njnLsw - Online Python3 Interpreter & Debugging Tool

# Digital roots.
# @see en.wikipedia.org/wiki/Digital_root

# Formal definition.
# A natural number n is a digital root if it is a fixed point for digit_sum
# (which occurs if digit_sum(n) equals n).

def fixed_point(f, guess, equal):
    while not equal(guess, result := f(guess)):
        guess = result
    return guess

def digit_sum(n):
    return sum(map(int, str(n)))

def digital_root_1(n: int) -> int:
    return fixed_point(digit_sum, n, lambda x, y: x == y)

# Direct formulas.

def digital_root_2(n: int) -> int:
    if n == 0:
        return 0
    n %= 9
    return n if n != 0 else 9

def digital_root_3(n: int) -> int:
    if n == 0:
        return 0
    return 1 + (n - 1) % 9

def digital_root_4(n: int) -> int:
    if n == 0:
        return 0
    return n - (n - 1) // 9 * 9 # flooring division

# Show.

def digital_root_show_all(n):
    fs = [
        digital_root_1,
        digital_root_2,
        digital_root_3,
        digital_root_4
    ]
    for f in fs:
        print(list(map(f, range(n))))

if __name__ == '__main__':
    digital_root_show_all(12)