FIN312: Design and implement a function common_letters(words_list) that returns a list of letters that appear in all the words: Mathematics and Programming for FinTech Assignment, SUSS, Singapore

Question 1

a) Design and implement a function common_letters(words_list) that returns a list of letters that appear in all the words of words_list.

Requirements:

• Uppercase and lowercase letters are considered the same.
• The result must be in uppercase, sorted alphabetically, and have no duplicates.

For example:

Explanation: The letters that appeared in all three words are ‘A’, ‘L’, and ‘M’ as
highlighted: McDonald’s, HappyMeal, LemonTea.

(b) Given the following 5 test cases, print the results from your function using this code:

for t in cases:
print(f”Result: {common_letters(t)}”)

Question 2

(a) Let 𝐴 = (𝑎1, 𝑎2, …, 𝑎𝑛) and 𝐵 = (𝑏1, 𝑏2, …, 𝑏𝑛) be two points in the 𝑛-dimensional space ℝ𝑛. We can think of each point as a tuple of 𝑛 real numbers.

Define the proximity-𝒑 metric between A and B using the formula:

where the symbol |𝑥| represents the absolute value of 𝑥. The proximity-𝑝 metric is a generalized way to measure ‘distance’ between 𝐴 and 𝐵.

Example: Suppose 𝐴 = (1,1) and 𝐵 = (5,4) in the 2-dimensional plane.

• When p = 1, we get the distance to travel along the lines of a square grid. In this case, 𝐷1 (𝐴, 𝐵) = 𝑝𝑟𝑜𝑥𝑖𝑚𝑖𝑡𝑦(1, (1,1), (5,4)) = 7.
• When p = 2, we get the familiar ‘Euclidean distance’ from Pythagoras’ Theorem. In this case, 𝐷2 (𝐴, 𝐵) = 𝑝𝑟𝑜𝑥𝑖𝑚𝑖𝑡𝑦(2, (1,1), (5,4)) = 5.

Task: Implement the function 𝑝𝑟𝑜𝑥𝑖𝑚𝑖𝑡𝑦(𝑝, 𝐴, 𝐵) that takes in an integer 𝑝, point A and point B (each represented as a tuple of 𝑛 real numbers). The function should compute and return the value of 𝐷𝑝 (𝐴, 𝐵) using the given formula.

(b) Given the following 5 test cases, print the results from your function using this code:

for p, A, B in cases:
print(f”Result: {proximity(p, A, B):.3}”)