project_euler/problem_47/sol1.py

project_euler/problem_47/__init__.py

@@ -0,0 +1 @@
+

project_euler/problem_47/sol1.py

@@ -0,0 +1,112 @@
+"""
+Combinatoric selections
+
+Problem 47
+
+The first two consecutive numbers to have two distinct prime factors are:
+
+14 = 2 × 7
+15 = 3 × 5
+
+The first three consecutive numbers to have three distinct prime factors are:
+
+644 = 2² × 7 × 23
+645 = 3 × 5 × 43
+646 = 2 × 17 × 19.
+
+Find the first four consecutive integers to have four distinct prime factors each.
+What is the first of these numbers?
+"""
+
+from functools import lru_cache
+
+
+def unique_prime_factors(n: int) -> set:
+    """
+    Find unique prime factors of an integer.
+    Tests include sorting because only the set really matters,
+    not the order in which it is produced.
+    >>> sorted(set(unique_prime_factors(14)))
+    [2, 7]
+    >>> set(sorted(unique_prime_factors(644)))
+    [2, 7, 23]
+    >>> set(sorted(unique_prime_factors(646)))
+    [2, 17, 19]
+    """
+    i = 2
+    factors = set()
+    while i * i <= n:
+        if n % i:
+            i += 1
+        else:
+            n //= i
+            factors.add(i)
+    if n > 1:
+        factors.add(n)
+    return factors
+
+
+@lru_cache
+def upf_len(num: int) -> int:
+    """
+    Memoize upf() length results for a given value.
+    >>> upf_len(14)
+    2
+    """
+    return len(unique_prime_factors(num))
+
+
+def equality(iterable: list) -> bool:
+    """
+    Check equality of ALL elements in an interable.
+    >>> equality([1, 2, 3, 4])
+    False
+    >>> equality([2, 2, 2, 2])
+    True
+    >>> equality([1, 2, 3, 2, 1])
+    True
+    """
+    return len(set(iterable)) in (0, 1)
+
+
+def run(n: int) -> list:
+    """
+    Runs core process to find problem solution.
+    >>> run(3)
+    [644, 645, 646]
+    """
+
+    # Incrementor variable for our group list comprehension.
+    # This serves as the first number in each list of values
+    # to test.
+    base = 2
+
+    while True:
+        # Increment each value of a generated range
+        group = [base + i for i in range(n)]
+
+        # Run elements through out unique_prime_factors function
+        # Append our target number to the end.
+        checker = [upf_len(x) for x in group]
+        checker.append(n)
+
+        # If all numbers in the list are equal, return the group variable.
+        if equality(checker):
+            return group
+
+        # Increment our base variable by 1
+        base += 1
+
+
+def solution(n: int = 4) -> int:
+    """Return the first value of the first four consecutive integers to have four
+    distinct prime factors each.
+    >>> solution()
+    134043
+    """
+    results = run(n)
+    return results[0] if len(results) else None
+
+
+if __name__ == "__main__":
+    print(solution())