[+] A4 Add starter files

assignments/a4/a4_part2.py

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+"""CSC110 Fall 2021 Assignment 4, Part 2: Generating coprime numbers
+
+Instructions (READ THIS FIRST!)
+===============================
+Implement each of the functions in this file. As usual, do not change any function headers
+or preconditions. You do NOT need to add doctests.
+
+You may create additional helper functions to help break up your code into smaller parts.
+
+Copyright and Usage Information
+===============================
+
+This file is provided solely for the personal and private use of students
+taking CSC110 at the University of Toronto St. George campus. All forms of
+distribution of this code, whether as given or with any changes, are
+expressly prohibited. For more information on copyright for CSC110 materials,
+please consult our Course Syllabus.
+
+This file is Copyright (c) 2021 David Liu, Mario Badr, and Tom Fairgrieve.
+"""
+import math
+
+
+def coprime_to_2_and_3(n: int) -> list[int]:
+    """Return the natural numbers less than n that are coprime to both 2 and 3.
+
+    The returned list is sorted.
+
+    Preconditions:
+      - n >= 6
+
+    >>> coprime_to_2_and_3(20)
+    [1, 5, 7, 11, 13, 17, 19]
+
+    Implementation note: recall negative list indexing from Assignment 3.
+    For all lists lst and integers i between 0 and len(lst) - 1 inclusive,
+    lst[-i] == lst[len(lst) - i].
+    """
+    nums_so_far = [1, 5]
+    while nums_so_far[-2] + 6 < n:
+        # Note: Write four assert statements here expressing the four loop invariants from the
+        # assignment handout. These statements should be at the top of the loop body.
+
+        next_number = nums_so_far[-2] + 6
+        list.append(nums_so_far, next_number)
+
+    return nums_so_far
+
+
+def coprime_to_all(primes: set[int], n: int) -> list[int]:
+    """Return the positive integers less than n that are coprime to every number in primes.
+
+    The returned list is sorted.
+
+    Pay attention to the preconditions, as they are designed to help simplify your work for this
+    question.
+
+    Preconditions:
+        - primes != set()
+        - every element of primes is prime
+        - n >= math.prod(primes)
+
+    >>> coprime_to_all({2, 3}, 20)
+    [1, 5, 7, 11, 13, 17, 19]
+    >>> coprime_to_all({2, 3, 7}, 50)
+    [1, 5, 11, 13, 17, 19, 23, 25, 29, 31, 37, 41, 43, 47]
+
+    Implementation notes:
+        - You MUST use the provided helper function starting_coprime_numbers in your implementation,
+          and may NOT modify it (even though it is not as efficient as it could be!!).
+        - You will find the math.prod function useful.
+    """
+
+
+def starting_coprime_numbers(primes: set[int]) -> list[int]:
+    """Return the numbers up to the product of the given primes that are coprime to all of them.
+
+    Note: the length of the returned list is is exactly equal to phi(math.prod(primes)), where
+    phi is the Euler totient function.
+
+    Preconditions:
+        - primes != set()
+        - every element of primes is prime
+
+    >>> starting_coprime_numbers({2, 3})
+    [1, 5]
+    >>> starting_coprime_numbers({3, 11})
+    [1, 2, 4, 5, 7, 8, 10, 13, 14, 16, 17, 19, 20, 23, 25, 26, 28, 29, 31, 32]
+    """
+    nums_so_far = []
+    m = math.prod(primes)
+
+    for k in range(1, m):
+        is_coprime = True
+        for p in primes:
+            if k % p == 0:
+                is_coprime = False
+        if is_coprime:
+            list.append(nums_so_far, k)
+
+    return nums_so_far
+
+
+if __name__ == '__main__':
+    # When you are ready to check your work with python_ta, uncomment the following lines.
+    # (Delete the "#" and space before each line.)
+    # IMPORTANT: keep this code indented inside the "if __name__ == '__main__'" block
+    # Leave this code uncommented when you submit your files.
+    # import python_ta
+    #
+    # python_ta.check_all(config={
+    #     'extra-imports': ['python_ta.contracts', 'math'],
+    #     'max-line-length': 100,
+    #     'disable': ['R1705', 'C0200']
+    # })
+
+    import doctest
+    doctest.testmod()