[+] A4 P2.4, 2.5

assignments/a4/a4_part2.py

@@ -83,6 +83,30 @@ def coprime_to_all(primes: set[int], n: int) -> list[int]:
           and may NOT modify it (even though it is not as efficient as it could be!!).
         - You will find the math.prod function useful.
     """
+    increment = math.prod(primes)
+    nums_so_far = starting_coprime_numbers(primes)
+    period = len(nums_so_far)
+    while nums_so_far[-period] + increment < 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.
+
+        # Loop Invariant 1: every number k in nums_so_far is coprime to every prime
+        assert all(all(math.gcd(p, k) == 1 for p in primes) for k in nums_so_far)
+        # Loop Invariant 2: for all natural numbers i between 0 and len(nums_so_far) - period - 1 inclusive,
+        #   nums_so_far[i] + increment == nums_so_far[i + period].
+        assert all(nums_so_far[i] + increment == nums_so_far[i + period] for i in range(len(nums_so_far) - period))
+        # Loop Invariant 3: for all natural numbers i between 0 and len(nums_so_far) - 2 inclusive,
+        #   nums_so_far[i] < nums_so_far[i + 1] (this means that nums_so_far is always sorted).
+        assert all(nums_so_far[i] < nums_so_far[i + 1] for i in range(len(nums_so_far) - 2 + 1))
+        # Loop Invariant 4: for all natural numbers k between 0 and nums_so_far[-1] inclusive,
+        #   if k is coprime to all primes, then k in nums_so_far.
+        assert all(k in nums_so_far for k in range(nums_so_far[-1] + 1)
+                   if all(math.gcd(p, k) == 1 for p in primes))
+
+        next_number = nums_so_far[-period] + increment
+        list.append(nums_so_far, next_number)
+
+    return nums_so_far
 
 
 def starting_coprime_numbers(primes: set[int]) -> list[int]: