238. Product of Array Except Self

1. Description

Given an integer array nums, return an array answer such that answer[i] is equal to the product of all the elements of nums except nums[i].
The product of any prefix or suffix of nums is guaranteed to fit in a 32-bit integer.
You must write an algorithm that runs in O(n) time and without using the division operation.

2. Example

Example 1

Input: nums = [1,2,3,4]
Output: [24,12,8,6]

Example 2

Input: nums = [-1,1,0,-3,3]
Output: [0,0,9,0,0]

3. Constraints

• 2 <= nums.length <= $10^5$
• -30 <= nums[i] <= 30
• The input is generated such that answer[i] is guaranteed to fit in a 32-bit integer.

4. Solutions

Prefix Sum

n = nums.size()
Time complexity: O(n)
Space complexity: O(1)

class Solution {
public:
    vector<int> productExceptSelf(const vector<int> &nums) {
        const int n = nums.size();
        vector<int> products(n, nums.back());
        for (int i = n - 2; i >= 0; --i) {
            products[i] = products[i + 1] * nums[i];
        }

        int prefix = 1;
        for (int i = 0; i < n - 1; ++i) {
            products[i] = prefix * products[i + 1];
            prefix *= nums[i];
        }
        products.back() = prefix;

        return products;
    }
};