Happy Number – Solution & Complexity

def digit_square_sum(n):
    total = 0
    while n > 0:
        digit = n % 10
        total += digit * digit
        n //= 10
    return total

def is_happy(n):
    seen = set()
    while n != 1 and n not in seen:
        seen.add(n)
        n = digit_square_sum(n)
    return n == 1

def is_happy(n: int) -> bool:
    def digit_square_sum(value):
        total = 0
        while value > 0:
            value, digit = divmod(value, 10)
            total += digit * digit
        return total

    slow = n
    fast = digit_square_sum(n)
    while fast != 1 and slow != fast:
        slow = digit_square_sum(slow)
        fast = digit_square_sum(digit_square_sum(fast))
    return fast == 1