> For the complete documentation index, see [llms.txt](https://soumyajit4419.gitbook.io/ds-algo/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://soumyajit4419.gitbook.io/ds-algo/arrays/11.product-of-array-except-self.md).

# 10.Product of Array Except Self

```
Example
Input:  [1,2,3,4]
Output: [24,12,8,6]
```

## Solution I : (Using Extra Space)

1. Create two array prefix and suffix of length n, i.e length of the original array, initilize prefix\[0] = 1 and suffix\[n-1] = 1 and also another array to store the product.
2. Traverse the array from second index to end.
3. For every index i update prefix\[i] as prefix\[i] = prefix\[i-1] \* array\[i-1], i.e store the product upto i-1 index from the start of array.
4. Traverse the array from second last index to start.
5. For every index i update suffix\[i] as suffix\[i] = suffix\[i+1] \* array\[i+1], i.e store the product upto i+1 index from the end of array
6. Traverse the array from start to end.
7. For every index i the output will be prefix\[i] \* suffix\[i], the product of the array element except that element.

```cpp
class Solution
{
public:
    vector<int> productExceptSelf(vector<int> &nums)
    {

        int n = nums.size();
        vector<int> v;
        vector<int> pre(n);
        vector<int> suf(n);
        pre[0] = 1;
        suf[n - 1] = 1;
        for (int i = 1; i < nums.size(); i++)
        {
            pre[i] = pre[i - 1] * nums[i - 1];
        }

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

        for (int i = 0; i < n; i++)
        {
            v.push_back(suf[i] * pre[i]);
        }
        return v;
    }
};
```

##