{a}$.

Your task is to implement a function with the following signature:

def inverse(frac)

The function take as argument a fraction stored as a tuple frac where the first element of the tuple stores the top and the second element stores the bottom. It should return the multiplicative inverse of frac as a tuple where the first element of the tuple stores the top and the second element stores the bottom.

Example:

inverse((3, 4))   # This should return (4, 3)
inverse((-3, 4))  # This should return (-4, 3)

Hint: Remember that the top of the input fraction can be negative. When calculating the multiplicative inverse, the new bottom should not be negative. You must take into account the sign of the top and handle it so the sign is preserved and the new bottom is not negative.

Hint: Consider using the Python abs() function.

4h. Division of Fractions (2 points)

Dividing a fraction $\frac{a}{b}$ by $\frac{c}{d}$ is equivalent to multiplying $\frac{a}{b}$ by $\frac{d}{c}$.

Your task is to implement a function with the following signature:

def div(frac1, frac2)

The function take as argument two fractions stored as tuples frac1 and frac2 where the first element of the tuple stores the top and the second element stores the bottom. It should divide frac1 by frac2 according to the steps described above and return the new fraction as a tuple where the first element of the tuple stores the top and the second element stores the bottom.

Example:

div((3, 5), (4, 5))  # This should return (3, 4)
div((3, 4), (1, 6))  # This should return (9, 2)
div((3, 5), (-1, 6)) # This should return (-18, 5)

Hint: There exists a one/two line solution for this problem by using 4f. and 4g.

5. Implement cipher.py

Ciphers are programs for encrypting and decrypting data. A cipher converts a message, called plaintext, into ciphertext. This process is called encryption. The process to obtain plaintext from ciphertext reverses the encryption and is called decryption.

In this problem, you will implement encryption and decryption schemes for the ciphers specified below. All information you need is provided.

l337 Cipher

The l337 cipher encoding scheme is defined as below:

Character	Encoding
O	0
I	1
E	3
A	4
S	5
T	7
B	8

For example, EAT would be encoded as 347 and MANAN will be encoded as M4N4N.

5a. l337 Encryption (2 points)

Your task is to implement a function with the following signature:

def l337_encrypt(s)

The function take as argument a string s that represents a message and replaces each of the characters described in the table above (if it occurs in the string) with the corresponding encoding and returns the encoding as a string.

Example:

l337_encrypt('EAT')    # This should return '347'
l337_encrypt('MANAN')  # This should return 'M4N4N'

Hint: Consider using String .replace() function.

5b. l337 Decryption (2 points)

Your task is to implement a function with the following signature:

def l337_decrypt(s)

The function take as argument a string s that represents an encoding and replaces each of the encoded characters described in the table above (if it occurs in the string) with the corresponding character and returns the original message as a string.

Example:

l337_decrypt('347')    # This should return 'EAT'
l337_dncrypt('M4N4N')  # This should return 'MANAN'

Hint: Consider using String .replace() function.

Odd-Even Cipher

This cipher creates two substrings from the message:

• $s_1$: It comprises of all the characters at odd indices
• $s_2$: It comprises of all the characters at even indices. It then joins (concatenates) the $s_2$ to $s_1$. This is the required encoding.

For example, abcd generates the substrings bd and ac and thus, the encoding is bdac. Likewise, abcdef is encoded as bdface.

The decryption scheme is rather more involved.

• Step $1$: Convert the encoded string into a list. Now, you can access each letter in the encoded string.
• Step $2$: Read the first half of the encoded string. Access each letter in the string and store these letters at odd positions in the list.
• Step $3$: Read the second half of the encoded string. Access each letter in the string and store these letters at even positions in the list.
• Step $4$: Convert the list into a string. This string represents the original message.

5c. Odd-Even Encryption (2 points)

Your task is to implement a function with the following signature:

def odd_even_encrypt(s)

The function take as argument a string s that represents a message and performs the encoding process described above and returns the encoding as a string.

Example:

odd_even_encrypt('abcd')    # This should return 'bdac'
odd_even_encrypt('MANAN')  # This should return 'AAMNN'

5d. Odd-Even Decryption (3 points)

Your task is to implement a function with the following signature:

def odd_even_decrypt(s)

The function take as argument a string s that represents an encoding and reverses the encoding process described above and returns the original message as a string.

Example:

odd_even_decrypt('bdac')    # This should return 'abcd'
odd_even_decrypt('AAMNN')  # This should return 'MANAN'

Hint: For Step $4$, you can use the following where $l$ is the name of the list.

''.join(l)

l337 and two-shuffle cipher

Finally, let's use the two ciphers above to generate our own cipher! This cipher first encodes a message using the l337 scheme and then two times using the odd-even scheme.

Fun Fact: For the following two problems, you exclusively need to use 5a. - 5d.

5e. Encryption (1 point)

Your task is to implement a function with the following signature:

def cipher_encrypt(s)

The function take as argument a string s that represents a message and performs the encoding process described above and returns the encoding as a string.

Example:

cipher_encrypt('abcd')    # This should return 'dcba'
cipher_encrypt('MANAN')  # This should return '4N4MN'

5f. Decryption (1 point)

Your task is to implement a function with the following signature:

def cipher_decrypt(s)

The function take as argument a string s that represents an encoding and reverses the encoding process described above and returns the original message as a string.

Example:

cipher_decrypt('dcba')    # This should return 'abcd'
cipher_decrypt('4N4MN')  # This should return 'MANAN'

Grading Scale

Note that points may be obtained from anywhere, you do not need to try to complete work in any particular order.

There is also an abundance of possible points to obtain, giving you options in what you want to work on in order to get your total points within the desired range.

1: Below Standards: 0-5 points

2: Approaching Standards: 6-11 points

3: Meeting Standards: 12-17 points

4: Exceeding Standards: 18+ points