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]


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 * (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:


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