Product of Array Except Self — Interview Guide

• output[i] = (product of everything left of i) × (product of everything right of i).
• First pass left-to-right accumulates the running left product.
• Second pass right-to-left multiplies in the running right product.

def product_except_self(nums):
    res = [1] * len(nums)
    left = 1
    for i in range(len(nums)):
        res[i] = left
        left *= nums[i]
    right = 1
    for i in range(len(nums) - 1, -1, -1):
        res[i] *= right
        right *= nums[i]
    return res

• Handle zeros (division would be impossible anyway — this solution already does).
• Return the result modulo a prime to avoid overflow.
• Generalize to product of all except a range [l, r].