TheAlgorithms-Python/maths/ugly_numbers.py

"""
Ugly numbers are numbers whose only prime factors are 2, 3 or 5. The sequence
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, … shows the first 11 ugly numbers. By convention,
1 is included.
Given an integer n, we have to find the nth ugly number.

For more details, refer this article
https://www.geeksforgeeks.org/ugly-numbers/
"""


def ugly_numbers(n: int) -> int:
    """
    Returns the nth ugly number.
    >>> ugly_numbers(100)
    1536
    >>> ugly_numbers(0)
    1
    >>> ugly_numbers(20)
    36
    >>> ugly_numbers(-5)
    1
    >>> ugly_numbers(-5.5)
    Traceback (most recent call last):
        ...
    TypeError: 'float' object cannot be interpreted as an integer
    """
    ugly_nums = [1]

    i2, i3, i5 = 0, 0, 0
    next_2 = ugly_nums[i2] * 2
    next_3 = ugly_nums[i3] * 3
    next_5 = ugly_nums[i5] * 5

    for _ in range(1, n):
        next_num = min(next_2, next_3, next_5)
        ugly_nums.append(next_num)
        if next_num == next_2:
            i2 += 1
            next_2 = ugly_nums[i2] * 2
        if next_num == next_3:
            i3 += 1
            next_3 = ugly_nums[i3] * 3
        if next_num == next_5:
            i5 += 1
            next_5 = ugly_nums[i5] * 5
    return ugly_nums[-1]


if __name__ == "__main__":
    from doctest import testmod

    testmod(verbose=True)
    print(f"{ugly_numbers(200) = }")