First we accumulate the product from the left, storing the intermediate results. Then we accumulate the product from the right, multiplying the intermediate results with the stored left results.

```
class Solution {
public:
vector<int> productExceptSelf(vector<int>& nums) {
vector<int> result (nums.size(), 1);
int left = 1, right = 1;
for (int i = 1; i < nums.size(); ++i) {
left *= nums[i - 1], result[i] *= left;
}
for (int i = nums.size() - 2; i >= 0; --i) {
right *= nums[i + 1], result[i] *= right;
}
return result;
}
};
```