# 238 Product of Array Except Self

## Problem Statement

Given an integer array `nums`, return an array `answer` such that `answer[i]` is equal to the product of all the elements of `nums` except `nums[i]`.
The product of any prefix or suffix of `nums` is guaranteed to fit in a 32-bit integer.
You must write an algorithm that runs in `O(n)` time and without using the division operation.

Input: nums = [1,2,3,4]
Output: [24,12,8,6]

## Approach

The key to solve this problem is to find out, how the math works at each position. If we look at nums[1] we see that we want the product of the numbers to the left and the product of the numbers to the right:
`[1,2,3,4]`
1 * (3*4)

To do that we can make use of a postfix and a prefix, which tracks the products, as well as an extra results array which will be updated through two loops:

## Solution

``````const productExceptSelf => (nums) = {
let prefix = 1;
let postfix = 1;
let result = [];
for (let i = 0; i < nums.length; i++) {
result[i] = prefix
prefix *= nums[i]
}

for (let i = nums.length - 1; i >= 0; i--){
result[i] *= postfix
postfix *= nums[i]
}

return result
};
``````

LC

DSA MOC