Product of Array Except Self

Problem

Given an array of n integers where n > 1, nums, return an array output such that output[i] is equal to the product of all the elements of nums except nums[i].

Solve it without division and in O(n).

For example, given [1,2,3,4], return [24,12,8,6].

Follow up: Could you solve it with constant space complexity? (Note: The output array does not count as extra space for the purpose of space complexity analysis.)

Solution

Divide and Conquer: O(n) time, O(1) space

public class Solution {
    public int[] productExceptSelf(int[] nums) {
        int n = nums.length;
        int[] res = new int[n];
        res[0] = 1;
        for (int i = 1; i < n; i++) res[i] = res[i - 1] * nums[i - 1];
        int right = 1;
        for (int i = n - 1; i >= 0; i--) {
            res[i] *= right;
            right *= nums[i];
        }
        return res;
    }
}

Analysis

At my first trial, I used two arrays to calculate the left products and right products
It took extra spaces other than int[] res
In this solution, however, we apply the same idea and divide the res into left and right products
The first loop get the left and second loop populate the right products