project_euler/problem_47/sol1.py

project_euler/problem_47/__init__.py

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+

project_euler/problem_47/sol1.py

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+"""
+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:
+    """
+    Function to find unique prime factors of an integer.
+    Tests include sorting because only the set really matters,
+    not the order in which it is produced.
+    >>> set(sorted(unique_prime_factors(14)))
+    {2, 7}
+    >>> set(sorted(unique_prime_factors(644)))
+    {2, 23, 7}
+    >>> set(sorted(unique_prime_factors(646)))
+    {17, 2, 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(maxsize=5)
+def upf_len(num: int) -> int:
+    """
+    Helper function to 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
+    """
+    if iterable[:1]:
+        return iterable[1:] == iterable[:-1]
+
+
+def run(n: int) -> list:
+    """
+    Function that runs core process to find problem solution.
+    >>> run(3)
+    [644, 645, 646]
+    """
+
+    i = 2
+
+    success = 0
+
+    while success < 1:
+        # Increment each value of a generated range
+        group = list(map(lambda x, y=i: y + x, [i for i in range(n)]))
+
+        # Run elements through out unique_prime_factors function
+        # Append our target number to the end.
+        checker = list(map(upf_len, group))
+        checker.append(n)
+
+        # If all numbers in the list are euqal, increment our success variable
+        # to exit the while loop and return the current group of numbers.
+        if equality(checker):
+            success += 1
+            return group
+        i += 1
+
+
+def solution(N: int = 4) -> int:
+    """Returns the first value of the first four consecutive integers to have four
+    distinct prime factors each.
+    >>> solution()
+    134043
+    """
+    results = run(N)
+    if len(results) > 0:
+        return results[0]
+
+
+if __name__ == "__main__":
+    print(solution())