product.py

class OnlyProductInteger:
    def __init__(self, value):
        self._value = value

    def __str__(self):
        return str(self._value)

    def __eq__(self, other):
        return self._value == other._value

    def __mul__(self, other):
        if isinstance(other, int):
            other = OnlyProductInteger(other)
        return OnlyProductInteger(self._value * other._value)

    def __rmul__(self, other):
        return self.__mul__(other)

    __repr__ = __str__


def product(array: List[OnlyProductInteger]) -> List[OnlyProductInteger]:
    """
    Time Complexity: O(n)
    Space Complexity: O(n)

    >>> product([OnlyProductInteger(1), OnlyProductInteger(2), OnlyProductInteger(3)])
    [6, 3, 2]

    >>> product([OnlyProductInteger(7), OnlyProductInteger(2), OnlyProductInteger(3)])
    [6, 21, 14]

    >>> product([OnlyProductInteger(5)])
    [1]

    >>> product([])
    []

    """
    if len(array) <= 1:
        return [OnlyProductInteger(1)] * len(array)

    result = []
    length = len(array)
    one = OnlyProductInteger(1)
    left = [one] + [None] * (length - 1)
    right = [None] * (length - 1) + [one]
    for i in range(1, length):
        left[i] = OnlyProductInteger(left[i - 1] * array[i - 1])
    for j in range(length - 2, -1, -1):
        right[j] = OnlyProductInteger(right[j + 1] * array[j + 1])
    for l_, r_ in zip(left, right):
        result.append(l_ * r_)
    return result