Product of Array Except Self.cpp

/*
Product of Array Except Self
============================

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

Example:
Input:  [1,2,3,4]
Output: [24,12,8,6]
Constraint: It's guaranteed that the product of the elements of any prefix or suffix of the array (including the whole array) fits in a 32 bit integer.

Note: Please solve it without division and in O(n).

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

class Solution
{
public:
  vector<int> productExceptSelf(vector<int> &nums)
  {
    int n = nums.size();
    vector<int> left(n, 1), right(n, 1);

    int mult = 1;
    for (int i = 1; i < n; ++i)
    {
      mult = mult * nums[i - 1];
      left[i] = mult;
    }

    mult = 1;
    for (int i = n - 2; i >= 0; --i)
    {
      mult = mult * nums[i + 1];
      right[i] = mult;
    }

    for (int i = 0; i < n; ++i)
      nums[i] = left[i] * right[i];

    return nums;
  }
};