LeetCode #: 238

Difficulty: Medium

Topics: Array.

Given an array nums of n integers where n > 1, return an array output such that output[i] is equal to the product of all the elements of nums except nums[i].

Example:

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

Constraint: It's guaranteed that the product of the elements of any prefix or suffix of the array (including the whole array) fits in a 32 bit integer.

Note: Please solve it without division and in O(n).

Follow up: Could you solve it with constant space complexity? (The output array does not count as extra space for the purpose of space complexity analysis.)

The solution addresses the Note and Follow up sections, and makes use of the following theory:

result[i] = (products of elements on the left hand side of i) * (products of elements on the right hand side of i)

First, we loop through the elements from left to right to get the products of elements on the left hand side of i, and stored them in result array.

Then we do another loop from right to left, calculating the products of elements on the right hand side of i and storing it in a variable, and update the result array using the above formula as we go.

Time complexity: O(n). We travel through the nums array once from left to right, and another time from right to left.

Space complexity: O(1) constant space (excluding the result output array as mentioned in the Follow up section).