Python Data Types and Functions Quiz

Data Types and Expressions

• 'cat' in L evaluates to False because the list L does not contain the string 'cat', only the characters 'c', 'a', and 't'.
• len(L) == len('cat') evaluates to True because both L and 'cat' have a length of 3.
• d == {2: 6, 3: 9, 1: 3} evaluates to True due to the dictionary comprehension assignment where each element x in the list [1, 2, 3] is mapped to x * 3.
• d evaluates to {1: 3, 2: 6, 3: 9} because dictionaries are unordered.
• min(numbers_list) evaluates to 5 as numbers_list contains numbers from 5 to 49.
• max(numbers_list) evaluates to 49 as numbers_list contains numbers from 5 to 49.
• str.upper(gl) evaluates to 'GOOD LUCK, WE'RE ROOTING FOR YOU!' because the upper() method converts all characters in the string to uppercase.
• 'good' in gl evaluates to True as the substring 'good' is present in the string gl.

Function Basics

• f1(4) evaluates to 8 due to the function definition f1(x: int) -> int: return x * 2.
• f1(2) + f1(1) evaluates to 6 because f1(2) returns 4 and f1(1) returns 2, summing to 6.
• f1(x + 1) evaluates to 10 because x is 4, so x + 1 is 5, and f1(5) returns 10.
• x still evaluates to 4 as the function f1 does not modify the global variable x.
• f2(3, 2) evaluates to True because f1(3) returns 6, 6 % 2 is 0, and r == 0 is True.
• r is undefined in this context as it is a local variable within the f2 function.

Symbolic Logic and Python Translation

• All cute animals are fluffy: ∀a ∈ A, IsCute(a) ⇒ IsFluffy(a)
• At least one cute animal is fluffy: ∃a ∈ A, IsCute(a) ∧ IsFluffy(a)
• (¬(¬p)) ⇔ p: (not (not p)) == p
• ((p ∨ q) ∧ ¬p) ⇒ q: ((p or q) and not p) == q

Filtering Collections and String Methods

• def get_uppercase(lst: list[str]) -> list[str]:
  • return sorted([s for s in lst if s.isupper()])

If Statements

• def check_scores(scores: list[int]) -> str:
  • check_all = all([score >= 100 for score in scores])
  • check_at_least_one = any([score >= 100 for score in scores])
  • if check_all:
    • return 'Great work'
  • elif check_at_least_one:
    • return 'Good work'
  • else:
    • return 'Better luck next time'

Function Design Recipe - get_common_numbers

• def get_common_numbers(L1: list[int], L2: list[int]) -> set[int]:
  • """Return a set containing the common numbers in L1 and L2 (i.e., those numbers present in both lists).
  • >>> L1 = [10, 20, 30, 40, 50]
  • >>> L2 = [60, 70, 80, 30, 10]
  • >>> numbers = get_common_numbers(L1, L2)
  • >>> numbers == {10, 30}
  • True
  • >>> L1 = [10, 20, 30, 40, 50]
  • >>> L2 = [60, 70, 80]
  • >>> get_common_numbers(L1, L2)
  • set()
  • """
  • return set(L1) & set(L2)

Debugging and Testing - is_fibonacci

• def test_is_fibonacci_error() -> None:
  • """A test case for is_fibonacci that reveals an error in the given implementation.If we ran this test with pytest and the current implementation, we would expect
  • this test to *fail* because of the error in the function body."""
  • actual = is_fibonacci([0, 1, 1, 2, 3, 5, 8, 13, 21, 34])
  • expected = False
  • assert actual == expected
• Error: The original implementation fails to validate the first two elements of the list.
• def is_fibonacci(s: list[int]) -> bool:
  • """Return whether list s contains the Fibonacci sequence of length len(s).The Fibonacci sequence of length n is the sequence of n numbers
  • 0, 1, 1, 2, 3, 5, 8, 13,...Every number after the second is the sum of the previous two numbers.The first number must be 0 and the second number must be 1.Preconditions:
  • - len(s) > 2
  • >>> is_fibonacci([0, 1, 1, 2, 3, 5, 8, 13, 21])
  • True
  • >>> is_fibonacci([0, 1, 4, 9, 16, 25, 36, 49, 64, 81])
  • False
  • """
  • return s[0] == 0 and s[1] == 1 and all([s[i + 2] == s[i] + s[i + 1] for i in range(0, len(s) - 2)])

Proofs

• Statement (1) rewritten: ∃k ∈ Z, n = k * n
• Proof: To prove the statement, we need to show that there exists an integer k for any integer n such that n = k * n.
  • Choosing k = 1, we get: n = 1 * n which holds true for any integer n.
  • Therefore, the statement ∀n ∈ Z, n | n2 + n is proven.

Test your knowledge of Python data types and expressions with this quiz! Explore concepts such as lists, dictionaries, and string methods. Understand function basics and evaluate expressions relating to the different data structures in Python.