# Product of Array Except Self

## Description

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]
```

**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.)

## Solution

```cpp
class Solution {
public:
    vector<int> productExceptSelf(vector<int>& nums) {
        int n = nums.size();
        vector<int> ans(n);
        int prod = 1;
        for(int i = 0; i < n; ++i){
            ans[i] = prod;
            prod *= nums[i];
        }
        // at this point, ans[i] = product of first i elements
        prod = 1;
        for(int j = n - 1; j >= 0; --j){
            ans[j] *= prod;
            prod *= nums[j];
        }
        return ans;
    }
};
```
