gcd_of_n_numbers

maths/gcd_of_n_numbers.py

@@ -0,0 +1,76 @@
+"""
+Gcd of N Numbers
+Reference: https://en.wikipedia.org/wiki/Greatest_common_divisor
+"""
+
+from collections import Counter
+
+
+def get_factors(
+    number: int, factors: Counter | None = None, factor: int = 2
+) -> Counter:
+    """
+    this is a recursive function for get all factors of number
+    >>> get_factors(45)
+    Counter({3: 2, 5: 1})
+    >>> get_factors(2520)
+    Counter({2: 3, 3: 2, 5: 1, 7: 1})
+    >>> get_factors(23)
+    Counter({23: 1})
+
+    factor can be all numbers from 2 to number that we check if number % factor == 0
+    if it is equal to zero, we check again with number // factor
+    else we increase factor by one
+    """
+
+    if not isinstance(number, int):
+        raise TypeError("number must be integer")
+
+    if factors is None:
+        # first call of get factors and so there are no founded factors
+        factors = Counter()
+
+    if number == factor:  # break condition
+        # all numbers are factors of itself
+        factors[factor] += 1
+        return factors
+
+    if number % factor > 0:
+        # if it is grater than zero
+        # so it is not a factor of number and we check next number
+        return get_factors(number, factors, factor + 1)
+
+    factors[factor] += 1
+    # else we update factors (that is Counter(dict-like) type) and check again
+    return get_factors(number // factor, factors, factor)
+
+
+def get_greatest_common_divisor(*numbers: int) -> int:
+    """
+    get gcd of n numbers:
+    >>> get_greatest_common_divisor(18, 45)
+    9
+    >>> get_greatest_common_divisor(23, 37)
+    1
+    >>> get_greatest_common_divisor(2520, 8350)
+    10
+    """
+    # we just need factors, not numbers itself
+    data = [get_factors(number) for number in numbers]
+    same_factors: Counter = data[0]
+    for d in data[1:]:
+        same_factors = same_factors & d
+        # get common factor between all
+        # `&` return common elements with smaller value (for Counter type)
+
+    # now, same_factors is something like {2: 2, 3: 4} that means 2 * 2 * 3 * 3 * 3 * 3
+    mult = 1
+    # power each factor and multiply
+    # for {2: 2, 3: 4}, it is [4, 81] and then 324
+    for m in [factor ** same_factors[factor] for factor in same_factors]:
+        mult *= m
+    return mult
+
+
+if __name__ == "__main__":
+    print(get_greatest_common_divisor(18, 45))  # 9