Add new algorithm (is_K_power_of_N) to bit manipulation

bit_manipulation/is_K_power_of_n.py

@@ -0,0 +1,58 @@
+def is_power(n: int, k: int) -> bool:
+    """
+    Checks if a given integer k is a power of another integer n.
+
+    This function determines if there exists an integer x such that n^x = k.
+    It handles positive integers only and raises an error for non-positive inputs.
+    For more information, see: https://en.wikipedia.org/wiki/Power_of_two
+
+    Args:
+        n: The base integer (must be a positive integer).
+        k: The number to check if it's a power of n (must be a positive integer).
+
+    Returns:
+        True if k is a power of n, False otherwise.
+
+    Raises:
+        ValueError: If n or k are not positive integers.
+
+    Examples:
+    >>> is_power(2, 8)
+    True
+    >>> is_power(3, 81)
+    True
+    >>> is_power(10, 1)
+    True
+    >>> is_power(5, 120)
+    False
+    >>> is_power(1, 1)
+    True
+    >>> is_power(1, 5)
+    False
+    >>> is_power(0, 5)
+    Traceback (most recent call last):
+        ...
+    ValueError: Both n and k must be positive integers
+    >>> is_power(4, -16)
+    Traceback (most recent call last):
+        ...
+    ValueError: Both n and k must be positive integers
+    """
+    if n <= 0 or k <= 0:
+        raise ValueError("Both n and k must be positive integers")
+
+    if n == 1:
+        return k == 1
+
+    # Repeatedly divide k by n until it's no longer divisible.
+    while k % n == 0:
+        k //= n
+
+    # If k has been reduced to 1, it was a power of n.
+    return k == 1
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()