Add new algorithm (is_K_power_of_N) to bit manipulation

bit_manipulation/is_K_power_of_N.py

@@ -0,0 +1,52 @@
+def is_k_power_of_n(n: int, k: int) -> bool:
+    """
+    Given two positive integers, n and k, this function determines if k
+    is a power of n. A number k is a power of n if k = n^x for some
+    non-negative integer x.
+
+    >>> is_k_power_of_n(2, 8)
+    True
+    >>> is_k_power_of_n(3, 10)
+    False
+    >>> is_k_power_of_n(5, 5)
+    True
+    >>> is_k_power_of_n(10, 1000)
+    True
+    >>> is_k_power_of_n(4, 2)
+    False
+    >>> is_k_power_of_n(1, 1)
+    True
+    >>> is_k_power_of_n(1, 5)
+    False
+    >>> is_k_power_of_n(0, 16)
+    Traceback (most recent call last):
+        ...
+    ValueError: Both n and k must be positive integers
+    >>> is_k_power_of_n(2, -8)
+    Traceback (most recent call last):
+        ...
+    ValueError: Both n and k must be positive integers
+    >>> is_k_power_of_n(2, 'a')
+    Traceback (most recent call last):
+        ...
+    TypeError: n and k must be integers
+    """
+    if not isinstance(n, int) or not isinstance(k, int):
+        raise TypeError("n and k must be integers")
+
+    if n <= 0 or k <= 0:
+        raise ValueError("Both n and k must be positive integers")
+
+    if n == 1:
+        return k == 1
+
+    while k % n == 0:
+        k //= n
+    return k == 1
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()
+```