# Product Array

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**Given an array of integers, write a function buildProductArray that returns an array where each item is the product of all the items in the input array except for the item at that index.**

Constraints:

- Solve this without using division
- You can create a
`results`

array, and it won't count against your space complexity - Memory may be a concern though, so try to limit your use of additional data structures

```
// Input
const input = [1, 2, 3, 4, 5];
// Output: buildProductArray(input)
// [2*3*4*5, 1*3*4*5, 1*2*4*5, 1*2*3*5, 1*2*3*4]
[120, 60, 40, 30, 24];
```

### Validate My Answer

You may immediately recognize a brute force

*O(n*answer. You can get this down to^{2})*O(n)*.You may want to add additional arrays to get the

*O(n)*time complexity. However, you can solve this without any additional data structures other than your`results`

array.To get it to

*O(n)*without additional arrays, you may have to perform sequential*O(n)*time complexity operations.Does your solution handle 0 or negative numbers?